91视频

Mathematics

Bachelor's degree programme

Educational plan

Educational level (Bachelor/Master):
Bachelor
Programme title and code of specialty:
056101.01.6 - Mathematics
Specialization:
056101.01.6 - Mathematics
Qualification awarded:
Mathematics
Programme start academic year:
2025/2026
Mode of study (full time/part time):
Full time
Language of study:
???????

General educational component

Chair code Name of the course Credits
2-??? ??????????
?????????? ?????-????????? 2 ???
????. – 2, ????????? 2 ??? ??????????? ????????
MANDATORY
1602/?02
1. Purpose of the Course
· ???????? ???????????? ?????????? ?????????? ? ??????????????? ??????????, ???????????????, ?????? ??? ???? ????? ????? ????????? ??? ?????????????????????? ?????,
. ????????????? ????????????? ? ???????? ?????????????? ??? ??????????? ?????????? ????????? ???????????
2. Educational Outcomes
?. ???????????? ??????? ? ???????????
1.?????????? ???????????? ???????? ???????????????? ?? ???????????,
2. ??????? ???????????? ? ????????? ?????????? ???????? ???????? ????? ?????? ???????????? ?????????????,


?. ????????? ???????????? ???????????????
3. ??????????? ?????? ? ??????? ???????????? ???????? ?????????, ???????????? ? ??????????????,
4. ???????? ? ??????????? ??????? ????????? ????? ?????????????? ???????????? ???????? ??????????, ?????????? ? ?????????? ??????? ???????????? ??? ??????? ???????????????? ???,


?. ???????????/????????? ???????????????
5. ??????????? ?????? ???????????? ?????? ?????????? ???????????? (???????? ????????????) ??????????????? ???????, ??????????? ??????????? ? ????????????? ?????????

3. Description
· ???????? ???????????? ?????????? ?????????? ? ??????????????? ??????????, ???????????????, ?????? ??? ???? ????? ????? ????????? ??? ?????????????????????? ?????,
. ????????????? ????????????? ? ???????? ?????????????? ??? ??????????? ?????????? ????????? ???????????
4. Teaching and Learning Styles and Methods
1.????????? ?????????? ???????? ??????????????,
2. ????????? ? ??????? ????????,
3. ????????? ? ??????? ????????????? ??????????,
4. ??????????? ????????:
5. Evaluation Methods and Criteria
????????? ????????? ? ??????????, ??? ???????????? ? ?????? ?????????? ? ??????? ?????????:
1. ?????? ???????? (????? ????? ???????? ?????? ????? ??????????),
2. ??????? ???????? (??????, ????????? ? ?????????? ???????????? ??????):
6. Basic Bibliography
  • Дорожкина В. “Английский язык для студентов математиков” Москва 2001.
  • Bates M./ Dudley T. - Evans “General Science” 1993.
  • Allan R. Hoffer “Mathematics in Action” 1989.
7. Main sections of the course
1. ???????????? ????? ???????????? ?????????????????????
2. ?????????? ???????????? ?????? ? ??????? ???????? ????????? ??????????????
3. ????????????? ????????? ?????? ?????? ?????????? ?????? ???????
4. ?????? ???????????? ???????????? ?????????????? ??????? ?????? ????????? ? ?????????
5. ?????? ???????? ?????????????? ???????????? ?????????? ????????????:
5-?? ????????
?????????? ?????- ????????? 2 ???
??????????????-1 ???, ??????? -1 ???, ????????? 4 ??? ??????????? ????????
MANDATORY
1302/?12
1. Purpose of the Course
??? ?????????? ?????????? ????-?????? ????????????????????? ????????????? ???????? ? ????????????? ???????????? ?????????????????????? ?????,?????????? ????????????? ???????? ????????????? ??????? ?? ??????????????? ???????????????,
?????????? ?????? ????????? ? ??????????? ??????? ???????????? ???????????? ? ????????? ????????????????
2. Educational Outcomes
?. ???????????? ??????? ? ???????????
1. ?????????? ??????????????? ??????? - ?????????????, ??????????????? ? ????????????? ??????????????,
2. ???????? ???????????? ? ???????????, ???????? ? ??????, ????????? ? ?????????? ????????????? ????????????,
3. ?????????? ????????????? ????????????? ??????????????????? ?? ???? ??????????:

?. ????????? ???????????? ???????????????
4. ????????????? ??????? ??????????? ?????, ?????? ?????????? ????????????, ??????????? ?????????????,???????? ??????????? ???????????? ? ????????????? ????????????,
5. ????????? ????????????? ??????????? ? ???????????????? ????????????

?. ???????????/????????? ???????????????
6. ??????? ???????????????? ????????? ???????????? ???????????? ?????????,??????????? ??????? ?????????? ??????? ? ??? ???????????? ?????? ??????? ?? ?????? ??????,

3. Description
??? ?????????? ?????????? ????-?????? ????????????????????? ????????????? ???????? ? ????????????? ???????????? ?????????????????????? ?????,?????????? ????????????? ???????? ????????????? ??????? ?? ??????????????? ???????????????,
?????????? ?????? ????????? ? ??????????? ??????? ???????????? ???????????? ? ????????? ????????????????
4. Teaching and Learning Styles and Methods
1. ?????????????????, ??????? ????????????? ? ????????????,
2. ???????? ??????????? ? ????????????? ??????????? ??????????????,
3. ?????? ???????????? ????????? ??????????????
5. Evaluation Methods and Criteria
????????? ????????? ? ???????????

????????? ?????????? ??????? ??????? ??? ?????????? ?????????:
????????? ???????????? ????? ?????? ????????? ? ??????????????? ???????, ???????????? ?????????????????? ? ?????????????????, ??????? ?????????? ??????? ???????????, ??????????? ???????????:
6. Basic Bibliography
  • ??????? ?., ????????????????. ?????????????????? ????????????, ??. 2016?
  • Введение в философию, под ред. Фролов И.Т., М. 2012.
  • Канке В. А., Основы философии, М., 2014.
  • Губин В. Д. Философия, М., 2013.
  • Бучило Н. Ф., Философия, М., 2013.
7. Main sections of the course
1. ????????????????? ????? ?????? ? ??????? ???? ??????????? ???????:
2. ????????????? ????????? ??????????????????????:
3. ?????????????????? ??????:
4. ????????? ????????????? ?????????:
5. ????????? ????????? ??????????????????????:
6. ???????? ?????? ??????????:
7. ?????????? ????????? ? ???????????:
8. ?????????????, ????????????, ?????:
9. ??????? ????????????? ?????????:
10. ?????????? ? ????????????????:
11. ?????? ? ????????????? ?????? ??????????:
12. ??????????????? ????? ?????????????? ????????:
13. ?????????? ????????????? ????????? :
14. ???????? ? ????????????????:
15. ??????????? ?????? ?????????:
16. ?????????? ???????????????? ? ??????????? ??????:
4-?? ?????????? ????????
2 ?????????? ?????- ????????? 2 ???
. 2 ??? ???., ????????? 2 ??? ??????????? ????????
MANDATORY
0708/?10
1. Purpose of the Course
??????????? ??? ???????? ??????????? ? ??????? ??????????` ????? ?????????, ???????????????, ?????? ??????????? ?????????????? ???????????, ????????????? ? ????????? ????????????? ????????? ?????,
???????? ???????? ?????????? ?????????-?????????????? ??????????? ?????????? ??????????????, ???????? ??? ????????????? ????????? ????????? ?????:
2. Educational Outcomes
?. ???????????? ??????? ? ???????????
1.????????? ??????????` ????? ????????? ????????? ????????????, ???????? ?????????? ?????????? ??????????? ? ??????????????????????
2.????????? ????????????, ??????????? ? ?????????? ????????????
3. ????????? ??????????? ?????? ????????? ????????????,?????????? ????????? ? ??????????? ??????, ??????? ? ?????? ??????????? ???????? ??????????? ?????????, ???????? ?????? ? ?????????? ?????????????? ????????? ????????? ???????????? ? ???????????????????:

?. ????????? ???????????? ???????????????
4.??????? ? ???????????? ??????????? ?? ??????? ???????????, ??????????????????? ? ??????????? ??? ??????? ????? ??????? ???????????, ???????????? ??????????????????????? ???????? ??????? ????????????? ? ??????????? ??????????? ????????????? ?????? ????????? ?????? ??????????,

?. ???????????/????????? ???????????????
5.????????? ??????? ? ??????? ??????????????,
6. ??????????? ???????????? ? ??????????? ???????????:

3. Description
??????????? ??? ???????? ??????????? ? ??????? ??????????` ????? ?????????, ???????????????, ?????? ??????????? ?????????????? ???????????, ????????????? ? ????????? ????????????? ????????? ?????,
???????? ???????? ?????????? ?????????-?????????????? ??????????? ?????????? ??????????????, ???????? ??? ????????????? ????????? ????????? ?????:
4. Teaching and Learning Styles and Methods
??????????? ?????
????????? ?????? ??????? ??????????? /Moodle ??????????/ ? ?????????????????:
??????????????? ?????
??????????? ????????` ???????????? ?????????, Moodle ??????????? ???????? ?????????????????? ?????????, ?????????????? ???????? ? ??????? ????????????:
5. Evaluation Methods and Criteria
????????. ????????? ?????????? ? ???????? ??????????, online, ?????? ? ????????????? 32 ????, ??????? ??????? ??????????:
6. Basic Bibliography
  • ????????? ?.?., ?????? ?.?., ????????? ?.?., ???????? ?.?., ????????? ?.?., ????????? ?.?. ??????????? ? ???????? ???????????? ???????????: ??????????? ???????, ??????-97, ?????, 2010, 224 ??:
  • ???????????? ?., ???????? ?., ????????? ?. ??????????????????????????, ?????: ?????? ???, 2014, 136 ??.
  • ?????? ?.?., ?????????? ?.?. ???????????????? ??????????? ?????????? ? ?????????-????????? ?????????????? ????????, ?????, ????????, 2010?., 222 ??:
  • ?????????? ?.?., ???????? ?.?. ???????????????? ???????????, ?????, 2010?., 311 ??:
  • ????????? ?.?., ?????? ?.?. ??? ????? ?????? ??????????? ????????????????? ? ??????????????????, ??????????, 2007, 215 ??:
  • ??????????? ?.?. ? ???????? ??????? ????????? ??????????????, ?????, 2005?.:
7. Main sections of the course
????????????: ?????????? ??????? ???????????, ???????????, ??????? ? ???????:
???????????? ????????? ????????? ? ??????????? ??????????:
?????? ?????????? ???????? ???????????:
??????????????? ????????: ?????????????: ?????????????:
???????? ??????????????? ????????????????: ?????????????? ??????????????: ?????????:
?????? ???????????????? ???????? ???:
????????? ??????????????: ????? ??????? ??????????? ? ??????????? ??????????????:
?????? ????????? ??????????????: ??????? ????????? ??????????????:
????? ???????????? ????????????????: ??????????????????? ??????????????:
?????? ????????? ? ?????? ?????????????:
2-??` ?????????? ????????
?????????? ?????- ????????? 2 ???
2 ??? ??????????????, ????????? 2 ??? ??????????? ????????
MANDATORY
1106/?09
1. Purpose of the Course
????????? ??????? ????? ??? ?? ????????? ?????? ?????????? ?????????? ??????? ?????????? ???????????? ???????? ?????????? ?????????? ? ???????????????? ????????, ????????? ??????? ????????????? ??????? ???????????? ????????????? ???????? ?:
2. Educational Outcomes
?. ???????????? ??????? ? ???????????
1. ????????????? ????? ?????????? ??? ? ????????? ?????? ???????????? ???????,
2.?????????? ????? ????????????? ???????????? ????? ????? ??????????? ??????? ????????? ? ????????? ??????? ?? ??????????????????????,
3. ??????????? ????????? ???????????????? ????? ????????????? ????????????? ?? ??????????? ????????????? ? ?? ???????????? ??? ????????????? ????? ?????????????? ???????????? ????????? ????????????? ??????????????:

?. ????????? ???????????? ???????????????
4. ???????????? ????????????? ??? ?????? ??????????? ? ???? ??????????,
5. ????????? ????? ?????????? ??? ? ????????? ?????? ???????????? ???????????? ?????????? ???? ????? ??????????? ??????????? ???????????:

?. ???????????/????????? ???????????????
6. ????????? ?????????? ?????? ?????? ???????????? ??? ???????-??????????? ??????? ? ????? ?????????????? ???????????? ????????? ????????????? ????????? ?????????????:

3. Description
????????? ??????? ????? ??? ?? ????????? ?????? ?????????? ?????????? ??????? ?????????? ???????????? ???????? ?????????? ?????????? ? ???????????????? ????????, ????????? ??????? ????????????? ??????? ???????????? ????????????? ???????? ?:
4. Teaching and Learning Styles and Methods
1. ??????????????,
2. ???????,
3. ?????????:
5. Evaluation Methods and Criteria
????????? ????????? ? ???????????
????????? ??????? ?????????? ? ????????, ??? ???????????? ? ??????? ??????? ???????: ????????????? ???????? ?????? ? ????? ????: ???????? ?????????? ??????? ? ??????? ???????? ??????, ??????? ????? ????????????? ???????:
6. Basic Bibliography
  • ???????????? ?., ???????? ?. ? ????????, ????? ???????????, ???.? ??. ?????????, ?., ??? ????., 2012:
  • ????????? ?., ?????????? ?., ?????-??????? ?., ???????? ?., ??? ???????? ??????????? (?????? ????? XVIII ???? ?????), ???.? ?. ?????-????????, ??? ????., ?., 1975:
  • ????? ???????????, ???.? ?. ?????????? ? ?????????, ???????-97? ????.,?., ?? ??? ????. ????., ?. III, ?. I, 2010, ?. III, ?. II, 2015, ?. IV, ?. I, 2010, ?. IV, ?. II, 2016:
7. Main sections of the course
1. ??? ??????????? ???????? XVI ?. ??????? ????? XVIII ?.: 2. ??????????? ??????? ?????????? ? ?????????? 1722-1730 ??.: 3. ????-????????? ? ????-????????? ???????????? ? ????????? XIX ?. ?????? ?????????????: ???????? ????? ???????????????: 4. ??? ????????? ?????????????????? ?????????? ? ??? ??????????? ???????? XIX ?. ?????? - XX ?. ??????: 5. ????? ????????????????: 6. ???????? ?????????????: ????????? ?????? ???????????????? (1918-1920 ??.): 7. ?????????? ????????? (1920-1991 ??.): 8. ?????? ??????????????? ??????? ?????????????: 9. ???????? ???????? (1988-1991 ??.) ? ????????? (1991-1994 ??.): 10. ????????? ?????? ???????????????? (1991 ????????):
1-??` ????????? ????????
?????????? ?????- ????????? 2 ???
5.2 ??? ??????????????, ????????? 2 ??? ??????????? ????????
MANDATORY
1106/?07
1. Purpose of the Course
????? ??? ?? ????? ?????? ?????????? ?????????? ??????? ?????????? ???????????? ???????? ?????????? ?????????? ? ???????????????? ????????, ????????? ??????? ????????????? ??????? ???????????? ????????????? ????????:
2. Educational Outcomes
?. ???????????? ??????? ? ???????????
1. ????????????? ????? ?????????? ??? ? ????? ?????? ?????????????? ????????????,
2. ??????? (???????????) ????????? ???????????? ????? ?????????? ??? ? ????? ?????? ?????????????? ???????????? ????? ???? ?????????? ??????????,
3. ?????????? ????? ????????????? ????????? ? ????????? ??????? ?? ?????????????????????? ??? ? ????? ????????? ?????????? ? ?? ???????????? ???????????? ??? ????????????? ????? ?????????????? ???????????? ????????? ????????????? ??????????????:

?. ????????? ???????????? ???????????????
4. ???????????? ????????????? ??? ?????? ??????????? ? ???? ??????????,
5. ????????? ????? ?????????? ??? ? ????? ?????? ?????????????? ???????????? ???????????? ?????????? ???? ????? ??????????? ??????????? ???????????:


?. ???????????/????????? ???????????????
6. ?????? ????????????????? ? ??????????????????????? ??????? ??????????????? ???? ???????, ???????????, ?????????? ? ??????????,
7. ????????? ?????????? ?????? ?????? (????????, ????????? ? ?????) ???????????? ??? ????? ?????????????? ???????????? ????????? ????????????? ?????????? ?? ?????????????:
3. Description
????? ??? ?? ????? ?????? ?????????? ?????????? ??????? ?????????? ???????????? ???????? ?????????? ?????????? ? ???????????????? ????????, ????????? ??????? ????????????? ??????? ???????????? ????????????? ????????:
4. Teaching and Learning Styles and Methods
1. ??????????????,
2. ???????,
3. ?????????:
5. Evaluation Methods and Criteria
????????? ??????? ?????????? ? ????????, ??? ???????????? ? ??????? ??????? ???????: ????????????? ???????? ?????? ? ????? ????: ???????? ?????????? ??????? ? ??????? ???????? ??????, ??????? ????? ????????????? ???????:
6. Basic Bibliography
  • ???????????? ?., ???????? ?. ? ????????, ????? ???????????, ???.? ??. ?????????, ??? ????., ?????, 2012:
  • ????????? ?., ?????????? ?., ?????-??????? ?., ???????? ?., ??? ???????? ??????????? (?????? ????? XVIII ???? ?????), ???.? ?. ?????-????????, ??? ????., ?????, 1975:
  • ????? ???????????, ?. II, ?. II, ???.? ?. ?????????? ? ?????????, ???????-97? ????., ?????, ?? ??? ????. ????., 2014:
7. Main sections of the course
1. ???????? ??????????. ????????????? ?????, ??????? ? ?????? ??????????: 2. ??? ???????? ?????? ?????????? ? ??? ??????? ??????????????? ???????? ?????????????: 3. ???? ??????????????? (?.?. IX-VII ??.): ????????? ?????????????? ??????????? ???? (?.?. VI-III ??.): 4. ??? ????? ??????????????? ?????????? (?.?. 189-1 ??.) ? ??????????? (66-428 ??.) ???????????????? ????: 5. ????? ????????? ????????: ????????? ??????????? ????????? ????? (428-885 ??.): 6. ????? ??????????????? ???????????? ??????????? (885-1045 ??.) ????: 7. ????????? ???????? ??????????? (1080-1375 ??.): 8. ?????????? ?????? ???????????? ????????: 9. ???-???????? ?????????????? ? ???????????? ?????????????: 10. ????????? ??? ???????????:
3-??? ????????? ????????
?????????? ?????- ????????? 2 ???
2 ?????. ???, ????????? 2 ??? ??????????? ????????
MANDATORY
1705/?06
1. Purpose of the Course
· ???????? ? ???????? ??????????????? ????????? ??????????? ??????????? ???????????? ?????,
· ??????????? ??? ???????? ??????? ??????????, ??????????? ? ???????? ????????? ???????? ??????????? ?????????? ??? ???????????? ??????????????, ?????? ? ??????????,
. ?????? ???????? ?????????????? ????? ????????? ??????? ???????????? ??????????? ?????????, ????? ????????? ????????? ?????????:
2. Educational Outcomes
?. ???????????? ??????? ? ???????????

1. ????????? ?????? ? ??????? ?????? ???????? ????????, ?????????????, ???????? ???????????????,
2. ????????? ???? ?????? ????? ???????? ???????,
3. ???????? ???????????? ???????? ????????? ????????? ?????? ????????????? ??????????????:

?. ????????? ???????????? ???????????????
4. ??????? ?????? ????? ??????????? ???????,
5. ???????? ????? ????????, ????????????? ? ???????? ???????? ????????????, ???????? ? ???????? ???????? ? ??????????? ????? ?????? ??????????????,

?. ???????????/????????? ???????????????
6. ?????????????? ??????? ??????? ???????????:
3. Description
· ???????? ? ???????? ??????????????? ????????? ??????????? ??????????? ???????????? ?????,
· ??????????? ??? ???????? ??????? ??????????, ??????????? ? ???????? ????????? ???????? ??????????? ?????????? ??? ???????????? ??????????????, ?????? ? ??????????,
. ?????? ???????? ?????????????? ????? ????????? ??????? ???????????? ??????????? ?????????, ????? ????????? ????????? ?????????:
4. Teaching and Learning Styles and Methods
1. ????????? ?????????????
2. ??????? ????? ?????????? ??????? ??????????????, ????????????,
3. ??????????? ???????? ? ???????????????????:
5. Evaluation Methods and Criteria
????????? ???????? ? 2 ?????? ??????? ? ??????: ????????? ?????????? ? ???????????? ??????? ????? ??????????: ???????????? ??????? ?? ????????????? ????? ?????? ??????? ???????, ????? ???? ?? ????????? ? ??????? ????????? ??? ?????? ????? ??????????? ??????? (????????, ????????????? ? ????????):
6. Basic Bibliography
  • Введенская Л.А. Русский язык и культура речи. Москва, 2002.
  • Воронцова Т.А. Культура речи. Ижевск, 2011.
  • Голуб И.Б. Риторика: учитесь говорить правильно и красиво. Москва, 2013.
  • Розенталь, Д.Э. Большой справочник по русскому языку. Москва, 2017.
  • Розенталь, Д.Э. Словарь трудностей русского языка. 20000 слов: 20 000 слов. Москва, 2012
  • Розенталь Д.Э. Справочник по правописанию и литературной правке. Москва, 2003.
  • Розенталь, Д.Э. Справочник по русскому языку. Практическая стилистика. Москва, 2011
  • Розенталь, Д.Э. Русский язык. Орфография. Пунктуация. Орфографический словарь (Классический справочник). Москва, 2011.
  • Русский язык и культура речи. По ред. Максимова В.И., Голубевой А.В. Санкт-Петербург, 2010.
  • 0. - ?Грамотная речь, или Учимся говорить по-русски?. Словари.
  • - Справочно-информационный Интернет-портал ?Русский язык?.
  • - Электронная библиотека словарей русского языка.
7. Main sections of the course
1. ?????????? ??????:
2. ????????????? ??????:
3. ???????? ?????????????? ?????????:
4. ????????????? ??????:
5. ???????? ?????? (????? ????????? ???????? ???????):
6. 2-?? ????????? ??????????
4. ?????????? ?????- ????????? 2 ???
5. ?????????-2 ???, ????????? 2 ??? ??????????? ????????
MANDATORY
1608/?15
1. Purpose of the Course
? ??????????? ?????? ??????? ?????????? ????????? ???????????,
? ?????????? ???? ????? ?????????? ???????? ? ????????? ???????????,
? ??????????? ????? ?????????? ????????????? ??????????? ? ?????????? ??????????? ????????? ?????????????,
. ??????????? ????? ??????????? ???????? ???????????????? ? ????????????????:
2. Educational Outcomes
?. ???????????? ??????? ? ???????????
1. ?????????? ???? ????? ??????????? ?????????? ?????????????? ????????????,
2. ????????? ?????????? ??????????? ? ????????? ???????????? ? ??????????.

?. ????????? ???????????? ???????????????
3. ??????? ???????? ???????????` ??????? ????????????? ??????????? ?????????? ????????????,

?. ???????????/????????? ???????????????
4. ?????????? ???????????? (???????????) ??????????? ?????? ? ??????? ??????:
3. Description
? ??????????? ?????? ??????? ?????????? ????????? ???????????,
? ?????????? ???? ????? ?????????? ???????? ? ????????? ???????????,
? ??????????? ????? ?????????? ????????????? ??????????? ? ?????????? ??????????? ????????? ?????????????,
. ??????????? ????? ??????????? ???????? ???????????????? ? ????????????????:
4. Teaching and Learning Styles and Methods
1. ????????? ???????? ??????????????,
2. ???????? ? ??????? ????????,
3. ?????????? ????????,
4. ?????? ????????? ?????????? ????? ????????? ? ?????????:
5. Evaluation Methods and Criteria
????????? ????????? ? ??????????, ??? ???????????? ? ??????????? ???????:
6. Basic Bibliography
  • Parizet, M.L., E. Grandef, M. Corsain Collection activités pour le cadre commun. Activités pour le cadre européen commun de référence. B. 2. ClE International, 2006.
  • Boulares, M., J.L. Frerot Grammaire progressive du francais Niveau avancé. ClE International, 2004.
7. Main sections of the course
1. ?????????? ?????????? ?????????? ??????????? ????????????????????:
2. ?????????? ?????????? ????????????? ??????????? ? ??????????? ????????? ????????????:
3. ?????????? ??????????? ???????? ???????????????? ? ????????????????:
4. ?????????? ??????? ??????????????????????:
2-?? ????????? ??????????
?????????? ?????- ????????? 2 ???
2 ??? ????., ????????? 2 ??? ??????????? ????????
MANDATORY
1205/?15
1. Purpose of the Course
· ???????????? ?????????? ???????? ????????, ?????????????????, ???????????? ???????????? ?????????????,
· ???????????? ??????????? ??????????? ???????? ???????????????, ??????????, ????????????? ? ??????????? ??????????????????????,
· ??????????? ??? ???????? ?????????? ????????? ????? ???????????? ? ?????? ???????? ?????????????? ????????? ?????,
· ??????????? ??? ????????? ????????????? ??????? ?????????????? ??? ????? ????????? ? ??????????????? ?????:
2. Educational Outcomes
?. ???????????? ??????? ? ???????????
1. ??????????? ?????? ????, ?????? ??? ???????????? ????????? ????? ?????,
2. ??????????? ???????? ??????????? ?????????? ?????? ???????? ??????????????????? (??????????, ???????, ????????, ?????????? ?????????????????? ?????, ????????????? ? ?????????????? ??????????????????????),
3. ???????????? ???????? ????????? ? ??????????? ???????? ?????????? (??? ???????? ??????, ???????????? ??????????????????????? ??????????, ?????????? ? ????)?

?. ????????? ???????????? ???????????????
4. ?????????? ????????? ????,
5.???????????? ????????????? ???? ?????????????? ???? ?????? ????????????,
6. ?????????? ????????????? ?????? ??????????? ??????? ????? ???????? ?????????????, ??????????? ? ?????? ????????????? ??????? ???????????? ????????

?. ???????????/????????? ???????????????
7.?????????? ????? ??? ???????? ?????? ????????? ????????, ?????????? ?????????????, ??????????? ???? ???????:

3. Description
· ???????????? ?????????? ???????? ????????, ?????????????????, ???????????? ???????????? ?????????????,
· ???????????? ??????????? ??????????? ???????? ???????????????, ??????????, ????????????? ? ??????????? ??????????????????????,
· ??????????? ??? ???????? ?????????? ????????? ????? ???????????? ? ?????? ???????? ?????????????? ????????? ?????,
· ??????????? ??? ????????? ????????????? ??????? ?????????????? ??? ????? ????????? ? ??????????????? ?????:
4. Teaching and Learning Styles and Methods
· ????????? ????????? ??????????? ?????? ?? ????? ??????? ?????? ??????????? ???????????? ???????? ?????,
· ???????? ?? ?????? ????????????????? ???????????? ?????????,
· ?????? ?? ????? ??????? ???????????? ???????????? ?????? ????? ???? ????????,
· ????????????? ? ???? ?????? ??? ???????????? ?????????,
· ??????????? ?????? ?? ????? ?????? ????? ?????????? ??????????? ? ???????????,
· ????? ?? ??????? ?????????????? ???? ?????? ???????,
· ???????? ?? ???????????? ?????? ?????????????? ????? ????????????,
· ???????????? ? ????? ????????????? ?????????????? ????????? ?????????? ??????????? ????????,
· h????? ?? ????? ???????????? ??????????? ????? ??????????,
?????? ????????????? ??????????? ?? ?????????? ????? ?????? ?????????, ? ????????? ?????? ?????????????????????? ??????????:
5. Evaluation Methods and Criteria
?????????
???????? ??????? ??????, ??????? ? ???????? ???????, ??? ???????????? ? ???????? ?????????????? ????: ?????????????? 3-? ??, ??????? ???????? ??????, ????????? ??????? ? ???????? ?????????
6. Basic Bibliography
  • 刘珣著，《新实用汉语课本》1学生书, 北京语言大学出版社，2006年
  • 刘珣著，《新实用汉语课本》1练习册, 北京语言大学出版社，2006年
  • 姜丽萍著，《HSK标准教程》1学生书， 北京语言大学出版社，2015年
  • 姜丽萍著，《HSK标准教程》1练习册， 北京语言大学出版社，2015年
  • 刘珣著，《新实用汉语课本》2学生书, 北京语言大学出版社，2006年
  • 刘珣著，《新实用汉语课本》2练习册, 北京语言大学出版社，2006年
  • 姜丽萍著，《HSK标准教程》2学生书， 北京语言大学出版社，2015年
  • 姜丽萍著，《HSK标准教程》2练习册， 北京语言大学出版社，2015年
7. Main sections of the course
???? 1：第十二课 你在干什么呢（正在……呢，每……都……，星期的表达法）
???? 2：第十三课 我去图书馆借书 （连动词，A不A/V不V）
???? 3：第十四课 我喜欢浅颜色的（挺+adj，有点儿）
???? 4：第十五课 明天是我朋友的生日（单元语言点小结）
???? 5：第十六课 周末你干什么（太……了，动词中叠，地点状语）
???? 6：第十七课 做客（（是）A还是B，就是，会）
???? 7：第十八课 做客（得，反问句，如果……，就……）
???? 8：第十九课 现在习惯了（了，还，年龄表达法）
???? 9：第二十课 看病人（单元语言点小结）
???? 10：第二十一课 我喝了半斤白酒（又，了，好像）
???? 11：第二十二课 他感冒了（能，，最好，日期表达法）
???? 12：第二十三课 你学了多长时间汉语（了，“就”的小结）
???? 13：第二十四课 你吃了早饭来找我（反问句，了，时间状语、地点状语的语序）
2-?? ? ?????????? ????????
?????????? ?????- ????????? 2 ???
????.-2, ????????? 2 ??? ??????????? ????????
MANDATORY
1803/?13
1. Purpose of the Course
·?????????? ??????????? ?????? ?????????,
·???????? ????????? ??????? ?????????????? ???????????????,
. ????????? ????????? ????????? ? ??????????? ??????? ??????? ??????????? ??????????????:
2. Educational Outcomes
?. ???????????? ??????? ? ???????????
1. ????????????? ?????????? ??????????? ??????????????????????
2. ?????????? ?????????? ?????????? ?? ?????????????:

?. ????????? ???????????? ???????????????
3. ????????????? ????????? ???????????????? ? ???? ???????,
4. ??????????? ??????????? ??????? ? ????????? ????????? ????? ?????????? ???????:

3. Description
·?????????? ??????????? ?????? ?????????,
·???????? ????????? ??????? ?????????????? ???????????????,
. ????????? ????????? ????????? ? ??????????? ??????? ??????? ??????????? ??????????????:
4. Teaching and Learning Styles and Methods
1. ????????? ???????? ?????????, ??????????????,
2. ???????? ? ????????????????? ????????????
3. ??????? ????? ?????????
5. Evaluation Methods and Criteria
????????? ????????? ? ??????????, ??? ???????????? ? ?????? ?????????? ? ??????? ?????????:
1.?????? ???????? (????? ????? ???????? ?????? ????? ??????????),
2. ??????? ???????? (??????, ????????? ? ?????????? ???????????? ??????):
6. Basic Bibliography
  • ???????? ?., ?????????? ?., ???????????? ?., ?????????? ????????, ???? ?, ???????? ?????????? ??????????????? (???????????? ? ?? ??? ?????? ????? ???????? ??????? ??????????? ?????), ?????, ??????? ???? ????., 2015:
  • Ergin M., Türk Dil Bilgisi, ?stanbul, 1980.
  • Hengirmen M., Türk?e ??reniyoruz, c. 1-3, Ankara 1999.
  • Щека Ю. В., Интенсивный курс турецкого языка: Учебник, М., 1996.
7. Main sections of the course
???? 1? ??????????? ?????????? ??????????? ?????????:
???? 2? ???????? ????, ??????, ??????????????? ????????? ????????????:
???? 3? ?????????? ??????, ???? ?????? ???:
???? 4? ????????? ?????????? ???????????? ????????????:
???? 5? ?????-???????????? ??????????? ??????????? ????????????:
???? 6? ??????????? ???????????? ?????? ???:
???? 7? ?????????? ??????? ????? ????????? ?????????? ?????? ??????????;
???? 8? ?????? ???????? ???????????:
2-?? ????????? ??????????
?????????? ?????-????????? 2 ???
????.-2 , ????????? 2 ??? ??????????? ????????
MANDATORY
1604/?13
1. Purpose of the Course
·?????????? ??????????? ??????????,
·???????? ? ??????????? ?????????????? ??????, ??????????, ?????? ??????????????,
. ???????? ???????????? ?????????????? ???????????????? ? ????????????????:
2. Educational Outcomes
?. ???????????? ??????? ? ???????????
1. ???? ???????????? ?????????????? ????? ???????????? ???????? ??????????? ?? ????????? ????????? ?????,
2. ???? ???????????? ?????????????? ????? ???????? ?????????? ?????? ????????????, ???????? ????? ??????????? ?? ????? ???????:

?. ????????? ???????????? ???????????????
3. ?????????? ??????? ????????? ????? ???????????? ?? ????????,
4. ???????????? ??????????? ????????????? ???? ?????????? ??????????????? ???????? ????????:

?. ???????????/????????? ???????????????
5. ??????????? ???????? ???????????? ?????? ???????????? (???????? ????????????) ??????????????? ???????, ??????????? ??????????? ? ????????????? ???????? ? ?????????? ???? ????? ?????????? ?????????????? ??????, ?????????????? ?? ???????????????????? ??? ? ???? ?????????? ?? ????????????:
3. Description
·?????????? ??????????? ??????????,
·???????? ? ??????????? ?????????????? ??????, ??????????, ?????? ??????????????,
. ???????? ???????????? ?????????????? ???????????????? ? ????????????????:
4. Teaching and Learning Styles and Methods
1. ????????? ?????????? ???????? ??????????????,
2. ????????? ? ??????? ????????,
3. ????????? ? ??????? ????????,
4. ??????????? ????????,
5. ??????? ???????????/ ??????????? (????????? ??????????? ??????? ???????????),
6. ?????? ? ??????? ????????/ ???????,
7. ???????????? ????????? ?????????:
5. Evaluation Methods and Criteria
????????? ????????? ? ??????????: ??????.
?????? ??????? ?????? ?????????, ?????????????? ? ????????????:
?????????? ????????:
?????? ???????? ?????:
??????????? (???????????) ?????? ???????? ?????:
6. Basic Bibliography
  • Meltonjan G., Soghomonjan K., Diwanjan N. Deutsch (für Stufen A2-B1). Jerewan, Verlag der Universit?t Jerewan, 2022.
  • DaF kompakt neu A1 - B1. Klett Verlag Stuttgart, 2016.
  • Dreyer,R. Schmitt. Lehr - und ?bungsbuch der deutschen Grammatik. München: Max Hueber Verlag für Deutsch, 2001. - 320 с.
7. Main sections of the course
· ??????????????. ???????? ?????????? ? ????????????? ??????????? ?? ??????, ????? ?????????????????????? ???????:
· ??????????? ????????????? ? ?????????? ????????????????????:
???????? ??????????????? ? ????? ???????? ???????????? /?????? ?? ???????/:
6. 1-??? ????????? ????????
?????????? ?????- ????????? 2 ???
????????? -2 ???, ????????? 2 ??? ??????????? ????????
MANDATORY
1401/?01
1. Purpose of the Course
· ??????????? ????? ??????? ????????? ??????????????????????,
· ?????????? ???????? ????? ????????????,
· ????????? ???????? ?????????????? ???? ??????? ??????????? ?? ?????????????????????
2. Educational Outcomes
?. ???????????? ??????? ? ???????????
1. ??????????? ???????? ???????????? ????????????????????,
2. ???????? ????? ???????? ?????????????? ?? ????? ??????????,
3. ?????? ???????? ???? ?????:
?. ????????? ???????????? ???????????????
4· ???????????? ??????????? ??????????? ?????????????????,
5· ?????????? ???????? ??? ??? ??? ??????? ????????????:
?. ???????????/????????? ???????????????
6· ????? ??? ???????? ???????? ???????????? ???????? ?????:
3. Description
· ??????????? ????? ??????? ????????? ??????????????????????,
· ?????????? ???????? ????? ????????????,
· ????????? ???????? ?????????????? ???? ??????? ??????????? ?? ?????????????????????
4. Teaching and Learning Styles and Methods
1.??????????????,
2.????????? ????????,
3.???????????? (??????) ??????????,
4. ??????????? ???????? ? ???????????????????:
5. Evaluation Methods and Criteria
????????? ??????? ?: ????????? ?????????? ? ???????????? ??????? ????? ??????????. ????????????? ????????? ?????? ? 4-5 ????: ?????????? ?????????? ? ??? ?????? ????????? ????????? ???????? ??????? ????????? ????????? (??????????, ????????????, ????????????? ?????????? ? ????) ?????????:
6. Basic Bibliography
  • ????????? ???., ???????? ?., ?????? ?. ? ????????, ????? ????? ? ????? ????????, ??., 2016:
  • ??????? ?., ????? ?????,, ?????, 2007:
  • ???. ????????? ? ????????, ????? ????? ? ????? ???????? (????????? ???????????? ??????? ?????????? ????????????? ??????????? ?????), ??., 2016:
7. Main sections of the course
1. ????????????, ???????????????, ??????????? ????????????????????,
2. ????????????? ???????????????? ?? ?????????????,
3. ?????????? ? ????????????? ??????????? ??????????????????????:
2-??? ?????????? ????????
?????????? ?????- ????????? 2 ???
2 ??? ????. , ????????? 2 ??? ??????????? ????????
MANDATORY
1705/?04
1. Purpose of the Course
·???????? ? ???????? ??????????????? ????????? ??????????? ??????????? ???????????? ?????,
·??????????? ??? ???????? ??????? ??????????, ??????????? ? ???????? ????????? ???????? ??????????? ?????????? ??? ???????????? ??????????????, ?????? ? ??????????,
· ?????? ???????? ?????????????? ????? ????????? ??????? ???????????? ??????????? ?????????,????? ????????? ????????? ?????????:
2. Educational Outcomes
?. ???????????? ??????? ? ???????????
1. ????????? ?????? ? ??????? ?????? ???????? ????????, ?????????????, ???????? ???????????????,
2. ????????? ???? ?????? ????? ???????? ???????,

3. ????????? ???????????? ???????? ????????? ????????? ?????? ????????????? ??????????????:
?. ????????? ???????????? ???????????????
4.??????? ?????? ????? ??????????? ???????,
5. ???????? ????? ????????, ????????????? ? ???????? ???????? ????????????, ???????? ? ???????? ???????? ? ???????????? ????? ?????? ???????????????
?. ???????????/????????? ???????????????
6.?????????????? ??????? ???? ????? ???????????:

3. Description
·???????? ? ???????? ??????????????? ????????? ??????????? ??????????? ???????????? ?????,
·??????????? ??? ???????? ??????? ??????????, ??????????? ? ???????? ????????? ???????? ??????????? ?????????? ??? ???????????? ??????????????, ?????? ? ??????????,
· ?????? ???????? ?????????????? ????? ????????? ??????? ???????????? ??????????? ?????????,????? ????????? ????????? ?????????:
4. Teaching and Learning Styles and Methods
1. ????????? ?????????????,
2. ??????? ????? ?????????? ??????? ??????????????, ????????????,
3. ??????????? ???????? ? ???????????????????:
5. Evaluation Methods and Criteria
????????? ???????? ? 2 ?????? ??????? ? ??????: ????????? ?????????? ? ???????????? ??????? ????? ??????????: ???????????? ??????? ?? ????????????? ????? ?????? ??????? ???????, ????? ???? ? ????????? ? ??????? ????????? ??? ?????? ????? ??????????? ??????? (????????, ????????????? ? ????????):
6. Basic Bibliography
  • Введенская Л.А. Русский язык и культура речи. Москва, 2002.
  • Введенская Л.А. Словарь ударений для работников радио и телевидения. Ростов-на-Дону, 2012.
  • Вербицкая Л.А. и др. Давайте говорить правильно! Трудности современного русского произношения и ударения: Краткий словарь-справочник. Москва, 2003.
  • Воронцова Т.А. Культура речи. Ижевск, 2011.
  • Голуб И.Б. Риторика: учитесь говорить правильно и красиво. Москва, 2013.
  • Розенталь, Д.Э. Большой справочник по русскому языку. Москва, 2017.
  • Розенталь, Д.Э. Словарь трудностей русского языка. 20000 слов: 20 000 слов. Москва, 2012
  • Розенталь Д.Э. Справочник по правописанию и литературной правке. Москва, 2003.
  • Розенталь, Д.Э. Справочник по русскому языку. Практическая стилистика. Москва, 2011
  • 0. Розенталь Д.Э. Русский язык. Орфография. Пунктуация. Орфографический словарь. (Классический справочник). Москва, 2011.
  • Русский язык и культура речи. Под ред. Максимова В.И., Голубевой А.В. Санкт-Петербург, 2010.
  • - ?Грамотная речь, или Учимся говорить по-русски?. Словари.
  • - Справочно-информационный Интернет-портал ?Русский язык?.
  • - Электронная библиотека словарей русского языка.
7. Main sections of the course
????? ???????? ????? ???????????? ??????: ????? ??????????? ????: ?????? ? ??????? ????? ??????????????????????: ???? ?????? ????? ??????? ?????????: ??????????? (???????????) ??????: ??????????? ??????:
6. 2-??? ?????????? ????????
?????????? ?????-????????? 2 ???
????????? – 2 ???, ????????? 2 ??? ??????????? ????????
MANDATORY
1401/?03
1. Purpose of the Course
· ??????????? ????? ?????????????-????????????? ?????????,
· ?????????? ????? ?????????? ??????????????
2. Educational Outcomes
?. ???????????? ??????? ? ???????????
1.?????? ?????????? ????,
2.??????????? ????? ?????????? ????? ??????????????????????,
3.?????? ??????????? ?????? ????????:
?. ????????? ???????????? ???????????????
4. ???????????? ??????? ???????????? ????? ?????????,
5. ???????? ????? ????????
?. ???????????/????????? ???????????????
6. ?????? ??????? ? ?????? ??????? ?????
3. Description
· ??????????? ????? ?????????????-????????????? ?????????,
· ?????????? ????? ?????????? ??????????????
4. Teaching and Learning Styles and Methods
1.??????????????,
2.????????? ????????,
3.???????????? (??????) ??????????,
4. ??????????? ???????? ? ???????????????????:
5. Evaluation Methods and Criteria
????????? ??????? ?: ????????? ?????????? ? ???????????? ??????? ????? ??????????. ????????????? ????????? ?????? ? 4-5 ????: ?????????? ?????????? ? ??? ?????? ????????? ????????? ???????? ??????? ????????? ????????? (??????????, ????????????, ????????????? ?????????? ? ????) ?????????:
6. Basic Bibliography
  • ????????? ???., ???????? ?., ?????? ?. ? ????????, ????? ????? ? ????? ????????, ??., 2016:
  • ??????? ?., ????? ?????,, ?????, 2007:
  • ???. ????????? ? ????????, ????? ????? ? ????? ???????? (????????? ???????????? ??????? ?????????? ????????????? ??????????? ?????), ??., 2016:
7. Main sections of the course
1. ????? ?????????????-????????????? ??????????
2. ????? ?????????? ?????????????
3. ???-???? ? ??????? ??????
4.???????????? ???? ? ???????? ???????
5.????? ???????
6.??????????? ?????
1-???????????? ????????
?????????? ?????- ????????? 2 ???
???. – 0,5 ??? (??????),
MANDATORY
0002/?14
1. Purpose of the Course
??????????? ??? ???????? ????????? ??????????? ???????? ???????????? ?????, ???????? ?????????????? ???????? ?????????????, ??????????? ???????????? ???????????? ?????????? ????????????? ? ?????????? ??????????? ??????? ???????? ???????????? ? ??? ?????????????? ??????? ?????? ????????????? ??????????? ????????? ???????????????:
2. Educational Outcomes
?. ???????????? ??????? ? ???????????
1.???????? ?????????? ??-? ? ?????????? ?????????? ????????,
2.??????????? ??-? ? ????????? ??????? ??????????? ?????????????? ??????? ?????????????? ? ???????????? ??????????????,
3. ???????? ??????? ?????? (????????? ? ??????????? ??????), ????????? ?????? ?? ???????????? ? ??????????? ?????? ?????????????? ???????????? ??????????????,?????????? ????????????? ?????????????? ?????? ???????? ???????? ???????? ? ????????????? ?????:

?. ????????? ???????????? ???????????????
4. ??????? ????????? ?????????????, ?????????? ??-?????? ?????????? ???????? ?????????? ???????????,
5. ?????????? ?????? ?????????????? ?????????? ???????????? ? ?????????????? ?????????,?????????? ???? ?????? ??????????????? ?? ? ????????? ??????? ????????? ?????? ??????????? ?????????????? ?????????:

?. ???????????/????????? ???????????????
6. ??????? ???? ?????? ??????? ??????????? ????????????, ????????? ????????? ? ??????? ????????? ???????????????? ?? ? ???????? ?????:

3. Description
??????????? ??? ???????? ????????? ??????????? ???????? ???????????? ?????, ???????? ?????????????? ???????? ?????????????, ??????????? ???????????? ???????????? ?????????? ????????????? ? ?????????? ??????????? ??????? ???????? ???????????? ? ??? ?????????????? ??????? ?????? ????????????? ??????????? ????????? ???????????????:
4. Teaching and Learning Styles and Methods
1. ??????????????, ????????? ? ????????? ??????????:
2. ????????? ? ??????????? ???????????:
3. ??????? ??????????? ?????, ??????????? ??????????? ??????????:
4. ????????????????? ???????:
5. Evaluation Methods and Criteria
????????. ??? ? ??????? ???????? ???????? (??????????????? ???????????? ????? ?????????? ???????? ??????????? ??????? ????????? ?????????):
6. Basic Bibliography
  • ????????? ?.?., ???????????? ?.?., ?????????? ?.?.,????????????? ?.?., ????????????? ?.?., ??????????? ?.?., ????????? ?.?., ????????? ?.?. ????????????????? ? ???????? ???????????? ????????????, ?????? ??????. ????., 2006, 238 ??:
  • ??????????? ????????, ????????????? ??????????? ???????????? ???????? ???????????????, ??????????? ????????, ?????? ??????. ????., 2007, 224 ??:
  • ?.?.????????, ?????-??????? ??????????????? ???????????? ????????? ??????????? (????????????????? ????????), ??., ?????? ??????. ????., 2007, 44 ??:
  • ?.?.???????, ??????????? ????????????, ????????????????? ????????, ??., ?????? ??????. ????., 2011, 36 ??:
  • ?.?.?????????, ?.?.???????? ????????? ???????????? ? ???????????? ????????????? ????????????, ??????????? ???????, ??., ?????? ??????. ????., 2017?
7. Main sections of the course
1. ???????? ??????????? ?? ??????????:
2. ???????????? ??????????????:
3. ??-??? ??????????? ?????? ??????????????:
6. 1-?? ????????? ?????????
4. ?????????? ?????- ????????? 2 ???
5. ?????????- 2 ???, ????????? 2 ??? ??????????? ????????
MANDATORY
1608/?13
1. Purpose of the Course
? ????????? ??????? ???????? ???????? ? ??????????? ????????????????,
? ?????????? ??????? ?????????? ?????? ?????????????? (??????????? - ????????????, ???????, ??????????-?????????????, ??????) ????????? ???????????????????????, ????????? ??????? ???????????? ???????????????:
2. Educational Outcomes
?. ???????????? ??????? ? ???????????
1.?????????? ??????? ?????????? ???????? ??????????? ? ?????????????? ??????????????????????,
2.???????????? ???????????? ????????????????? ??????? ?????? ????????:

?. ????????? ???????????? ???????????????
3.????????? ??????? ???????? ????????????? ??????? ??????????????,
4. ???????????? ????????? ?????? ??????? ???????? ??????????? ??????? ? ????????? ????????? ?????????????????? ??? ???????? ????????????? ?????????????? ????????????? ????????????:

?. ???????????/????????? ???????????????
5. ???????? ?????????????? ????????? ???????????? (???????????? ??????????, ??????? ????????? ? ????),
6. ?????????? ??????????? ????????? ??? ???? ??????? ??????????? ????????????? ?????????? ????????????????????????:
3. Description
? ????????? ??????? ???????? ???????? ? ??????????? ????????????????,
? ?????????? ??????? ?????????? ?????? ?????????????? (??????????? - ????????????, ???????, ??????????-?????????????, ??????) ????????? ???????????????????????, ????????? ??????? ???????????? ???????????????:
4. Teaching and Learning Styles and Methods
1. ????????? ??????????,
2. ???????????? ???????????? ?????????,
3. ????????????,
4. ??????????? ??????????????,
5. ??????? ???????? ???????????,
6. ??????????? ????????, ?????????? ? ????:
5. Evaluation Methods and Criteria
????????? ??????? ?: ????????? ?????????? ? ???????????? ??????? ????? ??????????. ????????????? ????????? ?????? ? 4-5 ????:
6. Basic Bibliography
  • Parizet, M.L., E. Grandef, M. Corsain Collection activités pour le cadre commun. Activités pour le cadre européen commun de référence. B. 1. ClE International, 2006.
  • Boulares, M., J.L. Frerot Grammaire progressive du francais Niveau avancé. ClE International, 2004.
7. Main sections of the course
1. ??????? ?? (?????? ?????, ???????? ??????????????????????, ?????????:
2. ??????? ?????????? ??????????-????????????? ??????????????????????:
3. ??????? ????? ??????? ???????????????????:
4. ?????????? ??????????? ???????? ???????????? ????????????:
5. ?????????? ?????????? ???????? ????????:
6. ?????????? ???????? ??????? ?????????? ??????????? ?????????????????????? ??????????:
7. ????????? ??????????????????? ?????????? ?????????????: ????????? ????? ???????? ????????????????? ????????????? ????:
1-?? ????????? ?????????
2 ?????????? ?????- ????????? 2 ???
2 ??? ????., ????????? 2 ??? ??????????? ????????
MANDATORY
1205/?13
1. Purpose of the Course
·???????????? ?????????? ???????? ????????, ?????????????????, ???????????? ???????????? ?????????????,
·???????????? ??????????? ??????????? ???????? ???????????????, ??????????, ????????????? ? ??????????? ??????????????????????,
·??????????? ??? ???????? ????????? ?????????? ????????? ????? ???????????? ? ?????? ???????? ?????????????? ????????? ?????,
·??????????? ??? ????????? ????????????? ??????? ???????? ?????????????? ??? ????? ????????? ? ??????????????? ?????:
2. Educational Outcomes
?. ???????????? ??????? ? ???????????
1.??????????? ?????? ????, ?????? ??? ???????????? ????????? ????? ?????,
2.??????????? ???????? ??????????? ?????????? ?????? ???????? ??????????????????? (??????????, ???????, ????????, ?????????? ?????????????????? ?????, ????????????? ? ?????????????? ??????????????????????)?

?. ????????? ???????????? ???????????????
3. ?????????? ????????????? ?????? ??????????? ??????? ????? ???????? ?????????????,
4. ??????????? ? ?????? ????????????? ??????? ???????????? ???????,

?. ???????????/????????? ???????????????
5.?????????? ????? ??? ???????? ?????? ????????? ????????,
6.?????????? ?????????????, ??????????? ???? ???????:

3. Description
·???????????? ?????????? ???????? ????????, ?????????????????, ???????????? ???????????? ?????????????,
·???????????? ??????????? ??????????? ???????? ???????????????, ??????????, ????????????? ? ??????????? ??????????????????????,
·??????????? ??? ???????? ????????? ?????????? ????????? ????? ???????????? ? ?????? ???????? ?????????????? ????????? ?????,
·??????????? ??? ????????? ????????????? ??????? ???????? ?????????????? ??? ????? ????????? ? ??????????????? ?????:
4. Teaching and Learning Styles and Methods
·????????? ????????? ??????????? ?????? ?? ????? ??????? ?????? ??????????? ???????????? ???????? ?????,
· ???????? ?? ?????? ????????????????? ???????????? ?????????,
· ?????? ?? ????? ??????? ???????????? ???????????? ?????? ????? ???? ????????,
· ????????????? ? ???? ?????? ??? ???????????? ?????????,
· ??????????? ?????? ?? ????? ?????? ????? ?????????? ??????????? ? ???????????,
· ????? ?? ??????? ?????????????? ???? ?????? ???????,
· ???????? ?? ???????????? ?????? ?????????????? ????? ????????????,
· ????????????? ? ????? ????????????? ?????????????? ????????? ?????????? ??????????? ????????,
· ?????? ?? ????? ???????????? ??????????? ????? ??????????,
· ?????? ????????????? ??????????? ?? ?????????? ????? ?????? ?????????, ? ????????? ?????? ?????????????????????? ??????????:
5. Evaluation Methods and Criteria
1.?????????
2.???????? ??????? ??????, ??????? ? ???????? ???????, ??? ???????????? ? ???????? ?????????????? ????: ?????????????? 3-? ??, ??????? ???????? ??????, ????????? ??????? ? ???????? ?????????
6. Basic Bibliography
  • 刘珣著，《新实用汉语课本》1学生书, 北京语言大学出版社，2006年
  • 刘珣著，《新实用汉语课本》1练习册, 北京语言大学出版社，2006年
  • 姜丽萍著，《HSK标准教程》1学生书， 北京语言大学出版社，2015年
  • 姜丽萍著，《HSK标准教程》1练习册， 北京语言大学出版社，2015年
7. Main sections of the course
???? 1：语音 （声母、韵母、声调）
???? 2：语音 （声调、音变、拼写规则）
???? 3：第一课 你好（“是”字句，“吗”疑问句）
???? 4：第二课 你是哪国人（们、也、呢）
???? 5：第三课 那是你的书吗（这、那，特殊疑问句，定语）
???? 6：第四课 课图书馆在哪儿（在，是，哪儿，方位名词）
???? 7：第五课 在北京大学的东边（语音点小结）
???? 8：第六课 现在几点（钟点表达法，数字表达法）
???? 9：第七课 明天你有课吗（“有”句子，吧，方位名词，时间名词做状语）
???? 10：第八课 你的电话号码是多少（吧，呢，号码表达法，“几”和“多少”）
???? 11：第九课 多少钱一瓶（“几”和“多少”，“二”和“两”，量词，钱数表达法）
???? 12：第十课 你家有几口人（语音点小结）
???? 13：第十一课 北京的冬天比较冷（怎么样，不A不B，形容词谓语）
1-??? ????????? ????????
?????????? ?????- ????????? 2 ???
????.-2, ????????? 2 ??? ??????????? ????????
MANDATORY
1803/?13
1. Purpose of the Course
· ?????????? ??????????? ?????? ?????????? ???????????, ???????????, ????????????? ??????????????????????,
. ???????? ????????? ??????? ????????????? ???????????????, ????????? ????????? ????????? ? ??????????? ??????? ??????? ??????????? ??????????????:
2. Educational Outcomes
?. ???????????? ??????? ? ???????????
1.????????????? ?????????? ??????????? ?????????,
2. ?????????? ?????????? ??????????? ??????????????????????:

?. ????????? ???????????? ???????????????
3.????????????? ????????? ???? ?????????????????,
4.??????????? ??????????? ??????? ? ????????? ????????? ???? ???????:

?. ???????????/????????? ???????????????

3. Description
· ?????????? ??????????? ?????? ?????????? ???????????, ???????????, ????????????? ??????????????????????,
. ???????? ????????? ??????? ????????????? ???????????????, ????????? ????????? ????????? ? ??????????? ??????? ??????? ??????????? ??????????????:
4. Teaching and Learning Styles and Methods
1. ????????? ???????? ?????????, ??????????????,
2. ????????????????? ??????? ? ??????? ????,
3. ??????????? ? ????????????? ?????????????????????? ?????????????? ? ????????????????
5. Evaluation Methods and Criteria
????????? ????????? ? ??????????, ??? ???????????? ? ?????? ?????????? ? ??????? ?????????:
1.?????? ???????? (????? ????? ???????? ?????? ????? ??????????),
2. ??????? ???????? (??????, ????????? ? ?????????? ???????????? ??????):
6. Basic Bibliography
  • ???????? ?., ?????????? ?., ???????????? ?., ?????????? ????????, ???? ?, ???????? ?????????? ??????????????? (???????????? ? ?? ??? ?????? ????? ???????? ??????? ??????????? ?????), ?????, ??????? ???? ????., 2015:
  • Ergin M., Türk Dil Bilgisi, ?stanbul, 1980.
  • Hengirmen M., Türk?e ??reniyoruz, c. 1-3, Ankara 1999.
  • Щека Ю. В., Интенсивный курс турецкого языка: Учебник, М., 1996.
7. Main sections of the course
???? 1? ??????????? ?????????? ??????????? ?????????:
???? 2? ???????? ????, ??????, ??????????????? ????????? ????????????:
???? 3? ?????????? ??????, ???? ?????? ???:
???? 4? ????????? ?????????? ???????????? ????????????:
???? 5? ?????-???????????? ??????????? ??????????? ????????????:
???? 6? ??????????? ???????????? ?????? ???:
???? 7? ?????????? ??????? ????? ????????? ?????????? ?????? ??????????;
???? 8? ?????? ???????? ???????????:
1-?? ????????? ?????????
?????????? ?????-???????? 2 ???
????.-2?. , ????????? 2 ??? ??????????? ????????
MANDATORY
1604/?13
1. Purpose of the Course
?????????? ??????????? ??????????????? ? ??????????? ??????????????????????? ? ?????????? ??????????? (??? ????????? ????` A1-A2 ??? A2-B1 ????????),
???????? ? ??????????? ?????????????? ????????, ?????????? ? ????????????? ??????????????:
2. Educational Outcomes
?. ???????????? ??????? ? ???????????
1.???????? ??????????? ? ?????????? ????????? ????????????? ??????? ???? ??????????,
2. ???? ???????????? ?????? ?????????????? ???????? ????? ???????????:

?. ????????? ???????????? ???????????????
3.????????????? ?????? ???????? ?????????, ?????????????? ? ?????? ?????????????? ? ??????????????,
4. ?????? ??????? ???????? ???????????? ?? ????????:


?. ???????????/????????? ???????????????
5.??????????? ???????? ???????????? ?????? ???????????? (???????? ????????????) ??????????????? ???????, ??????????? ??????????? ? ????????????? ???????? ? ?????????? ???? ????? ?????????? ?????????????? ??????, ?????????????? ?? ???????????????????? ??? ? ???? ?????????? ?? ????????????:

3. Description
?????????? ??????????? ??????????????? ? ??????????? ??????????????????????? ? ?????????? ??????????? (??? ????????? ????` A1-A2 ??? A2-B1 ????????),
???????? ? ??????????? ?????????????? ????????, ?????????? ? ????????????? ??????????????:
4. Teaching and Learning Styles and Methods
1. ????????? ?????????? ???????? ??????????????,
2. ????????? ? ??????? ????????,
3. ????????? ? ??????? ????????,
4. ??????????? ????????,
5. ??????? ???????????/ ??????????? (????????? ??????????? ??????? ???????????),
6. ?????? ? ??????? ????????/ ???????,
7. ???????????? ????????? ?????????:
5. Evaluation Methods and Criteria
????????? ????????? ? ??????????: ??????.
1. ?????? ??????? ???????? ?????????, ?????????????? ? ????????????:
2. ?????????? ????????:
3. ?????? ???????? ?????:
4. ??????????? (???????????) ?????? ???????? ?????:
6. Basic Bibliography
  • Meltonjan G., Soghomonjan K., Diwanjan N. Deutsch (für Stufen A2-B1). Jerewan, Verlag der Universit?t Jerewan, 2022.
  • DaF kompakt neu A1 - B1. Klett Verlag Stuttgart, 2016.
  • Dreyer,R. Schmitt. Lehr - und ?bungsbuch der deutschen Grammatik. München: Max Hueber Verlag für Deutsch, 2001. - 320 с.
7. Main sections of the course
· ??????????????. ???????? ?????????? ? ????????????? ??????????? ?? ??????, ????? ?????????????????????? ???????:
· ??????????? ????????????? ? ?????????? ????????????????????:
. ???????? ??????????????? ? ????? ???????? ???????????? /?????? ?? ???????/:
1-??? ?????????
?????????? ?????-????????? 2 ???
????. – 2?., ????????? 2 ??? ??????????? ????????
MANDATORY
1602/? 13
1. Purpose of the Course
1. ????????? ????????? (General English) ???????? ???????? ?????????????? ?????????,
2. ???????????? ????????? (Professional English) ??????????? ??????????,
3. ???????? ???????????? ??????????, ????????? ???????????? ??????????
?????????? ? ?????????,
4. ???????????? ?????????????? ?????????? ??????? ? ??????? ?????? ??????????? ?
??????????:
2. Educational Outcomes
?. ???????????? ??????? ? ???????????
1. ???????? ????????? ????????????? ??????????? ? ???? ??????? ??????????? ???????????,
2.??????????? ???????????? ??????? ????? ???????? ?????????????????,

?. ????????? ???????????? ???????????????
3.??????? ?????? ????? ???????? ??????????????,
4. ???????????? ????????? ? ???????????? ?????????? ????????? ??????? ????? ???????? ??????????????,

?. ???????????/????????? ???????????????
5. ?????? ??????????????? ??????? ???????????? ?????????? ????????????:
3. Description
1. ????????? ????????? (General English) ???????? ???????? ?????????????? ?????????,
2. ???????????? ????????? (Professional English) ??????????? ??????????,
3. ???????? ???????????? ??????????, ????????? ???????????? ??????????
?????????? ? ?????????,
4. ???????????? ?????????????? ?????????? ??????? ? ??????? ?????? ??????????? ?
??????????:
4. Teaching and Learning Styles and Methods
1. ????????? ?????????? ???????? ??????????????,
2. ????????? ? ??????? ????????,
3. ????????? ? ??????? ????????????? ??????????,
4. ??????????? ????????:
5. Evaluation Methods and Criteria
????????? ????????? ? ??????????, ??? ???????????? ? ?????? ?????????? ? ??????? ?????????:
1. ?????? ???????? (???? ????? ???????? ?????? ????? ??????????):
2. ??????? ???????? (??????, ????????? ? ?????????? ???????????? ??????):
6. Basic Bibliography
  • Mkhitaryan Ye. “Basic English for University Student” Yerevan 2008.
  • Karapetyan K. Grigorian V. “English for University students” Yerevan 2004.
  • Margaryan Y. “A Guide to Science” Yerevan 2014.
7. Main sections of the course
1. ????????? ??????????? ???????????,
2. ????????? ?????????? ?????????,
3. ???????????? ????????? ???????? ??????????,
4. ???????????? ???????? ?????? ?????? ? ??????? ???????? ????????? ??????????:
Chair code Name of the elective course Credits
4-??? ?????????? ????????
?????????? ?????- ????????? 2 ???
???.-2 , ????????? 2 ??? ??????????? ????????
OPTIONAL
1501/?16
1. Purpose of the Course
· ???????, ??? ?????????, ????, ????????????, ???????????????? ???? ????????????? ? ????????????? ????????? ???????????? ??? ??????????,
· ???????????????? ???????????????????, ?????????? ???? ??????? ????????????????? ? ??????? ???????? ????????? ??????????????????,
. ?????? ??????????? ??????????????, ???????????????? ??????????? ?????????, ?????????, ???????????? ???????????????????? ????????????? ???????????? ???????????????? ?????????:
2. Educational Outcomes
?. ???????????? ??????? ? ???????????
1. ???????? ??????, ??? ??????? ?? ?????????, ????????? ??????? ???????????? ?? ???????? ??????????????,
2. ??????????? ??????? ????????????? ?? ??? ?????????????? ??????? ???????? ????????????, ???????? ???????????????? ??????????????????? ?? ??????? ?????????? ????,
3. ??????????? ??????? ???????? ????? ?? ?????????:

?. ????????? ???????????? ???????????????
4. ??????????? ????????? ?????????????????????????, ??????? ????????????????????? ?????????? ?????????????????? ? ????????? ???????????? ??????????,
5. ?????????? ?????????, ???????????? ???????????????????? ?????????????, ??????????? ???????????? ??????????????, ??????? ?????????

?. ???????????/????????? ???????????????
6. ??????? ??????? ???????????? ???, ??????? ????????????? ?????? ?????????, ???????/?????? ????????????? ? ?????????? ??????????????, ??????????? ?????????:
3. Description
· ???????, ??? ?????????, ????, ????????????, ???????????????? ???? ????????????? ? ????????????? ????????? ???????????? ??? ??????????,
· ???????????????? ???????????????????, ?????????? ???? ??????? ????????????????? ? ??????? ???????? ????????? ??????????????????,
. ?????? ??????????? ??????????????, ???????????????? ??????????? ?????????, ?????????, ???????????? ???????????????????? ????????????? ???????????? ???????????????? ?????????:
4. Teaching and Learning Styles and Methods
· ??????????????,
· ??????? ??????????,
· ?????????,
· ??????? ???????????,
. ??????????? ???????????? ???????????:
5. Evaluation Methods and Criteria
????????? ????????? ? ??????????:
????????? ?????????? ??????? ??????? ??? ?????????? ??????????
????????? ???????????? ????? ?????? ????????? ? ??????????????? ????????, ???????????? ?????????????????? ? ??????????????????, ??????? ?????????? ??????? ???????????, ??????????? ???????????:
6. Basic Bibliography
  • ??????????????? ???????? ??????? ????????? ??????????? ?????, ????? ??????????????????? ???????, 2017:
  • ouchard Julie, Candel ?tienne, Cardy Hélène, Gustavo Gomez-Mejia (dir.), La médiatisation de l’évaluation, Peter Lang, 2015.
  • outant Alexandre, Thomas Stenger (coord.), Identités numériques, L’Harmattan, coll. ?Communication et civilisation?, 2014.
  • ichael O'Shaughnessy, Jane Stadler, and Sarah Casey, Media and Society, 2016.
  • Stanley J. Baran, Introduction to Mass Communication, Bryant University, 2022. ...
7. Main sections of the course
· ?????. ??????????, ?????????, ?????????, ????????????, ??????????????, ??? ? ??? ?????????????:
· ????????????????? ????????????. ?????? ??????????? ????????? ?????????????:
· ??????? ????????:
· ??????? ??????????. ??????:
· ???????????? ???????????? ? ???????????? ??????????????:
. ???????????????? ???????????: ??????? ?????????? ????: ?????????????????? ? ??????????????????:
3-???????????? ??? 4-??? ??????????
?????????? ?????- ????????? 2 ???
???.-2?., ????????? 2 ??? ??????????? ????????
OPTIONAL
1311/?16
1. Purpose of the Course
??????????? ??? ???????? ? ????????? ??????????? ???????????? ????????????? ? ?????????, ???? ??????? ????? ????? ?????? ???????????, ??????????? ? ?????? ???????? ??????????? ???????? ???????????? ?? ???????????, ??????? ????????????? ????????? ???????????? ? ???????????????? ????????, ?????????????? ??????????? ???????????????????? ?? ???????????, ???????? ??????????? ????????????????? ? ??????????????????????
2. Educational Outcomes
?. ???????????? ??????? ? ???????????.
1. ????????????? ???? ??????????? ????????????? ????????? ??????????????????????,
2. ???????????? ????????????? ????????????, ????????????? ??????????????? ??????????????, ???????????? ????? ????????? ?????????,
3. ??????????? ???????? ? ?? ???????? ????????????? ??????????? ???? ?????????????? ????????????? ???????????

?. ????????? ???????????? ???????????????.
4. ??????????? ???? ??????????? ?????? ????????? ??????????????????????,???????? ??????????? ???????????? ????????? ?????????,
5. ???????????? ??????????? ???????????????????? ? ????????, ???????????????? ???????? ?????? ?????? ??????????? ????? ?????????????,
6. ?????????? ?????????????? ??????????? ???????????????????, ??????????? ????????????????, ????????? ????????

?. ???????????/????????? ???????????????
7. ??????????? ??????????? ? ?????????????? ????????? ???????????? ?????????????????????? ? ????????? ?????????????? ??????????,
8. ?????????????????? ??????????, ?????????, ??????? ? ????????? ?????? ?????????? ?????????, ??? ????????? ??????? ????? ???????? ???????????? ???????????????????
3. Description
??????????? ??? ???????? ? ????????? ??????????? ???????????? ????????????? ? ?????????, ???? ??????? ????? ????? ?????? ???????????, ??????????? ? ?????? ???????? ??????????? ???????? ???????????? ?? ???????????, ??????? ????????????? ????????? ???????????? ? ???????????????? ????????, ?????????????? ??????????? ???????????????????? ?? ???????????, ???????? ??????????? ????????????????? ? ??????????????????????
4. Teaching and Learning Styles and Methods
1. ??????????????,
2. ?????????? ?????????,
3. ???????????? ??????????????,
4. ????????????? ??????? ???????,
5. ?????? ????????? ?????????? ???????????? ? ??? ?????? ???????? ?????? ? ??????????
5. Evaluation Methods and Criteria
????????? ????????? ? ??????????? ??????????? ???????? ????? ??????????? ? ????????? ???????????? ????????? ????????? ?????? ????? ???? ????????? ????????????? ????????? ??????????? ? ??????????? ????????? ????????? ?????? ??????????
6. Basic Bibliography
  • ??????? ?., ????????????????. ?????????????????? ????????????, ???????? ????., ?????, 2016:
  • ???????? ?.?., ?????? ?????????????? ????????, ??????? ????????????????, ?????, 1967?
  • ??????, ?. ???????? ?????. ????????/???????. URL: .
  • ??????, ?. ???????? ????????????.?. ?. ???? II .. URL: .
  • ??????, ?. ???????? (????????????). ?. ?. ???? I. URL: .
  • Cialdini, R. (2021). Influence: The Psychology of Persuasion. 7th edition.
  • Frege, G. [As reprinted in A.W. Moore (ed.) Meaning and Reference. Oxford: Oxford University Press.]. URL:
  • Gabora, L., & Russon, A. (2011). The evolution of human intelligence. In R. Sternberg & S. Kaufman (Eds.), The Cambridge handbook of intelligence (pp. 328-350). doi:10.1017/CBO9780511977244.018
  • Jung, Sebastian. (2021). The 5 Axioms of Communication by Watzlawick, Beavin and Jackson. URL: .
  • 0. Pease, Allan & Barbara (2004). BODY LANGUAGE. URL: .
7. Main sections of the course
1. ???????????? ?????????? ? ???????? ??????????, ???????????? ???????? ???????????????
2. ?????????????? ?????? ????????, ??????????? ???????????? ?????????????? ??????????? ????????? ?????????????
3. ??????????? ??????????????????? ? ???????????: ????? ??????????????????? ? ??????? ????? ????
4. ????????????? ? ????????????, ???? ? ?????????, ???? ?????
5. ????????? ?????????????? ? ???????????
6. ??????????? ????????? ???????????? ????????
7. ??????????? ????????? ???????????????? ????????
8. ???????????? ?????????. ??????????????? ? ????????????????
9. ??????????? ????????????. ???????? ????????? ? ????????? ?????????????-????????-???? (II). ????????? ? ?? ??????????
3-??? ????????? ???????? ???
?????????? ?????- ????????? 2 ???
???. – 2 , ????????? 2 ??? ??????????? ????????
OPTIONAL
1207/?16
1. Purpose of the Course
·???????????????? ????????????? ???????????????????? ??????????? ????????? ? ???????????????? ??????????????,
·???????????????? ????????????? ?????????? ?????????????????? ?? ???????????????????? ?????????????????????? ??????????????? ???????????,
. ??????????????? ??? ?????????? ???????????? ???????????????? ???????????????? ??????????? ???????????????:
2. Educational Outcomes
?. ???????????? ??????? ? ???????????.
1.????????? ????????????? ???????? ????????????????? ?? ?????????????, ????? ?????? ?? ??????????????,
2.??????????? ??????????????? ??????? ? ????????? ????????????? ??????? ???????????? ?????????,
3.??????????? ????????????? ?????????????? ?????????? ???????????? ???????? ? ??????? ??????????????????

?. ????????? ???????????? ???????????????.
4.??????? ????????????? ?????????????????,
5.???????????? ????????? ??????????????? ?????????????????????? ??????????? ?????????, ????????? ??????? ? ????????? ??????????????? ???? ?????????????

?. ???????????/????????? ???????????????.
6. ?????? ???????????? ????????????????
3. Description
·???????????????? ????????????? ???????????????????? ??????????? ????????? ? ???????????????? ??????????????,
·???????????????? ????????????? ?????????? ?????????????????? ?? ???????????????????? ?????????????????????? ??????????????? ???????????,
. ??????????????? ??? ?????????? ???????????? ???????????????? ???????????????? ??????????? ???????????????:
4. Teaching and Learning Styles and Methods
1. ?????????????????, ??? ????? ???????????? ????????????? ??????????:
2. ?????????????? ???????????????? ???????? ???? ????????????? ??????? ??????????:
3. ??????? ?????????????:
5. Evaluation Methods and Criteria
????????? ????????? ? ??????????:
????????? ?????????? ??????? ??????? ??? ?????????? ?????????,
????????? ???????????? ????? ?????? ????????? ? ??????????????? ????????, ???????????? ?????????????????? ? ??????????????????, ??????? ?????????? ??????? ???????????, ??????????? ???????????:
6. Basic Bibliography
  • ????????????????: ??????????? ???????, ?????? ???. ??????., ??., 2006:
  • ????????? ?. ?., ????????? ???????????? ???????????: ???. ??????? ??????? ?????: ??????-97:
  • ????????? ???????????? ????????? ?????????????? ???. ???????? ??? ?????????????????
  • Антология мировой политической мысли в 5т. М., 1997.
  • жиев К.С. Политическая философия. М., 1999.
7. Main sections of the course
????? 1? ? ??????????????? ?????????? ????? ??????????: ???????????????? ??????? ? ???????: ??????????????? ??????? ? ?????????? ????? 2? ????????? ??????????? ?????????, ??????????? ? ?????????????????? ????? 3? ????????????? ????????? ?????????? ??????????? ????????? ????????? ??????? ?????????? ????? 4? ????????? ?????????????????? ? ??????????? ??????????? ????? 5? ? ????????? ????????????: ?????????????? ? ???????? ??????????: ??????? 6?? ????????? ?????????????????????: ??????? 7`? ????????? ??????? ? ???????????????:
3-??? ????????? ???????? ??? 4-??? ?????????? ????????
?????????? ?????- ????????? 2 ???
2 ??? ?????????????? , ????????? 2 ??? ??????????? ????????
OPTIONAL
1311/?16
1. Purpose of the Course
·???????? ??? ???????? ????????? ???????????? ??????-???????????? ???????????? ?????????? ??????????? ??????????, ???????????? ????????????????? ????????????? ?? ????????? ???????????????,
·????????? ???????????? ??????????? ?????????? ??????? ???????????? ???????, ??????? ??????????? ??????? ? ??????????? ????????????, ??????????? ???????????????? ??????????:
2. Educational Outcomes
?. ???????????? ??????? ? ???????????
1.??????????? ???? ???????????,
2.????????-?????????? ???????????? ????????? ? ???????? ?????????, ????? ????????? ?? ?????????????????? ?????????????????, ???????????? ???????? ????????? ??????????? ? ??????????? ??????????????:

?. ????????? ???????????? ???????????????
3.???????? ???????????? ??????????? ????????? ? ?????????????? ????????????? ???????????? ?????? ?????????????,
4.???? ??????? ? ???????? ?????????????????, ????????????????, ?????????????? ??? ??????, ?????? ??? ?????????? ? ??????? ???????????? ?????????????????, ?????? ?? ????? ????????,
5.?????????? ???????????? ???????? ?? ?????????????? ???? ??????????? ? ????????? ?????????????????????? ???????:

?. ???????????/????????? ???????????????
???????? ???????????? ???????????? ????????? ????????` ?????????? ????????? ???????????? ?????????????, ?????????????????, ????????????????? ? ???????????????? ???????? ???????????? ?? ??????? ???? ???????? ??????? ??????????:
3. Description
·???????? ??? ???????? ????????? ???????????? ??????-???????????? ???????????? ?????????? ??????????? ??????????, ???????????? ????????????????? ????????????? ?? ????????? ???????????????,
·????????? ???????????? ??????????? ?????????? ??????? ???????????? ???????, ??????? ??????????? ??????? ? ??????????? ????????????, ??????????? ???????????????? ??????????:
4. Teaching and Learning Styles and Methods
1. ??????????????,
2. ?????????,
3. ????????? ????????:
5. Evaluation Methods and Criteria
????????? ????????? ? ??????????
????????? ?????????? ?????????? ????????? ????????? ?????? ????????? ??????? ? ????????? ???????????????? ???????? ??????????????,
????????? ???????????? ????? ?????? ????????? ? ??????????????? ????????, ???????????? ?????????????????? ? ??????????????????, ??????? ?????????? ??????? ???????????, ??????????? ???????????:
6. Basic Bibliography
  • ???????? ?.?., ?????????????? ????????: ??., 1987:
  • ???????? ?.?., ???????????????: ??., 1998:
  • Ивлев Ю.В., Логика. Учебник. 3-е издание. М., 2005.
  • Ивин А.А., Практическая логика. Учебное пособие. М.,2002.
  • иллов В.И., Орлов Г.А.,Фокина Н.И., Упражнения по логике. Учебное пособие. М., 2005.
7. Main sections of the course
?????????????? ??????? ? ??????????????: ???? ? ?????: ?????????????: ???????????? ?????? ???????????????? ? ?????????: ???????????? ???????????????? ????????????????? ???: ???????????? ?????? ???????? ?????????, ????????? ?? ?????????: ????????? ?????????, ????????? ?? ?????????: ??????????? ????????? ????????? ?? ?????????: ??????????? ????????? ? ?????: ???? ? ???? ???????????????, ????? ?????????: ???????????? ???????????? ???????? ?????????: ????????? ?????????????, ????? ????????? ? ?????????. ??????????, ???????????, ??????? ? ????????? ?????????????: ?????????: ????? ?????????????: ????????? ?????????????: ????????? ? ?????????: ?? ???? ??????????? ?????????: ????????? ?????????? ????????: ??????????????: ?????? ????? ???????? ???????? ????????? ?????????????? ?????????:
?????????? ? ???????, ??????? ? ??????????: ?????? ????? ???????? ???????? ?????????? ? ??????? ?????????: ??????????, ?????????????, ????????????, ????????:
3-??? ?????????? ??? 4-??? ????????? ????????
?????????? ?????- ????????? 2 ???
???.-2 ???, ????????? 2 ??? ??????????? ????????
OPTIONAL
0107/?16
1. Purpose of the Course
·???????????? ????????? ?????????? ??????????????? ????????? ?????????????????? ???????? ???????????? ??????????:
·???????????? ?????????? ??????????????? ????????? ?????????????? ????????????? ???????? ?????????????, ????? ? ???? ?? ??????????? ?????
????????? ??????????????? ??????? ?????:
2. Educational Outcomes
?. ???????????? ??????? ? ???????????
1.??????????? ??????? ? ????????? ????? ??????? ????? ???????? ??????? ??????????, ??????? ???????????, ??????? ?????????, ????????????????? ? ????????????????? ??????????,
2.????????? ?????? ????????????????, ?????????????????? ? ?????????????
3.????????? ???????? ???????? ????????????,
4.??????????? ?????????????? ???????? ???????????? ? ????????????????? ?????????, ?????????????? ????????? ??????? ????????? ?????? ???????????????????? ??????????? ??????????? ???????????,

?. ????????? ???????????? ???????????????
5.?????? ????? ? ?????????????????? ???? ????????,??????? ????????????? ????????????????? ?? ???? ??????????????, ?????????? ????? ????????????:

?. ???????????/????????? ???????????????
6.?????? ??????? ?????? ???????????? (???????????? ??????????, ???????????? ???????????, ??????? ????????? ? ?????????????????),
7.????????? ?????????????????, ??????????? ????? ????????????, ?????
???????????? ?????????:
3. Description
·???????????? ????????? ?????????? ??????????????? ????????? ?????????????????? ???????? ???????????? ??????????:
·???????????? ?????????? ??????????????? ????????? ?????????????? ????????????? ???????? ?????????????, ????? ? ???? ?? ??????????? ?????
????????? ??????????????? ??????? ?????:
4. Teaching and Learning Styles and Methods
1.??????????????
2.??????? ????????
3. ??????????? ????????
5. Evaluation Methods and Criteria
????????? ?????????? ? ???????: ?????? ? 4 ???? ??????? ??????????
???????????
6. Basic Bibliography
  • McConnell, Economics, 2021.
  • Сидорович А.В.-Курс экономической теории-2001.
  • ????????, ?. ?????????, ???????????????? ???????????, ?????, ??? ????., 2017?.?
7. Main sections of the course
??????????????? ????????? ??????? ? ??????: ?????????? ????????? ????????: ?????????? ????? ??????????: ???????????? ??????????: ?????????? ?????????? ?????????: ??????? ???????????? ?????????, ??????????, ????????????? ?????????????: ?????????????? ???????????? ????????????? ? ???????, ???????? ??????????: ????????? ???????????, ?????????????? ? ???????????????: ?????????? ????????? ? ???????: ???? ? ???????? ?????????: ?????????? ? ?????????? ?????????:
1-??? ????????? ??? 2-?? ??????????? ????????
?????????? ?????-????????? 2 ???
????.-2, ????????? 2 ??? ??????????? ????????
OPTIONAL
2301/?16
1. Purpose of the Course
●???????????? ???????? ????????? ?????????? ??????????????, ????? ??????????, ????????? ? ??????????? ????????? ??????????,
●??????? ????????? ?????? ?????????? ?????????? ?????????????? ??? ????????? ????????????????? ?? ????????????????? ????????? ?????:
2. Educational Outcomes
?. ???????????/????????? ???????????????
1.??????? ??????, ?????????? ??????????, ???????????? ???,
2.??????? ??????????, ?????? ?????????? ? ?????????,
3.??????????? ??????? ?? ??????????????? (????????? ? ????????? ???????????, ??????????? ????????, ????????????? ????? ????????? ?????????? ? ????)?

3. Description
●???????????? ???????? ????????? ?????????? ??????????????, ????? ??????????, ????????? ? ??????????? ????????? ??????????,
●??????? ????????? ?????? ?????????? ?????????? ?????????????? ??? ????????? ????????????????? ?? ????????????????? ????????? ?????:
4. Teaching and Learning Styles and Methods
1.?????? ?????????? ?? ?????????? ???????, ????????????? ?? ???????? ? ??????????? ?????????????:
2. ???????????? ???????? ? ??????????? ????????? ?????????????? ??????????? ?? ???????????? ???????????? ??????? ?????????? ?? ???????????? ?????? ??? ????????? ??. ??????:
5. Evaluation Methods and Criteria
????????? ?????????? ? ?????????? ???????? ???????? ??????? ????????? ????? ???? ?????????????? ??????? ?? ????????? ????????? ????? ???????? ????
????????????? ?????????? ???????? ? ????????? ??????? ?????? ????????:
6. Basic Bibliography
  • Серогородский В., Сурин Д., Тихомиров А., Microsoft Office 2016 / Office 365, 2017 Наука и техника.
  • Katherine Murray, First Look Microsoft Office 2010, Microsoft Press.
  • Ю. Стоцкий, А. Васильев, И.Телина, Microsoft Office 2010, Питер.
  • ??????????? ???????????? ??????:
7. Main sections of the course
????? 1 - ?????????? ??????????? ? ????????? ???????? ?????????????
????? 2 - Windows ????????? ????????? ?????????? ?????????? ??? ????????? ???????? ????????????:
????? 3 - ????????? ??????????? ???????? ? ??????? ?????????????:
????? 4 - ?????????? ???????????? ??????????????, ??????????, ??????????
????? 5 - ??????????? ??????????? ?????????????? ???????? ? ??????????:
1-?? ?????????/ 2-?? ?????????? ????????
?????????? ?????- ????????? 2 ???
2 ??? ?????????????? , ????????? 2 ??? ??????????? ????????
OPTIONAL
2203/?16
1. Purpose of the Course
???????????? ???????? ?????????? ????????????? ???????? ??????????? ? ??????????? ????????? ??????????? ???????????? ???????????? ????????????????? ???????? ? ????????????? ???????????? ????????????????????????:
2. Educational Outcomes
?. ???????????? ??????? ? ???????????
1. ???????????? ???????????? ????? ????????? ?????????????? ????????????,
2. ????????????? ????????????` ????? ????????? ???????? ?????????????, ?????????????? ??????????? ???????????? ???? ?? ????, ???????????? ??????????????? ? ???????? ??????????????????????, ????????????????? ???????,
3. ??????????? ???????? ????????????? ????????????, ????????? ???????, ?????? ??? ????????????? ??? ???? ??????? ?? ???? ?????????? ???????????? ?? ?????? ?????????? ?????????????, ?????????? ???????????? ? ????????????? ?????????? ??????????? ?????????????????:

?. ????????? ???????????? ???????????????
4. ???????? ????????????? ????????????? ?????????????` ???????????? ??????????? ????????????? ?? ??????????????:
3. Description
???????????? ???????? ?????????? ????????????? ???????? ??????????? ? ??????????? ????????? ??????????? ???????????? ???????????? ????????????????? ???????? ? ????????????? ???????????? ????????????????????????:
4. Teaching and Learning Styles and Methods
????????? ????????? ? ?????????????????, ????????? ??????????? ??? ????? ??????????, ??? ?????????????? ??????????????, ?????? ???? ???????????? ???????????? ?????????????? ?????????:
5. Evaluation Methods and Criteria
????????? ????????? ??????? ???????? ????????: ??????? ???????? ?????????? ??????????? ? 2 ????:
6. Basic Bibliography
  • Гидденс Э. “Социология”// 2-е изд., полн. перераб. и доп., М.: Эдиториал УРСС, 2005.
  • Миллс Ч. Р. “Социологическое воображение”// Пер. с англ. О. А. Оберемко. Под общей редакцией и с предисловием Г. С. Батыгина. - М.: Изда-тельский Дом NOTA BENE, 2001, 264 с.
  • Штомпка П. “Социология. Анализ современного общества” М.: Логос, 2005, 664 с.
  • Macionis J.J. “Sociology”// USA: Pearson Education, Inc., 14th ed., 2012.
7. Main sections of the course
1.??????????? ????? ??????????. ???????? ??????????????????????
2.???????????? ??????? ?? ???????. ??????????? ? ??????? ????????????
3.??????????? ?????????????? ???????????
4.????????????? ??????????? ? ????????????? ?????
5.????????????? ???????? ???????????
6.???? ? ???????????????, ?????? ?? ????????????? ?????????, ??? ? ??????????
7.????????, ????????? ??????
8.??????????????? ????? ???????????? ????????????????? ??????
9.????????????? ?????????? ???????????. ?????????? ????????????
10.?????????? ????? ? ???????????????????
11.?????????????? ? ???. ?????????? ??????????????? ? ???????????????
12.?????? ???? ? ?????????? ????????????????
13.?????????? ????????????????. ??????????? ? ????????????
14.????????????????, ???????????? ? ????????
15. ?????????? ???????????????, ???????????? ? ???????????
4-??? ?????????? ????????
?????????? ?????- ????????? 2 ???
2 ??? ????., ????????? 2 ??? ??????????? ????????
OPTIONAL
1705/?16
1. Purpose of the Course
???????? ??????????? ???????? ??????????? ? ????????????? ?????????????? ????????????? ????? ???????????,
???????? ??????????? ????? ???? ????? ???????? ??????????? ? ?????????????? ????????? ???????????? ???????????, ???????? ??????????????? ??????? ???????? ???????????? ????????????
2. Educational Outcomes
?. ???????????? ??????? ? ???????????
1. ???????? ???????????? ????? ?????????? ???????? ???????????,
2. ??????????? ???????????? ?????? ??????????? ? ?????????? ??????????????????????,????????? ????? ?????????? ??? ??????????? ? ?????????????? ?????????????????????? ????????????

?. ????????? ???????????? ???????????????
3. ????????? ???????????? ????? ?????????????? ?????????,
4. ??????????? (???? ? ????????) ?????????/???????? ???????????? ?????? ? ?????????? ???,
5. ???????? ???????? ?????????????? ?????? ?????, ???????????? ???????????????????, CV, ??????, ????????????????? ???????? ???????????????, ?????? ??? ??????? ????????????? ??????????? ? ???????????????

?. ???????????/????????? ??????????????? (??? ???????? ???)
?????????? ??????????????? ???????? ???????????????????? ???????? ?????????? ?????????????
3. Description
???????? ??????????? ???????? ??????????? ? ????????????? ?????????????? ????????????? ????? ???????????,
???????? ??????????? ????? ???? ????? ???????? ??????????? ? ?????????????? ????????? ???????????? ???????????, ???????? ??????????????? ??????? ???????? ???????????? ????????????
4. Teaching and Learning Styles and Methods
1. ????????? ??????????
2. ??????????? ????????
3. ??????? ????????
4. ??????? ???????????
5. ?????? ? ??????? ???????
5. Evaluation Methods and Criteria
????????? ????????? ? ??????????, ??? ?????????? ? ??????? ? ??????? ? ????????? ????????? ????? ??????????? ???????????? ????????? ????? ????
6. Basic Bibliography
  • еляева Е.А., Голосная Н.П., Ефимова Д.А., Кондрашова Н.В., Нечаева Т.В., Стукова Е.Г. Русский язык как иностранный. Научный стиль речи: Учебное пособие. - Санкт-Петербург: Университет ИТМО, 2019.
  • уре Н.А., Волкова Л.Б., Косарева Е.В. Основы русской деловой речи. Учебное пособие для студентов высших учебных заведений, СПб, 2011.
  • алаян С., Айвазян М., Багдасарян А., Дпирян М., Мкртычян-Лалаян С. Грамматика в упражнениях - Ереван: изд-во ЕГУ, 2021, 232с.
  • алаян С., Айвазян М., Багдасарян А., Дпирян М., Мкртычян-Лалаян С. Русский язык. Учебник для гуманитарных факультетов вузов Армении. Издание 2-е, перераб. и доп. - Ереван: изд-во ЕГУ, 2021, 320с.
  • Лысакова И.П. Практическая стилистика русского языка. Учебное пособие, изд. 2-е, исправл., СПб, 1996.
  • Найденова Н.С., Сапрыкина О.А. Hаучный стиль речи. Теория, практика, компетенции. Учебное пособие. Издательство: ИНФРА-М, 2023 г.
  • Русский язык для делового человека:
  • Химик В.В. Практический синтаксис русского языка, СПб, 1995.
  • илов А.С. Читаем тексты по специальности. Вып. 2, Гуманитарные науки: учебное пособие по языку специальности, СПб, 2011.
7. Main sections of the course
· ?????????????. ????? ?????????? ??? ???????, ??????????? ? ?????????? ??????????????????????:
· ???????? ?????????????? ???? ?????, ???????????? ??????????????????, ???????, CV, ???????????????? ????????? ????? ? ????????????:
· ????? ??????? ??, ??????? ???? ?????? ????????????? ?????????????, ??????? ????????? ?????? ????????? ????????? ???????, ?????????? ? ?????????????:
???????????? ?????? ??????????????. ??????? ?????? ????????????? ????????? ???????? ????????:
3-??/4-?? ??????????/????????? ????????
?????????? ?????- ????????? 2 ???
2 ??? ??????????????, ????????? 2 ??? ??????????? ????????
OPTIONAL
1107/?16
1. Purpose of the Course
. ???????????? ?????????? ???????? ???????? ???????????? ? ???????? ????????? ????????????,
. ??????????? ??? ???????? ?????????, ?????? ??? ????? ?????????????? ??? ??????? ????????? ????????? ?? ???????????? ????? ??????????,
. ??????????? ??? ?????????? ???????? ??? ? ????????????? ???????????? ? ????? ??????????? ????????????? ?????:
2. Educational Outcomes
?. ???????????? ??????? ? ???????????
1. ??????????? ?????????? ???????????? ????????????? ?????????????,
2. ????????? ????????? ? ????????? ??????????????,
3. ??????????? ????????? ???????????, ????????????, ????????? ?????? ?
4. ????????? ???????? ????????????????????

?. ????????? ???????????? ???????????????
5. ?????????? ??????????? ??????????? ???????????? ?? ?????????????,
6. ?????????? ?? ??????????,
7. ?????????? ??????? ??????????? ??????????? ? ??????????????

?. ???????????/????????? ???????????????
8. ????????? ?????? ? ??????? ??????????????, ?????????????? ??????? ????????? ????? ?????? ??????????? ????????? ?????? ???????????:
3. Description
. ???????????? ?????????? ???????? ???????? ???????????? ? ???????? ????????? ????????????,
. ??????????? ??? ???????? ?????????, ?????? ??? ????? ?????????????? ??? ??????? ????????? ????????? ?? ???????????? ????? ??????????,
. ??????????? ??? ?????????? ???????? ??? ? ????????????? ???????????? ? ????? ??????????? ????????????? ?????:
4. Teaching and Learning Styles and Methods
??????????????,
????????? ??????????,
???????? ???????? ??????????
5. Evaluation Methods and Criteria
????????? ?????????? ? ????????? ???????: ????????? ?????????? ? ???????:
?????? ? ????????????? 4 ????`??????? ?????????? ??????????:
6. Basic Bibliography
  • ??????? ?. ??????????????????, ?., 2002:
  • Арутюнов С. А., Рыжакова С. И. Культурная антропология, М., 2004:
  • Кравченко А. И. Культурология, М., 2003.
  • Розин В.М. Культурология. М., 1998.
  • Armenian Folk Arts, Culture and Identity. Bloomington and Indianapolis, Indiana Univ. Press, 2001.
7. Main sections of the course
????????????????? ?????????????? ???????, ??????? ? ?????????:
?????????? ???????????? ?????????????, ????????? ???????, ?????? ? ????????? ?????????? ??????????????:
????????? ????????????? ???????????:
????????? ???????????, ????????????, ?????????????? ? ????????????:
??????????? ????????????:
??????????? ??????, ??????????? ? ??????????? ??????? ?????????????????:
??????????? ?????????? ? ????????, ??????????, ????????? ? ??????? ?????????????????:
????????? ? ??????????, ???????????? ? ??????? ?????????????????:
????????? ???????, ????????????????, ???????, ?????????????????? ????????????? ????????????:
????????? ? ???????:
????????? ? ?????????? ???????????:
????????? ????????? ? ????????? ??????????:
????????? ? ??????:
?????????????, ????????, ??????????? ???????? ??????????????????
????????????? ????????? ???????? ?????????????. ???????????, ?????????????, ??????????????????:
??? ????????? ???????? ?????????????. ???????????, ?????????????, ??????????????????:
??????????? ??????????? ????????????? ? ??????????? ??????:
3-?? ????????? ?????????
?????????? ?????- ????????? 2 ???
????. – 2, ????????? 2 ??? ??????????? ????????
OPTIONAL
1602/?16
1. Purpose of the Course
1. ???????? ???????????? ????????? ? ??????????? ? ???????????????? ??????????, ?????????????, ? ???????? ?????? ????? ????????? ??? ?????????????????????? ?????,
2. ????????????? ?????????? ? ???????? ?????????????? ??? ??????????? ?????????? ????????? ??????????,
3. ???????????? ????????????????? ? ?????????? ???? ????????,
4. ???????????? ???????? ???????? ? ????????????? ?????????????? ???????????
2. Educational Outcomes
?. ???????????? ??????? ? ???????????
1. ????????? ???????????? ?????? ??????????-??????? ???????? ??????????
2. ??????? ?? ?????????????? ????????. ?????????? ? ?????????? ?????? ???????????? ???????? ??????????
3. ???????????? ??? ????? ???????????? ??????????

?. ????????? ???????????? ???????????????
4. ??????? ?????? ????? ???????? ??????????????,
5. ?????? ????? ???????????? ?????????? ????????? ??????? ????? ???????? ??????????????,

?. ???????????/????????? ???????????????
6. ?????? ??????????????? ??????? ???????????? ????????????,
?????????? ? ?????? ?????? ????????????????? ????????? ?????? ??????????
3. Description
1. ???????? ???????????? ????????? ? ??????????? ? ???????????????? ??????????, ?????????????, ? ???????? ?????? ????? ????????? ??? ?????????????????????? ?????,
2. ????????????? ?????????? ? ???????? ?????????????? ??? ??????????? ?????????? ????????? ??????????,
3. ???????????? ????????????????? ? ?????????? ???? ????????,
4. ???????????? ???????? ???????? ? ????????????? ?????????????? ???????????
4. Teaching and Learning Styles and Methods
1.????????? ?????????? ???????? ??????????????
2.????????? ? ??????? ????????
3.????????? ? ??????? ????????????? ??????????
4.??????????? ????????
5. Evaluation Methods and Criteria
????????? ????????? ? ??????????, ??? ???????????? ? ?????? ?????????? ? ??????? ?????????:
1. ?????? ???????? (????? ????? ???????? ?????? ????? ??????????),
2. ??????? ???????? (??????, ????????? ? ?????????? ???????????? ??????):
6. Basic Bibliography
  • Edward R. Kolevzon, John A. Heine “Our world and Its People” the USA 1977
  • М.А. Васильева “English for the students of Geography part II ” Издательство “Менеджер”, 2001
  • Walker R. and Harding K ., Tourism 2. Oxford English for Careers, Oxford University Press,
  • 007.
7. Main sections of the course
1. ????????? ??????????? ??????????? ???????? ???????????? ??????????
2. ???????????? ?????????? ???????????
3. ?????????????? ???????? ?????? ? ??????? ????? ?????????
3-??? ????????? ????????
???.- 2 ???, ????????? 2 ??? ??????????? ????????
?????????? ?????- ????????? 2 ???
OPTIONAL
1308 / ?16
1. Purpose of the Course
· ????????????? ?????? ???????? ?????? ? ?????????, ??????????? ?????????? ????????????, ??????????????????? ? ??????????????????????,
· ?????????? ??????????? ????????????? ????????????????, ????? ???????? ???????????
2. Educational Outcomes
?. ???????????? ??????? ? ???????????
1. ?????????? ?????????????, ??????????? ???????????, ?????????????, ???? ??????? ??????????????????????,
2. ????????????? ???? ?????????????? ? ????????????????? ??????????????????????, ??????????????? ? ?????????????? ??????????,
3. ????????? ??????????? ??????????????????, ????? ?????????, ??????????? ???????? ? ????? ???? ????? ??????? ???????????,
?. ????????? ???????????? ???????????????
4. ??????????? ???????????, ???????-???????? ?????????????????? ????????? ? ?????????? ??? ?????? ?????? ? ??????? ??????????? ????????????? ??????????? ??????????????????????:
3. Description
· ????????????? ?????? ???????? ?????? ? ?????????, ??????????? ?????????? ????????????, ??????????????????? ? ??????????????????????,
· ?????????? ??????????? ????????????? ????????????????, ????? ???????? ???????????
4. Teaching and Learning Styles and Methods
1.??????????????,
2.??????? ??????????,
3.?????????,
4. ??????? ???????????
5. Evaluation Methods and Criteria
????????? ????????? ? ??????????
????????? ?????????? ??????? ????????,
????????? ???????????? ????-? ???????????:
6. Basic Bibliography
  • ????????? ?. ????????? ????????????? ?????????? ???? 1., ??., ?????. 1991, 512 ??
  • ??????????????. ??????, ?????? / ??????????? ???????., ????????? ?. ? ???????., ??. ??? ????. 2010, 204 ??:
  • ????????????? ??????????. ?. ?. ???????????/????????? ??????????? ??????. ??: ?????, ??? ????., 2008 ?., 64 ??
  • ???????????? ?. ???????????? ???????????? ?????????? (????????? ??????????????). ???. ???????, ?????, ??? ????., 2014 ?., 332 ??
  • ????????? ? ????????????? ??????????????:/????. ?. ?. ?????????? ??????????????. - ????????? ?. ?. ?????????. - ?????, ??????? ????????????????. - 1977.
  • Немов Р. С. Психология. Книга 3. М.: ВЛАДОС ИМПЭ им. А. С. Грибоедова, 2002.
  • Психология личности. Хрестоматия в 2-х т. / Под. Ред. Д. Я. Райгородского. - Самара: “Бахрар-М”, 2002.
  • roduction to Psychology// .
7. Main sections of the course
1.??????????? ????????????? ??????????????? ? ???????????????: ??????????? ????????????? ????????? ? ????????????: ????????????? ?????????? ? ?????????? ???????:
2.???????? ???????????? ??????? ??????????????, ????????, ????????????: ???????? ????????? ?????? ?????? ?? ??????????:
3.???? ???????????: ???? ??????????????: ????????? ?????? ??????????????:
4.??????????? ????????, ??????????? ?????????????????? ??????????????: ????????????: ???????????? ??????????? ???????????????????? ????????:
5. ?????????? ???????????? ?????????????? ??????????? ??????????????????????:
3-??? ????????? ??? 4-??? ?????????? ????????
?????????? ?????- ????????? 2 ???
???.- 2 ???, ????????? 2 ??? ??????????? ????????
OPTIONAL
1306 /?16
1. Purpose of the Course
· ???????????? ?????????? ???????????? ???????????????????????, ????????????? ? ????????????????????
???????? ????????????? ???????????? ??????????????????? ???????????? ??????
2. Educational Outcomes
?. ???????????? ??????? ? ???????????
1. ??????????, ??????? ???????????? ???????? ?????????????, ???????? ? ????????? ?????,
2. ????????? ???????????? ???????????? ??????????? ???????? ?????????????

?. ????????? ???????????? ???????????????
3. ???????? ? ???????? ???????????? ??????????????????,
4. ??????????? ???????????????? ????????? ? ???????? ???????? ???????????? ?????????? ?????????????,
5. ?????? ??????????? ???????????? ?????????? ? ????????? ?????:

?. ???????????/????????? ???????????????
6. ??????? ??????????? ??????????? ??????????? ???????????? ? ?????????????? ??????????????? ????????????? ?????:
3. Description
· ???????????? ?????????? ???????????? ???????????????????????, ????????????? ? ????????????????????
???????? ????????????? ???????????? ??????????????????? ???????????? ??????
4. Teaching and Learning Styles and Methods
1. ??????????????,
2. ??????? ????????? ?????????:
3. ??????????? ????????
5. Evaluation Methods and Criteria
????????? ????????? ? ???????????
????????? ?????????? ??????? ?????????
????????? ???????????? ????????? ?????????? ? ??????? ????? ????????? ????? ???, ????????????? ????????? 3-???? ????? ?????????? ?????????? ? ??? ?????? ?????????? ????????? ???????? ??????? ????????? ????????? (???????????, ?????????????, ????????????? ?????????? ? ????) ??????????
6. Basic Bibliography
  • ????????? ?. ?????????? ??????????? ?????????? ???????????, ?????, 2007 ?.?
  • ?????????? ??????????????/ ????. ????????? ?., ????????? ?., ??????????? ???????, ?????, 2004?
  • ????????? ????????????? ?? ???? ??????/ ????. ????????, ??????????? ?????????, ?????, 2015?
  • Аминов, И.И. Психология делового общения: Учебник / И.И. Аминов. - М.: Юнити, 2018. - 270 c.
  • Берн, Э. Игры, в которые играют люди. Психология человеческих взаимоотношений. Люди, которые играют в игры, Л.,2012.
  • Волков, Б.С. Психология педагогического общения: Учебник для бакалавров / Б.С. Волков, Н.В. Волкова, Е.А. Орлова. - Люберцы: Юрайт, 2016. - 335 c.
  • Ильин, Е.П. Психология общения и межличностных отношений / Е.П. Ильин. - СПб.: Питер, 2013. - 576 c.
  • змайлова М. А. Деловое общение: Учебное пособие / М. А. Измай- лова. - 4-е изд. - М.: Издательско-торговая корпорация. ?Дашков и К°?, 2011. - 252 c.
  • Райгородский Д.Я. Психология менеджмента. Учебное посбие. Самара: Изд.дом ?Бахран-М?, 2005.-768с.
  • 0.Шеламова, Г.М. Деловая культура и психология общения: Учебник / Г.М. Шеламова. - М.: Academia, 2018. - 256 c.
  • S. Shyam Sundar ., (2015), The Handbook of the Psychology of Communication Technology.
  • The Business Communication Handbook Judith Dwyer 9th Edition//
  • The Handbook of Communication. By Owen Hargie. Skills//
7. Main sections of the course
????? 1? ??????????? ????????????, ???????? ??????????????????????:
?????? ???????? ? ???????????? ???????????? ?????????? ? ??????????????? ?????????? ????????????? ????????????: ????????????? ?????????? ? ??????????? ??????? ? ??????????? ?????????????? ????????????: ?????????? ?? ??????????? ???????????? ???????? ??????????????????????, ???????????????????, ????????????:
????? 2? ??????????? ????????? ???????????? ????????????:
?????? ???????? ? ?????????? ??????????? ???????? ??????????????????? ?? ????????????: ?????????? ?? ???????? ???????????? ? ????? ?????????, ????????????? ?????????: ?????????? ? ???????????? ??????????? ?????????? ?? ???????????? ????????????:
????? 3? ????????????? ?????????? ?????? ???????????:
?????? ???????? ? ?????????? ? ?????????????? ?????????? ???????? ???????????? ???????? ??????????????????? ?????: ?????? ? ?? ?????? ???????? ????????????, ???????? ????, ???????? ?????, ????????????????? ?????? ??????????????????????:
????? 4? ??????? ???????????? ?????????????????????? ? ??????????, ?????????????? ????????? ??????
?????? ???????? ? ??????? ???????????? ??????????, ???????????? ????? ????????????????
3-?? ????????? ??? 4-?? ?????????? ????????
?????????? ?????- ????????? 2 ???
???.-2 ???, ????????? 2 ??? ??????????? ????????
OPTIONAL
2101/?16
1. Purpose of the Course
· ??? ????????? ??????????? ?????????? ?????, ??? ???????? ????????????? ?????????, ????????? ? ?????????, ????????????? ? ?????? ???????? ??????????????? ?????, ?????????? ??????????? ?????????????? ??????? ???????????? ?? ???????????????, ????????? ?????????? ??????? ?????????, ????? ??????????? ?????????????, ???????????????????? ?? ???????????????????????,
· ??? ????????? ?????????? ????? ???????? ???????????????, ??????????????????, ?????????????? ?????????????????????? ? ?????????? ??????????,
???????????? ??????????? ?????? ??? ???????? ??????? ???????? ????????????? ???????? ????????????? ? ?????????????? ???????????????????????:
2. Educational Outcomes
?. ???????????? ??????? ? ???????????
1. ????????????? ????? ?????????? ? ???????????, ???? ?? ???? ????????????? ???,
2. ??????????? ??????????? ???????? ? ????? ???????? ????? ????????? ?? ????????? ????????????, ??????? ? ????????????? ???????? ??????????, ??????? ?????????????????????? ?? ???????? ?????, ?? ????????? ???????? ?????????????????????? ? ????????????,

?. ????????? ???????????? ???????????????
3. ??????????? ???????? ?? ???????????? ??????????????,
4. ???????????? ????? ???????? ? ????????? ?????????????, ??????????? ? ??????????? ?????? ???????,

?. ???????????/????????? ???????????????
5. ?????????? ??????????? ???????? ???????????????, ????????????? ? ?????????????????? ??????????????????????, ????????? ???? ?????? ??????????? ????????????:
3. Description
· ??? ????????? ??????????? ?????????? ?????, ??? ???????? ????????????? ?????????, ????????? ? ?????????, ????????????? ? ?????? ???????? ??????????????? ?????, ?????????? ??????????? ?????????????? ??????? ???????????? ?? ???????????????, ????????? ?????????? ??????? ?????????, ????? ??????????? ?????????????, ???????????????????? ?? ???????????????????????,
· ??? ????????? ?????????? ????? ???????? ???????????????, ??????????????????, ?????????????? ?????????????????????? ? ?????????? ??????????,
???????????? ??????????? ?????? ??? ???????? ??????? ???????? ????????????? ???????? ????????????? ? ?????????????? ???????????????????????:
4. Teaching and Learning Styles and Methods
1.??????????? ????????? ???????? ??????? ? ??????????????, ??? ? ??????? ????????? ???????????? ???????? ??????????:
2. ??????????? ????????? ?????????? ?? ?????????????????? ? ?????????? ??????? ??????????????:
???????????? ????????????? ? ???????????? ????????? ? ??????????? ????????:
5. Evaluation Methods and Criteria
????????. ????????? ?????????? ? ??????? ????? ??????????? ??????? ??????????? ????? ???:
6. Basic Bibliography
  • ???????????????: ??????????? ???????, ??? 1, ?????????????? ????????????, ?????, ??? ????., 2020, (???????.` ????????? ???. ?????????, ????????? ????????????, ????? ?????????, ????? ????????):
  • ?????????? ?????????? ???????????????, ?????, ????. ??????????., 2002?
  • История религии (учеб. Под общ. Ред. И. Н. Яблокова) Т. 1-2. М., 2007.
  • Лебедев В. Ю. Религиоведение; учебник для бакалавров, М. 2013.
  • Основы религиоведения (учеб. Под общ. Ред. И. Н. Яблокова) М., 2005.
  • Религиоведение, (учеб. Под общ. Ред. М. М. Шахнович), СПб, 2012.
7. Main sections of the course
???????????????? ???? ??????????: ??????????????? ??????????? ????????? ???????????, ????????????????, ???????? ????????????????? ? ????????????? ???????????? ?????? ??????????????, ???????????, ??????????????, ????? ????????????????? ? ?????????? ????? ????????????? ??????????????? ????? ??? ?????: ????????????? (???) ????????????????. ?????????????? ? ????: ?????????????????? ? ???????????????? ????? ??????????????: ??????? ? ????????????? ???????? ?????????? ?? ??????? ??????????: ??????????? ??????? ???????: ????? ??????????? ?????????: ?????????? ??????? ???????? (??????????, ???????, ???????), ????????? ? ????????? ??????? ????????, (???????????????, ???????????????????, ?????), ???????????????? ?????????? ? ???????????? ???????????????????????????? ????????????????? ?????????? ? ??????????, ????????????? ? ?????????????????? ??????????????????????, ???????? ???????????????: ?????????????? ?????????? ? ??????????: ?????????????? ????????????? ? ?????????????????? ??????????????????????: ???????????????. ????????????????. ???????????????????, ????????? ????????? ? ?? ????????? ??????????????????, ????? ???????? ????????????? ? ?????????????????? ??????????????????????: ?????? ?????????? ? ??????????, ????????????? ? ?????????????????? ??????????????????????, ???????? ???????????????: ????????? ?????????????????? ???????? ????????? ????????? ??????????:
4-??? ????????? ????????
?????????? ?????-????????? 4 ???
2 ??? ??????????????, 2 ??? ?????????, ????????? 8 ??? ??????????? ????????
OPTIONAL
0105/?44
1. Purpose of the Course
·??????????? ????????? ?????????????? ???????? ?????????,
·?????????? ?????? ??????? ?????????????? ????????? ????????? ???????? ???????? ?????,
. ??? ?????????? ????????? ?????????????? ?????? ??????????:
2. Educational Outcomes
?. ???????????? ??????? ? ???????????
1. ???????? ????????? ??????? ??????????? ????????? ???????????? ????????,
2. ???????? ?????? ???????????? ???????? ? ???????? ????? ?????? ???????????,
3. ??????? ???? ? ???? ???????????? ?????????,

?. ????????? ???????????? ???????????????
4. ?????????? ???????????? ????????????? ?????????? ????????? ???????? ?????,
5. ??????????? ???? ?????????? ??????? ???????????? ??????????????,
6. ??? ???????????? ????????? ??????????, ????????? ??????????? ?????????????? ?????????, ?????? ?????? ?????????????? ?????????????,
?. ???????????/????????? ???????????????
7. ??????????? ?????????? ???????????? ?????????? ?????????????? ??????? ??????? ???????????:
3. Description
·??????????? ????????? ?????????????? ???????? ?????????,
·?????????? ?????? ??????? ?????????????? ????????? ????????? ???????? ???????? ?????,
. ??? ?????????? ????????? ?????????????? ?????? ??????????:
4. Teaching and Learning Styles and Methods
1. ?????????????????,
2. ????????? ?????????????:
5. Evaluation Methods and Criteria
????????? ?????????? ? 20 ?????? ???????????? ???????.
· ??????? ??????????? ? ??????????? ????????? ?????? ????????????? 8 ?????? ???????????? ??????? (40%),
· ??????? ???????????? 3 ?????? ???????????? ??????? (15%),
. ????????? ??????????? ??????? ?? 9 ?????? ???????????? ??????? (45%):
6. Basic Bibliography
  • ????????? ?. ?., “??????? ? ????????? ?????????????? ??????????’’, ???1, “??????????’’ ????., ?????, 2015:
  • Ивченко Г. И., Медведев Ю. И., “Математическая статистика’’, кн. дом “ Либроком’’, М., 2014.
  • Gibbons J. D., Chakraborti S., “Nonparametric Statistical Inference’’, Marcel Dekker inc., 2003.
  • Montgomery D. C., Runger G. C., Applied Statistics and Probability for Engineers, 6-th edit., J. Wiley and Sons, 2013.
  • Jay Devore “Probability and Statistics for Engineering and the Sciences ”, California, CENGADE, 2016.
7. Main sections of the course
??????????? ???????????????: ??????? ?????????????` ??????????????, ????????? ????????: ???????????? ?????????????, ?????????? ???????? ????????? ???????????, ?????? - ??????? ????????? ? ??? ????????????????: ?? ???????????? ????????` ??????????????, ????????????? ? ??????????? ???????????:
3-??? ?????????? ??? 4-??? ????????? ????????
?????????? ?????- ????????? 2 ???
???.- 2 ??? , ????????? 2 ??? ??????????? ????????
OPTIONAL
1901/?16
1. Purpose of the Course
?????????? ??????????? ?????? ?????? ????????? ????????-??????????? ??????????? ???????????, ???????? ?????? ???????? ??????????? ???????????? ????????? ?????????????, ?????? ??? ???????? ???????? ??????????? ?? ?????????
2. Educational Outcomes
?. ???????????? ??????? ? ???????????
1. ?????????? ???????????? ???????? ?????????????????, ????????? ???? ?????, ???????? ??????????? ????????????, ????????? ????????? ???????? ????????, ????? ??????????? ???????? ???????????,
2. ???????? ???????????????, ???????? ? ????????? ????????, ???????? ?????????????????? ?????????????????,

?. ????????? ???????????? ???????????????
3.????????? ? ?????????? ???????????? ???????? ?????????????????, ????????? ???????????, ????? ????????????????????,
4. ??????????? ???????? ? ??????? ???????????? ????????????? ?????????????????
5.???????? ???????? ??????????? ? ???????? ????????:

?. ???????????/????????? ???????????????
6.??????????? ????????????? ???????? ??????????? ???????????,
7.?????? ???????? ?????????????? ????????? ???????????? (???????? ??????????, ??????????, ????????),
8.????????? ?????????????? ??????????, ?????????? ????????????, ?????? ?????? ? ???????? ????????? ?????????, ??????? ?????????????? ?????? ?????????????, ????????????????? ????????
3. Description
?????????? ??????????? ?????? ?????? ????????? ????????-??????????? ??????????? ???????????, ???????? ?????? ???????? ??????????? ???????????? ????????? ?????????????, ?????? ??? ???????? ???????? ??????????? ?? ?????????
4. Teaching and Learning Styles and Methods
1. ??????????? ????????,
2. ?????? ? ??????? ????????/ ???????,
3. ???????????? ????????? ?????????:
5. Evaluation Methods and Criteria
1.????????.

????????? ?????????? ? ??????? ??? ??????: ?????? ? ????????????? 4 ????` ??????? ?????????? ??????????:
6. Basic Bibliography
  • ?? ????????????????, 2015 ?. ?????????????:
  • ?? ????????????, ???????, ?????????, ????????????, ??????? ? ???????????? ????????????? ???????????:
  • ?.?. ????????? ''????????? ? ????????? ?????????? -1'', ?????????????????, ?????, 2016:
  • ?.?. ????????? ????????? ? ????????? ??????????-2, ?????????????????, ?????, 2016:
7. Main sections of the course
?????????????? ? ??????????: ????????: ???????? ??????????? ???????????? ? ????????? ?????????????? ????????? ?????: ????????? ?????????: ???????????????, ???????? ????????, ????????????: ??????????? ??? ??????? ???????? ????????????: ????????????? ????????: ??????? ???????????? ? ??????? ????????: ???????????? ????????: ???????????? ????????: ????????? ????????: ??????????? ????????: ???????
????????:
1-?? ????????? ???????? ??? 2-??
?????????? ?????- ????????? 2 ???
2 ??? ??????????????, ????????? 2 ??? ??????????? ????????
OPTIONAL
1005/?16
1. Purpose of the Course
·????????? ?????????????? ??????? ? ????????? ??????????????????????, ?????? ??? ?????????????? ????????? ?????????????? ?????????? ??????? ? ???????????,
· ?????????? ?????????????? ????-????????? ???????, ?????? ??? ?????????????? ???????????? ????-????????? ????????? ??????????????,
· ???????? ?????? ???????? ??????? ???????????????:
2. Educational Outcomes
?. ???????????? ??????? ? ???????????
1.???????? ??????????????? ?????????????? ????????? ? ???????? ?????????????????, ????????????, ?????????????? ???????? ????????? ??????????????????????,
2.??????????? ?????????????? ????-????????? ? ????-????????? ???????,
3. ?????????? ?????????????? ???????????? ?????, ?????????? ???????????? ? ????????????:

?. ????????? ???????????? ???????????????
4.????????? ? ?????????? ?????????????? ??????????? ?? ??????, ????? ??????? ????????? ???????? ????????????,
5.???????? ??-??? ???????? ?????????, ??????????? ?????????????? ????????? ???????????????????, ????????? ?? ???????, ?????????? ?????????????? ????????? ??????????????????? ?? ????????????,

?. ???????????/????????? ???????????????
6. ?????? ????????????-??????????? ????????? ????????????? ???????????? ??????????, ???????????? ???????????, ??????? ?????????, ?????????????????, ?????????? ???????????????????? ??????? ??????????, ??????? ????????? ??????????????????
3. Description
·????????? ?????????????? ??????? ? ????????? ??????????????????????, ?????? ??? ?????????????? ????????? ?????????????? ?????????? ??????? ? ???????????,
· ?????????? ?????????????? ????-????????? ???????, ?????? ??? ?????????????? ???????????? ????-????????? ????????? ??????????????,
· ???????? ?????? ???????? ??????? ???????????????:
4. Teaching and Learning Styles and Methods
1.?????????????????
2.??????????? ????????? ????? ????????? ?????? ????????? ?????? ??????????? ?????,
- ????????? ? ??????? ????????????,
- ???????????? ????????? ????????
5. Evaluation Methods and Criteria
????????. ??? ?????????? ? ??????? ????????? ???????? ????????? ?????????:
6. Basic Bibliography
  • ??????? ?., ??????? ??????????, ??????????? ???????, ?????, 2017 ?.?
  • Бекетова О.Н, В.И.Найденков, Бизнес-план, Уч.пособие для вузов, Теория и практика, М., 2009, 288с.
  • Буров В.Ю. “Основы предпринимательства” Уч.пособие Чита, 2011. - 441 с.
  • Питер Ф.Друкер, Бизнес и инновации, пер. с англ.-М: “И.Д.Вильямс”, 2009, 432с.
  • Business Management, L. loykie, M. Mushena, Robert A. Pierce, 2022
  • Principles of Business Management, Dr. S. C., Saksena, 2020.
7. Main sections of the course
???? 1. ?????????????? ????????? ? ????????? ???????? ????????????
???? 2. ???????????? ??????????? ???????? ??????????. ???????????? ??????????
???? 3. ??????????????? ?????????????? ????????????? ??????????? ? ???????????
???? 4. ????????? ????????????????? ???????????????? ? ???????????? ??????????
???? 5. ??????????????? ?????????????? ????????? ? ????? ?????????????:
???? 6. ?????????????? ????? ? ?????????
???? 7. ??????? ???????????? ?????????? ? ?????? ????????????????:
???? 8. ??????? ???????????? ???????????? ? ???????????? ???????????. ?????????? ???????? ??????????????????????:
???? 9. ??????? ???????????? ????? ??????? ? ???????????? ?????????? ????????? ????????????? ????????? (???????) ???????????? ?????????????:
???? 10. ??????????????? ?????????????? ?????????????. ?????? ????
???? 11. ??????? ???????????? ????????????????? ? ????????:
3-?? ??? 4-?? ????????
2 ?????????? ?????- ?????????.
???. – 2 ???
OPTIONAL
0604/?16
1. Purpose of the Course
??????????? ??? ???????? ?????????????? ??????????? ????????????? ????????, ??????? ? ??????????????, ????????? ???????????????, ?????? ????????????? ???? ?????? ???????????, ??????????? ??? ??????????? ??????????? ??????????:
2. Educational Outcomes
?. ???????????? ??????? ? ???????????
1.??????????? ??????????? ???????????? ??????????? ???????? ?????????????????????,
2.?????????? ???????????? ?????????????? ??????????? ??????????? ? ????????????? ????????? ???,

?. ????????? ???????????? ???????????????.
3. ??????? ??????????? ???????????? ??????????? ?????? ????????,

?. ???????????/????????? ??????????????? (??? ???????? ???).
4. ???????? ?????????? ??????????? ?????????? ?????????????? ?????? ???:
3. Description
??????????? ??? ???????? ?????????????? ??????????? ????????????? ????????, ??????? ? ??????????????, ????????? ???????????????, ?????? ????????????? ???? ?????? ???????????, ??????????? ??? ??????????? ??????????? ??????????:
4. Teaching and Learning Styles and Methods
1.?????????????????,
2. ??????????, ????????????:
5. Evaluation Methods and Criteria
????????? ?????????? ? ??????? ? ??????? ? ????????? ????????? ????? ?????? ??????????? ???????????? ???????????? ? ??????? ??????? ???? ????? ???????? ???: ????????? ????????? ?????? ? ????????????? 4 ????` ??????? ?????????? ??????????:
6. Basic Bibliography
  • M.D. Goldfein , A.V. Ivanov , Modern Concepts of Natural Science (Science, Evolution and Creationism), Nova Science Publishers , 2013, 247 p.
  • А.П. Садохин. Концепции современного естествознания. 445с. Москва, 2006.
  • Концепции современного естествознания. Учебник для вузов, Под редакцией Л. Михайлова, 335с. Москва, 2008.
  • А.А. Горелов, Концепции современного естествознания: учеб. посо?бие для студ. высш. учеб. заведений. 512с. Москва, 2010.
7. Main sections of the course
???? 1. ?????????????? ? ????????????? ????????? ???????: ??????? ?????????? ???????????????? ? ??????? ????????????????:
???? 2. ???????????? ???????????????????: ???????? ? ???????????? ??????????? ??????????????????????? ? ????? ????????????? ??????????? ?????????: ?????????????????: ?????????? ???????: ???????? ????????? ????? ? ???????? ????????????: ?????????? ?????????? ????????????? ?????????? ??? ? ??????? ????????????????????:
???? 3. ???????????? ???????????????????: ????????? ??????? ????????? ?????????? ? ?????????: ????????? ???????????? ??????????: ???????????, ??????????????, ???????????, ???????????? ? ????????? ???????????????? ??????? ? ??????????? ???????????????????:
???? 4. ?????????????? ?????????? ??????? ??????: ??????? ??????????: ????????: ??????? ???????? ????? ????????? ?????????????: ?????????? ???????????? ???????: ?????????? ??????? ??????????? ???????????: ???????????????? ???????????: ???-? ????? ?????????? ???????????? ??????? ????:
???? 5. ??????????? ???????????????????: ??????????? ????????? ? ???????? ???????????: 1.
3-??? ????????? ????????
?????????? ?????- ????????? 2 ???
???.-2. , ????????? 2 ??? ??????????? ????????
OPTIONAL
1302/?16
1. Purpose of the Course
·????????? ??????????? ????????????? ??????????????? ????????? ??????????????,
·?????????? ????????? ??????????? ??????? ??????????? ??????????? ? ????? ???????????,
. ?????????? ????, ????????, ?????? ??????, ?????, ????????? ????????? ?????????????:
2. Educational Outcomes
?. ???????????? ??????? ? ???????????
1.??????????? ????????? ?????????????????? ??????????? ? ???????????????,
2.????????? ???? ????????????, ???????? ??????????? ? ???? ????????????????? ???? ???????????????,
3.????????? ????????? ???????????? ??????? ? ??????????? ??????????????, ?????? ??????? ? ????????? ??????? ??????????? ????????????:

?. ????????? ???????????? ???????????????
4.??????????? ????????? ?????????? ??????????????? ??????? ?????????? ? ????????????, ?????? ?????? ????????????? ????????? ???????????? ??????????? ??????????? ?????????, ???????? ??????????????? ???? ??????????? ?????? ???????????? ?? ????????????? ???????:

?. ???????????/????????? ???????????????
5. ????????? ???? ????????????? ??????????????? ????????? ??????????????:
3. Description
·????????? ??????????? ????????????? ??????????????? ????????? ??????????????,
·?????????? ????????? ??????????? ??????? ??????????? ??????????? ? ????? ???????????,
. ?????????? ????, ????????, ?????? ??????, ?????, ????????? ????????? ?????????????:
4. Teaching and Learning Styles and Methods
1. ?????????????????, ??????? ????????????? ? ????????????,
2. ???????? ??????????? ? ????????????? ??????????? ??????????????,
3. ?????? ???????????? ????????? ??????????????
5. Evaluation Methods and Criteria
????????? ????????? ? ??????????:
????????? ?????????? ??????? ??????? ??? ?????????? ?????????,
????????? ???????????? ????? ?????? ????????? ? ??????????????? ???????,
???????????? ????????????????? ? ??????????????????, ??????? ?????????? ??????? ???????????, ??????????? ????????????
6. Basic Bibliography
  • Апресян Ю. Этика. М., 2004.
  • Бодрийяр Ж. Забыть Фуко. СПБ, 2011.
  • Матвеев П. Религиозная этика. М., 2014.
  • Фромм Э. Искусство любить. М., 2008.
  • Щвейцер А. Культура и этика. М., 2010.
7. Main sections of the course
1.??????????????? ????????? ? ???????????:
2. ????????? ?????????????????? ?????????
3.???????? ?????:
4.????????:
5.????????? ?????:
6.???? ??????????:
?????? ??????:

Professional educational component

Chair code Name of the course Credits
4th term
4 hours/week
Lect. 3 hours/week, pract. work 3 hours/week, individual work – 12 hours/week
MANDATORY
0112/?30
1. Purpose of the Course
introduce the main properties of arbitrary numerical series, functional sequences and series, introduce Taylor and Fourier series, parameter-dependent integrals, study curve and surface integrals.
2. Educational Outcomes
?. ???????????? ??????? ? ???????????
1. to determine the convergence of functional series and infinite integrals depending on the parameter, to present their properties,
2. define curve and surface integrals, present their calculation formulas,
?. ????????? ???????????? ???????????????
3. in simple cases, analyze the function of Taylor and Fourier series,
4. calculate curve and surface integrals.

3. Description
introduce the main properties of arbitrary numerical series, functional sequences and series, introduce Taylor and Fourier series, parameter-dependent integrals, study curve and surface integrals.
4. Teaching and Learning Styles and Methods
● lectures,
● practice work
● individual work
5. Evaluation Methods and Criteria
The course is valued at a maximum of 20 points.
● 2 midterm exams with a total value 8 points (40%),
● tests - maximum 3 points (15%),
● Final exam - maximum 9 points (45%).
6. Basic Bibliography
  • ?. ?. ????????, ????????????? ??????, I-II ??????
  • Г. М. Фихтенгольц, Курс дифференциального и интегрального исчисления, том ??, ???.
  • ?.?. ???????? ? ???????? - ????????????? ??????? ?????????, II ????
7. Main sections of the course
Arbitrary numerical series, functional sequences and series, parameter dependent integrals,
Fourier series, curve and surface integrals.
8nd term
6 hours/week
Lect. 3 hours/week, pract. work 3 hours/week, individual work – 12 hours/week
MANDATORY
0112/?41
1. Purpose of the Course
to acquaint the student with equations with partial derivatives frequently found in physical processes,
introduce the student to ways of solving problems with the wave equation.
2. Educational Outcomes
?. ???????????? ??????? ? ???????????
1. to derive Kirchhoff's formula for the wave equation,
2. to present the existence and uniqueness of the solution to the Gursa problem,
?. ????????? ???????????? ???????????????
3. classify equations with partial derivatives of the second order,
4. to use the Fourier method to solve mixed problems.
3. Description
to acquaint the student with equations with partial derivatives frequently found in physical processes,
introduce the student to ways of solving problems with the wave equation.
4. Teaching and Learning Styles and Methods
● lectures,
● practice work,
● individual work.
5. Evaluation Methods and Criteria
The course is valued at a maximum of 20 points.
tests - maximum 8 points (40%),
participation - 3 points (15%),
Final oral exam - maximum 9 points (45%).
6. Basic Bibliography
  • Evans L.C., Partial differential equations, 1997.
  • Тихонов А.Н. Самарский А.А., Уравнения математической физики, М., МГУ, 2004.
  • Владимиров В.С. , Жаринов В.В., Уравнения математической физики, М., 2004.
  • Владимиров В.С. Сборник задач по уравнениям математической физики, М., 2003.
  • Михлин С.Г., Курс математической физики, М., Лань, 2002.
  • Бицадзе А.В., Калиниченко Д.Ф., Сборник задач по уравнениям математической физики, М., Наука, 1985.
7. Main sections of the course
Classification of linear differential equations with second-order partial derivatives. A necessary condition for the correctness of the Cauchy problem in the general case. Characteristic surfaces. Cauchy-Kovalevskaya theorems. Solving the Cauchy problem for the vibration equation of a string. Dalembert's formula. Adamar's example of an incorrect problem. Existence and uniqueness of a solution to the Cauchy problem for the wave equation. Kirchhoff's formula. Method of landing. Existence and uniqueness of the solution of the Gursa problem for general second-order hyperbolic equations. solution of mixed problem for string vibration equation by Fourier method.
4th term
4 hours/week
Lect. 2 hours/week, pract. work 2 hours/week, individual work- 8 hours/week
MANDATORY
0105/?40
1. Purpose of the Course
familiarize with the basic methods of mathematical statistics,
teach students to apply the methods of mathematical statistics to solve practical problems,
give students ideas from different sections of mathematical statistics.
2. Educational Outcomes
?. ???????????? ??????? ? ???????????
1. receiving the necessary theoretical knowledge to formulate statistical problems,
2. consider different statistical models and estimate their unknown parameters, check simple and complex statistical hypotheses,
?. ????????? ???????????? ???????????????
3. use the appropriate criterions to solve the proposed problems;
4. analyzing the available data to make statistical conclusions,
5. with the help of a large amount of data, applying the methods of mathematical statistics, obtain estimates of various characteristics,
?. ???????????/????????? ???????????????
6. analyzing the proposed statistical data, creatively obtained knowledge.
3. Description
familiarize with the basic methods of mathematical statistics,
teach students to apply the methods of mathematical statistics to solve practical problems,
give students ideas from different sections of mathematical statistics.
4. Teaching and Learning Styles and Methods
● lectures,
● practice work
● individual work
5. Evaluation Methods and Criteria
The course is valued at a maximum of 20 points.
● 2 midterm exams with a total value 8 points (40%),
● tests - maximum 3 points (15%)
● Final exam - maximum 9 points (45%)
6. Basic Bibliography
  • Боровков А. А., Математическая статистика, СПБ, Лань, 2010.
  • Ивченко Г. И., Медведев Ю. И., Математическая статистика, книж. дом Либроком, Москва, 2014.
  • ????????? ?. ?., ???????? ? ????????? ?????????????? ???????????, ??? ??????, ?????????? ????., ?????, 2015:
  • ????????? ?. ?., “?????????????? ????????? ?????????’’, ??? ????., ?????, 2017:
  • Gibbons J. D., Chakraborti S., Nonparametric statistical inference, Marcel Dekker inc., 2003.
7. Main sections of the course
Sampling distribution and distribution function. Sample specifications. Some classes of parametric distributions, Point estimates. Interval grades. Statistical hypothesis testing. Indicators of agreement, independence and homogeneity.
7th term
4 hours/week
Lect. 2 hours/week, pract. 2 hours/week, individual work – 8 hours/week
MANDATORY
0112/?44
1. Purpose of the Course
to teach the foundations of the mathematical theory of optimization and the main ways of solving extreme problems.
2. Educational Outcomes
?. ???????????? ??????? ? ???????????
1. theoretically justify the main methods of solving extreme problems,
?. ????????? ???????????? ???????????????
2. make mathematical models of extreme problems encountered in practice,
3. choose the appropriate optimization method for solving the problem, depending on the mathematical setting of the problem,
?. ???????????/????????? ???????????????
4. use professional literature and other information sources.
3. Description
to teach the foundations of the mathematical theory of optimization and the main ways of solving extreme problems.
4. Teaching and Learning Styles and Methods
1. lectures,
2. individual work,
3. practical exercises.
5. Evaluation Methods and Criteria
The course is valued at a maximum of 20 points.
● Midterm exams and research work a total value 8 points (40%),
● Tests - maximum 3 points (15%),
● Participation- 1 point (5%),
Final oral exam maximum 8 points (40%).
6. Basic Bibliography
  • Карманов В.Г. Математическое программирование. М. Физматлит. 2004.
  • Васильев Ф.П. Численные методы решения экстремальных задач. М. Наук. 1988.
  • Алексеев В.М. и др. Сборник задач по оптимизации. М. Физматлит. 2005.
  • Ванько В.И., Вариационное исчисление и оптимальное управление. Изд. МГТУ. 2003.
  • ????????? ?.?., ???????? ?.?. ????????? ????? ? ??????? ??????????, ???, 2008.
7. Main sections of the course
Lagrange's principle for conditional extremum. Theorem on the existence of a saddle point. Basic and dual problems of linear programming. Kuhn Tucker and duality theorems. Theorems on nonuniqueness and corner point optimality in basic linear programming. Basic problems and lemmas of calculus of variations. Simple and generalized problems of calculus of variations. Boltz and isoperimetric problems of calculus of variations. The calculus of variations problem with fixed time and right free endpoint. Mathematical formulation and classification of optimal management problems. Pontryagin's maximum principle for optimal management
in problems. The simplest problem of optimality by speed.
6th term
4 hours/week
Lect. 2 hours/week, pract. work 2 hours/week, individual work-4 hours/week
MANDATORY
0112/?39
1. Purpose of the Course
introduce the main properties of Banach, Hilbert spaces and the functionals defined on them.
introduce the basics of operator theory.
2. Educational Outcomes
?. ???????????? ??????? ? ???????????
1. to use the principles of uniformly boundedness and open mappings,
2. to illustrate the Hahn-Banach theorem and use the separability properties of convex sets,
3. to describe conjugate spaces of certain Banach spaces,
?. ????????? ???????????? ???????????????
4. to apply properties of compact and self-conjugate operators when studying integral and differential equations,
5. to apply the acquired knowledge in the problems of the theory of functions.
3. Description
introduce the main properties of Banach, Hilbert spaces and the functionals defined on them.
introduce the basics of operator theory.
4. Teaching and Learning Styles and Methods
● lectures,
● practice work
● individual work
5. Evaluation Methods and Criteria
The course is valued at a maximum of 20 points.
● 2 midterm exams with a total value 8 points (40%),
● tests - maximum 3 points (15%)
● participation 1 point (5%)
● Final exam - maximum 8 points (40%)
6. Basic Bibliography
  • А. Н. Колмогоров, С. В. Фомин ,, Элементы теории функций и функционального анализа,, М. , Физматлит 2002.
  • Л. А. Люстерник, В. И. Соболев ,, Краткий курс функционального анализ,, М., Висшая школа , 1982.
  • В.А Треногин ,, Функциональный анализ,, М. , Физматлит 2002.
  • У. Рудин ,, Функциональный анализ,, М. , Лань 2005.
  • В. М. Кадец ,, Курс функционального анализа,, ХНУ 2006.
  • В.А Треногин, Б.М. Писаревский, Т.С. Соболева ,, Задачи и упражнения по Функциональному анализу,,М. Наука 1984.
7. Main sections of the course
Linear and normalized spaces, Minkowski functional, Hahn-Banach theorem. Metric space, completeness, fixed point principle, categories, compactness. Hilbert space, Bessel's inequality, Fourier series. Principle of open mappings, closed graph theorem. Point (strong) convergence, uniformly boundedness principle. Conjugate space, conjugate operator, weak convergence, weak compactness. Banach algebras. Spectrum of the linear operator. Compact operators, Fredholm theorems, spectrum description. Self-conjugate compact operators, Hilbert-Schmidt theorem. Fredholm integral equation of the second kind, Fredholm theorems. Non-negative operators, spectrum analysis of self-conjugate operator.
3rd term
4 hours/week
Lect. 2 hours/week, pract. work 2 hours/week, individual work - 8 hours/week
MANDATORY
0105/?38
1. Purpose of the Course
teach students to apply the methods of probability theory to solve practical problems,
develop a probabilistic mindset that will help students construct probabilistic models describing random phenomena.
2. Educational Outcomes
?. ???????????? ??????? ? ???????????
1. having received the necessary theoretical knowledge to apply different types of probabilistic models,
2. introduce the use of different types of distributions in the construction of probabilistic models,
?. ????????? ???????????? ???????????????
3. use the suggested problems to solve the relevant problems,
4. analyzing available data to use the law of large numbers;
5. effectively use the central limit theorem, Markov chains in applied problems,
?. ???????????/????????? ???????????????
6. analyzing the proposed problem to creatively apply probabilistic methods.
3. Description
teach students to apply the methods of probability theory to solve practical problems,
develop a probabilistic mindset that will help students construct probabilistic models describing random phenomena.
4. Teaching and Learning Styles and Methods
● lectures,
● practice work
● individual work
5. Evaluation Methods and Criteria
The course is valued at a maximum of 20 points.
● 2 midterm exams with a total value 8 points (40%),
● tests - maximum 3 points (15%),
● Final exam - maximum 9 points (45%).
6. Basic Bibliography
  • Ширяев А.Н., Вероятность, М., ''Наука'', 2004.
  • ????????? ?. ?., ????????? ?. ?., ???????????????????? ????????? ?????????, ???- ? ????., 2016.
  • Sheldon M. Ross, A first course in Probability, fifth edition, Prentice Hall, New Jersey, 1998.
  • Dimitri P. Bertsekas and John N. Tsitsiklis, Introduction to Probability, 2nd edition, Athena Scientific, Belmont, Massachusetts, 2008.
  • Sheldon Ross, Introduction to Probability Models, Academic Press, New York, 9th ed., 2007.
  • R. Durret, Probability theory and examples. 4th edition, Cambridge University Press, 2010.
7. Main sections of the course
Borel-Cantelli lemmas. Continuous random variables and distribution functions. Numerical characteristics of continuous random variables. Joint distributions of random variables. Characteristic function of a random variable. Types of convergence of sequences of random variables. Central limit theorems. Conditional distributions. Conventional math. Expectations.
6th term
4 hours/week
Lect. 2 hours/week, pract. work 2 hours/week, individual work - 8 hours/week
MANDATORY
0112/?37
1. Purpose of the Course
present numerical methods in different problems of mathematics and computer science.
2. Educational Outcomes
?. ???????????? ??????? ? ???????????
1. theoretically to justify the considered approximation methods,
?. ????????? ???????????? ???????????????
2. to use approximation methods for solving applied problems.

3. Description
present numerical methods in different problems of mathematics and computer science.
4. Teaching and Learning Styles and Methods
● lectures,
● practice work
● individual work
5. Evaluation Methods and Criteria
The course is valued at a maximum of 20 points.
● 2 midterm exams with a total value 8 points (40%),
● tests - maximum 3 points (15%),
● participation 1 point (5%),
● Final exam - maximum 8 points (40%).
6. Basic Bibliography
  • Ward Chency, David Kincaid, numerical Mathematics and Computing, On Edition, engage Learning, 2007.
  • Alex Gezerlis. Numerical Methods in Physics with Python, Cambridge University Press, 2020.
7. Main sections of the course
Interpolation problem, interpolation polynomials, interpolation minimization. Method of the least squares. Convergence of the interpolation process. Quadratic formulas, error estimates. Best approximation in normed spaces. The uniqueness of the best approximation element. Simple approximate methods for solving a system of linear equations. . The numerical method of solving nonlinear equations. Analytical methods of optimization problems in one-dimensional case.
5th term
4 hours/week
Lect. 2 hours/week, pract. work 2 hours/week, individual work - 8 hours/week
MANDATORY
0105/?35
1. Purpose of the Course
get acquainted with the basic methods of probability theory,
develop probabilistic thinking to help students build probabilistic models describing random phenomena.
2. Educational Outcomes
?. ???????????? ??????? ? ???????????
1. having received the necessary theoretical knowledge to apply different types of probabilistic models,
2. apply different types of distributions when building probabilistic models,
?. ????????? ???????????? ???????????????
3. use appropriate probabilistic models to solve the proposed problems,
4. by analyzing the available data, construct a representation of the distribution function;
5. effectively use the attachment-extraction principe.
3. Description
get acquainted with the basic methods of probability theory,
develop probabilistic thinking to help students build probabilistic models describing random phenomena.
4. Teaching and Learning Styles and Methods
● lectures,
● practice work
● individual work
5. Evaluation Methods and Criteria
The course is valued at a maximum of 20 points.
● 2 midterm exams with a total value 8 points (40%),
● tests - maximum 3 points (15%),
● Final exam - maximum 9 points (45%).
6. Basic Bibliography
  • Ширяев А.Н., Вероятность, М., ''Наука'', 2004.
  • ????????? ?., ????????? ?. , ???????????????????? ????????? ?????????, ???, 2016?
  • Sheldon M. Ross, A first course in Probability, fifth edition, Prentice Hall, New Jersey, 1998.
  • Dimitri P. Bertsekas and John N. Tsitsiklis, Introduction to Probability, 2nd edition, Athena Scientific, Belmont, Massachusetts, 2008.
  • Sheldon Ross, Introduction to Probability Models, Academic Press, New York, 9th ed., 2007.
  • R. Durret, Probability theory and examples. 4th edition, Cambridge University Press, 2010.
7. Main sections of the course
Axiomatic definition of probability. Properties of probability. Independence of events. Conditional probability. Discrete random variables and distribution functions. Numerical characteristics of discrete random variables. Chebyshev's inequality and the law of large numbers.
5th term
4 hours/week
Lect. 2 hours/week, pract. work 2 hours/week, individual work – 8 hours/week
MANDATORY
0112/?34
1. Purpose of the Course
introduce the questions of the theory of complex variable and analytic functions, give an idea about the Riemann sphere,
present Cauchy's integral theorems and formulas, analyze analytical functions with Taylor's series,
to give an idea about multivalued analytic functions and Riemann surfaces, introduce the theory and applications of residues.
2. Educational Outcomes
?. ???????????? ??????? ? ???????????
1. to formulate and verify the properties of analytic functions,
2. describe fractional functions, list their circular properties,
3. to classify multivalued analytic functions,
?. ????????? ???????????? ???????????????
4. perform operations with complex numbers and calculate integrals from functions of a complex variable,
5. perform conformal mappings in circular domains,
6. calculating integrals of functions of a complex variable using Cauchy integral formula.
3. Description
introduce the questions of the theory of complex variable and analytic functions, give an idea about the Riemann sphere,
present Cauchy's integral theorems and formulas, analyze analytical functions with Taylor's series,
to give an idea about multivalued analytic functions and Riemann surfaces, introduce the theory and applications of residues.
4. Teaching and Learning Styles and Methods
● lectures,
● practice work
● individual work
5. Evaluation Methods and Criteria
The course is valued at a maximum of 20 points.
● 2 midterm exams with a total value 8 points (40%),
● tests - maximum 3 points (15%),
● Final exam - maximum 9 points (45%).
6. Basic Bibliography
  • Ablomitz J. M., Fokas A. S., Complex Variables, 2013.
  • Brown J. W., Churchill R. V., Complex Variables and Applications, 1996.
  • Маркушевич А. И., Краткий курс теории аналитических функций, Москва, 2013.
  • Шабат Б. В., Введение в комплексный анализ, Москва, 2015.
7. Main sections of the course
Complex numbers and functions of a complex variable. Properties of exponential and logarithmic functions. Definition and properties of the integral of a function of a complex variable. Cauchy's integral theorem and Cauchy's integral formula. Cauchy type integral and its properties.
5th term
4 hours/week
Lect. 4 hours/week, individual work – 8 hours/week
MANDATORY
0112/?33
1. Purpose of the Course
introduce the theory of Lebesgue measure, measurable functions, Lebesgue integral
properties, properties of monotone functions and absolutely continuous functions, Lebesgue spaces.
2. Educational Outcomes
?. ???????????? ??????? ? ???????????
1. to determine the measurability of sets, functions,
2. to present the properties of the Lebesgue integral,
3. to present the properties of monotonic functions and absolutely continuous functions?.
?. ????????? ???????????? ???????????????
4. to calculate (estimate) the power and measure of the set, the Lebesgue integral and the norm of the function
5. to apply real analysis methods for solving problems.

3. Description
introduce the theory of Lebesgue measure, measurable functions, Lebesgue integral
properties, properties of monotone functions and absolutely continuous functions, Lebesgue spaces.
4. Teaching and Learning Styles and Methods
● lectures,
● practice work
● individual work
5. Evaluation Methods and Criteria
The course is valued at a maximum of 20 points.
● 2 midterm exams with a total value 8 points (40%),
● ests - maximum 3 points (15%)
● Final exam - maximum 9 points (45%)
6. Basic Bibliography
  • Rudin W., Real and complex analysis, 1986.
  • А.Н. Колмогоров, С.В. Фомин, Элементы теории функций и функционального анализа, М. 1976.
  • И.П. Натансон, Теория функций вещественной переменной. М. 1974.
  • Ю. С. Очан. Сборник задач по математическому анализу. М. 1982.
  • ?. ????????, ?. ??????, ?. ?????????? ? ?????? ??????? ??????????, ???, 2017?
7. Main sections of the course
Sets, cardinal numbers, open and closed sets on axis. Families of sets. The general theory of Lebesgue measure. Measurable functions. Almost everywhere and in measure convergences. Lebesgue's integral. Lp , 1
4th term
4 hours/week
Lect. 2 hours/week, pract. work 2 hours/week, individual work – 8 hours/week
MANDATORY
0104/?15
1. Purpose of the Course
introduce the applications of mathematical analysis in geometry,
introduce the basic ideas of the theory of curves: tangent, curvature, torsion, etc.,
to give the important ideas of the theory of surfaces through the first and second quadratic forms of surfaces.
2. Educational Outcomes
?. ???????????? ??????? ? ???????????
1. define curve tangent and normal, curve curvature and twist,
2. define asymptotic lines of surfaces, lines of curvature, explain the theorems of Rodriguez and Dupin,
3. classify surfaces of constant curvature using full curvature:
?. ????????? ???????????? ???????????????
4. find the equations of the tangent and the normal in different ways of giving the curve,
5. find the main directions of the surface, asymptotic lines, full and average curvatures,
6. find geodesic lines on surfaces.
3. Description
introduce the applications of mathematical analysis in geometry,
introduce the basic ideas of the theory of curves: tangent, curvature, torsion, etc.,
to give the important ideas of the theory of surfaces through the first and second quadratic forms of surfaces.
4. Teaching and Learning Styles and Methods
● lectures,
● practice work
● individual work
5. Evaluation Methods and Criteria
The course is valued at a maximum of 20 points.
● 2 midterm exams with a total value 8 points (40%),
● tests - maximum 2 point (10%),
● participation-maximum 2 points (10%),
● Final exam - maximum 8 points (40%).
6. Basic Bibliography
  • Рашевский П.К., Курс дифференциальной геометрии, УРСС, М., 2003.
  • Тайманов И.А. Лекции по дифференциальной геометрии. I. Новосибирск., 2005.
  • Игнатьев Ю.Г. Дифференциальная геометрия кривых и поверхностей, КФУ, 2013г.
  • Мищенко А.С., Фоменко А.Т., Краткий курс дифференциальной геометрии и топологии, М., 2004.
7. Main sections of the course
Theory of curves, Theory of surfaces, Internal geometry of surfaces.
4th term
6 hours/week
Lect. 2 hours/week, pract. work 4 hours/week, individual work – 12 hours/week
MANDATORY
0112/?31
1. Purpose of the Course
introduce the Cauchy problem statement for differential equations and properties of solutions of linear equations.
2. Educational Outcomes
?. ???????????? ??????? ? ???????????
1. present the theorems of existence and uniqueness,
2. present sufficient conditions for the solvability of boundary value problems,
?. ????????? ???????????? ???????????????
3. solve simple differential equations,
to use the theorems of existence and uniqueness in a number of problems of an applied nature.

3. Description
introduce the Cauchy problem statement for differential equations and properties of solutions of linear equations.
4. Teaching and Learning Styles and Methods
● lectures,
● practice work
● individual work
5. Evaluation Methods and Criteria
The course is valued at a maximum of 20 points.
● 2 midterm exams with a total value 8 points (40%),
● tests - maximum 3 points (15%),
● participation-maximum 1 point (5%),
● Final exam - maximum 8 points (40%).
6. Basic Bibliography
  • ???????? ?.?.,???????????? ?.?.,????????????? ?.?,?????????? ?.?., ????????? ??????????? ?????????????, ?????, 2002?
  • Понтрягин Л.С., Обыкновенные дифференциальные уравнения,М., Наука, 1982.
  • Бибиков Ю. Н., Курс обыкновенных дифференциальных уравнений, Высшая школа, 1991.
  • ???????? ?.?., ???????????? ?.?,?????????? ?.?., ?????????? ?.?., ????????? ??????????? ????????????? (?????????), ?????, 1989?
  • Филиппов А.Ф., Сборник задач по дифференциальным уравнениям, М., Наука, 2000.
7. Main sections of the course
Theorems about the existence and uniqueness of the solution of the Cauchy problem for the normal system of differential equations. Simply solvable differential equations. Linear differential equations and systems.
Existence and properties of the homogeneous fundamental system of equations.
1st term
Contact hours-6 hours/week
Lect. 3 hours/week, pract. work -3 hours/week, individual work - 12 hours/week
MANDATORY
0112/?18
1. Purpose of the Course
● introduce the elements of set theory, the construction of the set of real numbers,
● formulate the idea of the limit of a sequence, the limit of a function, the continuity of a function and their basic properties.
2. Educational Outcomes
?. ???????????? ??????? ? ???????????
1. introduce the concept and properties of the limit of a sequence,
2. introduce the properties of the limit and continuity of a function,
?. ????????? ???????????? ???????????????
3. use basic applied methods of mathematical analysis and calculate the limit of sequences, investigate the continuity of the function,
?. ???????????/????????? ???????????????
4. modeling and solve problems
3. Description
● introduce the elements of set theory, the construction of the set of real numbers,
● formulate the idea of the limit of a sequence, the limit of a function, the continuity of a function and their basic properties.
4. Teaching and Learning Styles and Methods
● lectures,
● individual work,
● practical exercises.
5. Evaluation Methods and Criteria
● 2 midterm exams with a total value 8 points (40%),
● Tests with total value 3 points (15%),
● Final exam with 9 points (45%).
6. Basic Bibliography
  • ?. ????????, ????????????? ??????, ??? 1,2, ??????, ?????, 2009, 2012
  • ?.?. ???????? ? ????????, ????????????? ??????? ?????????, ?????, ???, ??? 1,2, 2014
  • Г. М. Фихтенгольц - Курс дифференциального и интегрального исчисления, , М., Наука, том 1,2,3, 1970.
7. Main sections of the course
Sets. Real numbers: Exact upper and lower bounds of numerical sets. Numerical sequences. Infinite smalls: Converging sequences.
Monotone sequences. Bolzano-Weierstrass lemma. Cauchy convergence criterion. The definitions of function's limits. The properties of function’s limits. The limit of monotone functions. Cauchy convergence criterion for functions. Functions continuity of functions. Classification of discontinuities. Cauchy and Wejerstrass’s theorems. Continuity and discontinuities of monotone functions. Useful limits. Uniform continuity. Cantor’s theorem. Lemma.Borel.
3rd term
4 hours/week
pract. work 2 hours/week, individual work- 4 hours/week
MANDATORY
0104/?29
1. Purpose of the Course
to introduce the basic concepts of topology, the ideas of open, closed set, edge, point of accumulation,
introduce the concepts of continuous, open, closed mappings, homeomorphism, ideas of compact, connected, linearly connected spaces.
2. Educational Outcomes
?. ???????????? ??????? ? ???????????
1. to illustrate the ideas of open and closed set, edge, cumulative point,
2. introduce the idea of metrics,
3. to reproduce the topological generalizations of the ideas of continuous projection, convergent sequence,
4. to explain the concept of homeomorphism,
5. to introduce the ideas of compact and connected spaces,
?. ????????? ???????????? ???????????????
6. to determine out whether the set is open or closed,
7. to determine the continuity of mapping,
8. to construct metric spaces,
9. to apply the compactness criterion,
?. ???????????/????????? ???????????????
10. to analyze existing problems and propose ways to solve them.
3. Description
to introduce the basic concepts of topology, the ideas of open, closed set, edge, point of accumulation,
introduce the concepts of continuous, open, closed mappings, homeomorphism, ideas of compact, connected, linearly connected spaces.
4. Teaching and Learning Styles and Methods
● lectures,
● practice work
● individual work
5. Evaluation Methods and Criteria
The course is valued at a maximum of 20 points.
● Tests with total value 8 points (40%),
● Participation - maximum 3 points (15%),
● Final exam - maximum 9 points (45%).
6. Basic Bibliography
  • Александрян Р.А., Мирзаханян Э.А., Общая топология, М., Наука, 1979.
  • Kelley, John L. General Topology. Springer-Verlag, 2005.
  • James R Munk res, Topology. 2015.
  • Lynn Arthur Steen, Counterexamples in Topology. 2010.
7. Main sections of the course
Elements of set theory, metric and topological spaces, compact spaces, connected spaces.
3st term
4 hours/week
Lect. 2 hours/week, pract. work 2 hours/week, individual work- 8 hours/week
MANDATORY
0112/?28
1. Purpose of the Course
introduce the Python programming language.
2. Educational Outcomes
?. ???????????? ??????? ? ???????????
1. use the Python language to solve professional and other problems,
?. ????????? ???????????? ???????????????
2. make competent algorithms and programs for problem solving,
3. use various specialized packages of the Python language for numerical calculations, data processing and visualization.
3. Description
introduce the Python programming language.
4. Teaching and Learning Styles and Methods
● lectures,
● individual work,
● practical exercises.
5. Evaluation Methods and Criteria
The course is valued at a maximum of 20 points.
● 2 midterm exams with a total value 8 points (40%),
● Tests with total value 3 points (15%),
● Final exam with 9 points (45%)?
6. Basic Bibliography
  • David Beazley, Brian K. Jones, Python Cookbook, Third edition, O'Reilly Media, 2013.
  • Zed Shaw, Learn Python 3 the Hard Way, Addison-Wesley Professional, 2017.
  • Mark Pilgrim, Dive into Python 3, Apress, 2009.
  • Allen B. Downey, Think Python: How to Think Like a Computer Scientist, 2nd Edition, O'Reilly Media, 2015.
  • .
  • .
7. Main sections of the course
Familiarity with Python language, Jupyter Notebook and Pycharm systems. Basic data structures in Python. Familiarity with operators and functions. The Numpy package for data processing. Pandas package for processing data frames and time series. Matplotlib, seaborn packages for data visualization. The statsmodels package for statistical calculations. Basics of object oriented programming.
3st term
6 hours/week
Lect. 3 hours/week, pract. work 3 hours/week, individual work- 12 hours/week
MANDATORY
0112/?27
1. Purpose of the Course
1. present the elements of mathematical analysis in Rn,
2. introduce the definite integral and its applications in the multidimensional case, present the main properties of positive numerical series.
2. Educational Outcomes
?. ???????????? ??????? ? ???????????
1. to characterize the elements of differential calculus in the multivariate case,
2. to present the main properties of the definite integral in the multidimensional case,
?. ????????? ???????????? ???????????????
3. to calculate integrals and derivatives, to apply the integral to calculate area, volume,
4. to investigate functions of several variables,
5. count sum of series,
?. ???????????/????????? ???????????????
6. modeling and solving extremum problems.
3. Description
1. present the elements of mathematical analysis in Rn,
2. introduce the definite integral and its applications in the multidimensional case, present the main properties of positive numerical series.
4. Teaching and Learning Styles and Methods
lectures,
individual work,
practical exercises.
5. Evaluation Methods and Criteria
The course is valued at a maximum of 20 points.
● 2 midterm exams with a total value 8 points (40%),
● Tests with total value 3 points (15%),
Final exam with 9 points (45%)?
6. Basic Bibliography
  • ?. ?. ????????, ????????????? ??????, I-II ??????
  • Г. М. Фихтенгольц, Курс дифференциального и интегрального исчисления, том ??, ???.
  • ?.?. ???????? ? ???????? - ????????????? ??????? ?????????, II ????
7. Main sections of the course
The limit and continuity of a function of several variables.
Derivative, properties, extrema of a function of several variables.
Multidimensional integral.
Properties of numerical series.
3rd term
4 hours/week
Lect. 2 hours/week, pract. work 2 hours/week, individual work – 8 hours/week
MANDATORY
0104/?26
1. Purpose of the Course
● introduce the concepts of semigroup, group, properties, group order, element order, related class, normal subgroup, quotient group,
● introduce the concepts and properties of ideal, ring, ratio ring.
2. Educational Outcomes
?. ???????????? ??????? ? ???????????
1. to explain ideas, simple properties of semigroup, group,
2. to present Lagrange's theorem, the main theorem of homomorphism, the concepts of element order, related class, normal subgroup, quotient group
3. to present the main types and properties of rings, fields, the concept of ideal, quotient ring, describe the simple elements of classical rings,
?. ????????? ???????????? ???????????????
4. to determine the order, inverse, conjugate, homomorphism of the representation of the element of the group, to find its core,
5. to determine the order of the quantifier group, to construct a quantifier ring, a finite field, to determine the characteristic of the field,
?. ???????????/????????? ???????????????
6. to model the problems of the profession.
3. Description
● introduce the concepts of semigroup, group, properties, group order, element order, related class, normal subgroup, quotient group,
● introduce the concepts and properties of ideal, ring, ratio ring.
4. Teaching and Learning Styles and Methods
● Lecture
● Practic work
● Individual work
5. Evaluation Methods and Criteria
The course is valued at a maximum of 20 points.
● 2 midterm exams with a total value 8 points (40%),
● Tests with total value 3 points (15%),
● Participation - maximum 1 point (5%),
● Final exam - maximum 8 points (40%).
6. Basic Bibliography
  • E.B.Vinberg, A Course in Algebra. 2003.
  • Кострикин А.И. Введение в алгебру. Ч. 2. М., Физико-математическая литература, 2004.
  • Фадеев Д.К. Лекции по алгебре , изд. ?Лань? 2007.
  • ????????? ?., ?????????? ????????????, ???, 2005:
  • ????????? ???., ?????????? ? ????? ??????????, 2023:
7. Main sections of the course
Groups and subgroups, set of parents, homogeneous groups, related classes, Lagrange's theorem, homomorphisms, basic types of rings, simple elements and finite fields.
2nd term
4 hours/week
pract. work 4 hours/week, individual work – 8 hours/week
MANDATORY
0309/?25
1. Purpose of the Course
● to present the classification principles of modern programming languages, areas of application, methods of implementation,
● introduce the basics and features of procedural and object-oriented programming with an example of the C++ language,
● to develop the ability to create programs in integrated programming systems.
2. Educational Outcomes
?. ???????????? ??????? ? ???????????
1. to present the principles of construction and implementation of programming languages, the basics of procedural programming, the main elements of object-oriented programming,
?. ????????? ???????????? ???????????????
2. perform decomposition of the problem to be programmed,
3. create procedural programs in C++ language,
4. test programs using black and white box principles,
5. create and implement new data types:
?. ???????????/????????? ???????????????
6. make informed decisions related to programming the problems of the professional sphere:
3. Description
● to present the classification principles of modern programming languages, areas of application, methods of implementation,
● introduce the basics and features of procedural and object-oriented programming with an example of the C++ language,
● to develop the ability to create programs in integrated programming systems.
4. Teaching and Learning Styles and Methods
Work on computer,
Individual work.
5. Evaluation Methods and Criteria
The course is valued at a maximum of 20 points.
● 2 midterm exams with a total value 9 points (45%),
● Tests with total value 3 points (15%),
● independent work 5 points (25%)
● participation 3 points (15%)?
6. Basic Bibliography
  • Дейтел Х.М, Дейтел П.Дж. Как программировать на C++. - М., 2001.
  • Т.А. Павловская.C/C++. Программирование на языке высокого уровня. СПБ Питер, 2001г.
  • Дж. Либерти. Освой самостоятельно С++ за 21 день. Москва,2000г.
  • В.В.Подбельский.Язык C++.Изд-во “Финансы и статистика” ,2003г.
7. Main sections of the course
Current programming paradigms and programming language classification principles. Basic structures of C++ language: lexemes, operations, operators. Standard data types. Indicators: Fundamentals of structured programming. Functions: One-dimensional and two-dimensional arrays, relationship with pointers. Lines. User-created types. Basic data structures: linked lists, storage, queue. Fundamentals of object-oriented programming. Lessons, action reload, inheritance.
2nd term
6 hours/week
Lect. 3 hours/week, pract. work 3 hours/week, individual work - 12 hours/week
MANDATORY
0112/?24
1. Purpose of the Course
● present the basics of differential calculus, the basics of integral calculus,
● introduce the main applications of differential and integral calculus.
2. Educational Outcomes
?. ???????????? ??????? ? ???????????
1. present the main theorems of differential calculus,
2. present the main properties of indefinite and definite integrals,
3. use differential and integral calculus to solve applied problems,
?. ????????? ???????????? ???????????????
4. calculate derivative and differential,
5. calculate indefinite and definite integrals,
6. investigate functions.
?. ???????????/????????? ???????????????
7. modeling and solving problems.
3. Description
● present the basics of differential calculus, the basics of integral calculus,
● introduce the main applications of differential and integral calculus.
4. Teaching and Learning Styles and Methods
● lectures,
● individual work,
● practical exercises.
5. Evaluation Methods and Criteria
The course is valued at a maximum of 20 points.
● 2 midterm exams with a total value 8 points (40%),
● Tests with total value 3 points (15%),
● Final exam with 9 points (45%)?
** Prerequisite for participation in the course: to have passed mathematical analysis-1.
6. Basic Bibliography
  • ?. ????????, ????????????? ??????, ??? 1,2, ??????, ?????, 2009, 2012
  • ?.?. ???????? ? ????????, ????????????? ??????? ?????????, ?????, ???, ??? 1,2, 2014?
  • ??????? ?????????????.
  • Г. М. Фихтенгольц - Курс дифференциального и интегрального исчисления, , М., Наука, том 1,2,3, 1970.
7. Main sections of the course
Derivative of a function, growth formula of a function, one-way derivatives. Derivation rules. The derivative of functions superposition. The derivative of the inverse function. The physical and geometric means of the derivative. Differentiability and differential, rules of differentiation. Fermat's and Rolle's theorems. Lagrange's theorem, formula of finite increments. Cauchy's theorem. Lopital's rule. Higher order derivatives. Leibniz formula.
Taylor's formula, the Peano's formula for remainder. Extremes, critical points, necessary and sufficient conditions of extremas. Convex functions, properties. Primitive and indefinite integral, integration formulas. Change of variable and integration by parts in indefinite integral.
Definition of the Riemann integral (definite integral) and the necessary condition for its existence. Darboux sums, properties. Necessary and sufficient condition for the existence of an integral. The first mean value theorem, consequence. Generalized mean value theorem. Integral with variable boundary, Newton - Leibniz formula. Change of variable and integration by parts in definite integrals. Surface expression by integral.
Expression of volume using an integral. Curves, definition of curve length, curve length calculation formula. Length of a curve using polar coordinates. Concept of Stiltes' integral. Types of improper integrals. Properties of improper integrals.
2nd term
4 hours/week
Lect. 2 hours/week, pract. work - 2 hours/week, individual work - 8 hours/week
MANDATORY
0104/?23
1. Purpose of the Course
● to present the idea of linear space, to familiarize with the ideas of linear independence, rank, basis of linear space, dimension of a system of vectors,
● to introduce the idea of linear mapping and matrix of linear transformation, ideas of eigenvector, eigenvalue of linear transformation.
2. Educational Outcomes
?. ???????????? ??????? ? ???????????
1. to present the idea of linear space, its properties, to illustrate the ideas of linear independence, support, dimensionality of vectors,
2. to present the concept of linear representation, its main properties, the idea of its matrix, core and image,
?. ????????? ???????????? ???????????????
3. to count the rank of the system of vectors and of the matrix, the dimension of the space,
4. to calculate the dimension of the kernel and image of the linear mapping, to find the fundamental solutions of the system of homogeneous linear equations,
5. to apply the Gram-Schmidt orthogonalization algorithm, to calculate the eigenvalues and eigenvectors of the matrix, to apply Jacobi's and Sylvester's indicators.
?. ???????????/????????? ???????????????
6. modeling the problems of the profession using algebraic methods.
3. Description
● to present the idea of linear space, to familiarize with the ideas of linear independence, rank, basis of linear space, dimension of a system of vectors,
● to introduce the idea of linear mapping and matrix of linear transformation, ideas of eigenvector, eigenvalue of linear transformation.
4. Teaching and Learning Styles and Methods
● lectures,
● individual work,
● practical exercises.
5. Evaluation Methods and Criteria
The course is valued at a maximum of 20 points.
● 2 midterm exams with a total value 8 points (40%),
● Tests with total value 3 points (15%),
● Participation - maximum 1 point (5%)
● Final exam with 8 points (40%)?
6. Basic Bibliography
  • E.B.Vinberg, A Course in Algebra. 2003.
  • Кострикин А.И. Введение в алгебру. Ч. 1,2, М., Физико-математическая литература, 2004.
  • Фадеев Д.К. Лекции по алгебре , изд. ?Лань? 2007.
  • ????????? ?., ?????????? ????????????, ???, 2005:
  • ????????? ???., ?????????? ? ????? ??????????, 2023:
7. Main sections of the course
Basic properties of linear spaces, rank of vector system, dimensionality of space, sum of subspaces, linear projections, linear transformations, bilinear forms, quadratic for
2nd term
2 hours/week
Pract. work- 2 hours/week, Individual work – 4 hours/week
MANDATORY
0104/?22
1. Purpose of the Course
● to present the operations with sets, the ideas of n-place relation, equivalence relation, order, function, power of set, the idea of algorithm, elements of combinatorics, basic ideas of graph theory,
● resent the applications of propositional logic and Boolean functions.
2. Educational Outcomes
?. ???????????? ??????? ? ???????????
1. to illustrate the operations performed with sets, to explain the concepts of equivalence relation and order,
2. to present the main properties of combinations and arrangements,
?. ????????? ???????????? ???????????????
3. to find the intersection, the union and the cardinal number of sets, to apply the elements of combinatorics,
4. to apply planar graph notation and Euler's formula, to determine the types of graphs,
5. to construct the disjunctive and conjunctive normal forms of the Boolean function,
?. ???????????/????????? ???????????????
6. to analyze existing problems and propose ways to solve them.
3. Description
● to present the operations with sets, the ideas of n-place relation, equivalence relation, order, function, power of set, the idea of algorithm, elements of combinatorics, basic ideas of graph theory,
● resent the applications of propositional logic and Boolean functions.
4. Teaching and Learning Styles and Methods
● practic training
● individual work
5. Evaluation Methods and Criteria
● The course is valued at a maximum of 20 points.
● Tests with total value 8 points (40%),
● Participation - maximum 3 point (15%)
● Final exam with 9 points (45%).
6. Basic Bibliography
  • K.H.Rosen, Discrete Mathematics and its Applications, Mc. Graw Hill, 2012.
  • R.L. Graham, D.E. Knuth, O. Patashnik, Concrete mathematics, 2015.
  • Edward R. Scheinerman, Mathematics? A Discrete Introduction. 2013.
7. Main sections of the course
Sets and operations on them, relations on sets, power, elements of combinatorics, elements of graph theory, propositional logic and Boolean functions.
1th term
4 hours/week 4
Lectures - 2 hours/week, Pract. work - 2 hours/week, Individual work – 8 hours/week
MANDATORY
0104/?21
1. Purpose of the Course
● to present algorithms for solving the system of linear equations, introduce the operations with complex numbers, matrices, substitutions, the concept of determinant, properties, the concept of matrix inverse, calculation algorithms,
● introduce operations with polynomials, division by remainder, Euclid's algorithm for finding the greatest common divisor ?
2. Educational Outcomes
?. ???????????? ??????? ? ???????????
1. to present algorithms for solving the system of linear equations,
2. to explain algorithms for calculating matrix inversion,
?. ????????? ???????????? ???????????????
3. to count the product and sum of matrices and complex numbers, the sum, the product and sign of transpositions, the sign, the determinants of counting,
4. to count the product and the sum of matrices and complex numbers, the sign and the product of positions, calculate the determinants,
5. apply Euclid's algorithm to find the greatest common divisor,
?. ???????????/????????? ???????????????
6. to model the problems of the profession using algebraic methods.
3. Description
● to present algorithms for solving the system of linear equations, introduce the operations with complex numbers, matrices, substitutions, the concept of determinant, properties, the concept of matrix inverse, calculation algorithms,
● introduce operations with polynomials, division by remainder, Euclid's algorithm for finding the greatest common divisor ?
4. Teaching and Learning Styles and Methods
1. lectures,
2. practic training
3. individual work
5. Evaluation Methods and Criteria
● 2 midterm exams with a total value 8 points (40%),
● Tests with total value 3 points (15%),
● Participation - maximum 1 point (5%)
● Final exam with 8 points (40%)?
6. Basic Bibliography
  • E.B.Vinberg, A Course in Algebra. 2003.
  • Кострикин А.И. Введение в алгебру. Ч. 1,2,3. М., Физико-математическая литература, 2004.
  • Фадеев Д.К. Лекции по алгебре , изд. ?Лань? 2007.
  • ????????? ?., ?????????? ????????????, ???, 2005:
  • ????????? ???., ?????????? ? ????? ??????????, 2023:
7. Main sections of the course
Complex numbers, arithmetic operations with complex numbers, systems of linear equations, several methods of solving systems of equations, transpositions and substitutions, matrices, operations with matrices and determinants.
1st term
2 hours/week
2 hours/week, Individual work- 4 hours/week
MANDATORY
0108/?20
1. Purpose of the Course
● to provide students with knowledge of the history of information technology development and application, skills in the use of basic operating system tools and application programs)
● Study of MS Windows generation operating systems, use of MS Office package applications, particularly MS Word, MS Excel applications, use of Internet technologies, particularly Web 2.0 technology.
2. Educational Outcomes
?. ???????????? ??????? ? ???????????
1.Familiarize with computer technology, development of computers, technical characteristics, functional differences. Work with Windows 7,8,10 operating system, MS Word and MS Excel programs,
?. ????????? ???????????? ???????????????
2. work with any operating system with a visual interface, MS Word, MS Excel MS, use PowerPoint programs.
3. Description
● to provide students with knowledge of the history of information technology development and application, skills in the use of basic operating system tools and application programs)
● Study of MS Windows generation operating systems, use of MS Office package applications, particularly MS Word, MS Excel applications, use of Internet technologies, particularly Web 2.0 technology.
4. Teaching and Learning Styles and Methods
1. practical work,
2. individual work?
5. Evaluation Methods and Criteria
The course is valued at a maximum of 20 points.
● 2 midterm exams with a total value 9 points (45%),
● Tests with total value 8 points (40%),
● Participation - maximum 1 point (5%).
6. Basic Bibliography
  • Самоучитель Office 2010 Ю. Стоцкий, А.Васильев, И. Телина 2011?.?
  • ?????????? ???????????: ??????? ???????? 2009 ?.?
  • MS PowerPoint 2007: ????? ???????? 2009 ?. ?
  • Уокенбах Дж. - Microsoft Excel 2010. Библия пользователя.
7. Main sections of the course
● Study of the MS Office generation software packageUse of MS Word reference toolsWork with data
● Study the MS Excel
● Standard functions
● Study MS PowerPoint?
1st semester
4 hours/week
Lectures - 2 hours/week, Pract. work- 2 hours/week, Individual work - 8 hours/week 5
MANDATORY
0104/?19
1. Purpose of the Course
● present the equations of line and plane and canonical equations of ellipse, hyperbola and parabola, study their properties,
● illustrate algebraic surfaces of the second order by means of sections, introduce the concept of generators of surfaces of the second order.
2. Educational Outcomes
?. ???????????? ??????? ? ???????????
1. represent scalar, vector and mixed products of vectors,
2. represent the equations of direction and plane in different ways of giving them,
3. represent the basic properties of second-order algebraic curves and surfaces,
?. ????????? ???????????? ???????????????
4. to apply vector algebra when solving geometric problems,
5. solving problems about line and plane, finding the equations of ellipse, hyperbola and parabola,
?. ???????????/????????? ???????????????
6. coordinate and analyze the received information, draw conclusions.
3. Description
● present the equations of line and plane and canonical equations of ellipse, hyperbola and parabola, study their properties,
● illustrate algebraic surfaces of the second order by means of sections, introduce the concept of generators of surfaces of the second order.
4. Teaching and Learning Styles and Methods
● lectures,
● practic training
● individual work:
5. Evaluation Methods and Criteria
The course is valued at a maximum of 20 points.
● 2 midterm exams with a total value 8 points (40%),
● Tests with total value 3 points (15%),
● Participation - maximum 1 point (5%)
● Final exam with 8 points (40%)?
6. Basic Bibliography
  • П.С.Александров, Лекции по аналитической геометрии, ,,Наука,, М., 1968.
  • М.М.Постников, Аналитическая геометрия, ,,Наука,, М., 1986.
  • П.С.Моденов, А.С.Пархоменко, Сборник задач по аналитической геометрии, ,,Наука,, М. 1976.
  • ?.?. ??????????, ?.?. ????????, ??????????? ?????????????? ?????????, ?????? ???, ??? 2012?
  • ?.?. ??????????, ?.?. ????????, ??????????? ?????????????? ?????????, ??????? ???, ??? 2012?
7. Main sections of the course
Coordinate systems on plane and in space. The elements of vector algebra. The line on plane and in space. The plane’s equation. Second order algebraic curves (ellipse, hyperbola, parabola). Second order algebraic surfaces (cylinder, cone, ellipsoid, hyperboloids, paraboloids).
Chair code Name of the elective course Credits
5th term
4 hours/week
Lect. 2 hours/week, pract. work 2 hours/week, individual work - 8 hours/week
OPTIONAL
0112/?36
1. Purpose of the Course
introduce students to basic data structures
introduce the elements of the theory of algorithms.
2. Educational Outcomes
?. ???????????? ??????? ? ???????????
1. to use basic data structures,
2. to use basic (classical) algorithms,
?. ????????? ???????????? ???????????????
3. to use various classic algorithms for effective problem solving,
4. to find out the complexity of algorithms.
3. Description
introduce students to basic data structures
introduce the elements of the theory of algorithms.
4. Teaching and Learning Styles and Methods
● lectures,
● practice work,
● individual work.
5. Evaluation Methods and Criteria
The course is valued at a maximum of 20 points.
● 2 midterm exams with a total value 8 points (40%),
● tests - maximum 3 points (15%),
● Final exam - maximum 9 points (45%).
6. Basic Bibliography
  • Thomas, H. Cormen, Charles E. Leiserson, Ronald L. Rivest, Clifford Stein, Introduction to Algorithms, 3rd edition, by The MIT Press, 2009
  • R. Sedgewick. Algorithms in C++. Parts 1-4: Fundamentals, Data Structures, Sorting, Searching, Addison-Wesley, 1999
  • R. Sedgewick. Algorithms in C++. Part 5: Graph Algorithms, Addison-Wesley, 2002.
  • Donald Knuth, The Art of Computer Programming, Volumes 1-4A, Addison-Wesley, 2011.
7. Main sections of the course
Comparison of growth rates of functions. Divide and conquer principle. Basic data structures. Algorithms for sorting (sorting, sorting in ascending or descending order). Dynamic programming. Greedy algorithms. Algorithms on graphs.
7th term
4 hours/week
Lectures – 2 hours/week, Pract. work – 2 hours/week, Individual work- 8 hours/week
OPTIONAL
0112/?44
1. Purpose of the Course
introduce variational methods for solving differential equations.
apply these methods for solving operator equations.
2. Educational Outcomes
?. ???????????? ??????? ? ???????????
1. present Ritz and Galyorkin methods for solving differential equations.
?. ????????? ???????????? ???????????????
2. apply variational methods in theoretical and production problems,
3. apply the methods of the theory of monotonic operators,
4. build mathematical models for problems arising in various fields.
3. Description
introduce variational methods for solving differential equations.
apply these methods for solving operator equations.
4. Teaching and Learning Styles and Methods
lectures,
practice work,
individual work.
5. Evaluation Methods and Criteria
The course is valued at a maximum of 20 points.
● Midterm exams and research work a total value 8 points (40%),
● Tests - maximum 3 points (15%),
● Participation - 1 point (5%),
● Final oral exam maximum 8 points (40%).
6. Basic Bibliography
  • В.П.Михайлож-дифференциальные уравнения в частных производных, 1979.
  • С.Г.Михлин- линейные уравнения в частных производных, 1977.
  • Дубинский-Квазилинейные элиптические и параболические уравнения любого порядка.
  • Michiaki Onodera . Variational Methods in Differential Equations. Published in: A Mathematical Approach to Research Problems of Science and Technology Publisher: Springer Japan, 2014.
7. Main sections of the course
Functional spaces, Symmetric and positive definite operators, Construction of functional minimum and minimizing sequence.
6th term
4 hours/week
Lect. 2 hours/week, pract. work 2 hours/week, individual work - 8 hours/week
OPTIONAL
0105/?44
1. Purpose of the Course
present the main methods of applied statistics,
teach how to apply statistical methods to solve practical problems,
give ideas from different sections of applied statistics.
2. Educational Outcomes
?. ???????????? ??????? ? ???????????
1. receiving the necessary theoretical knowledge to formulate statistical problems,
2. consider different statistical models and estimate their unknown parameters,
3. check simple and complex statistical hypotheses,
?. ????????? ???????????? ???????????????
4. use the appropriate criterions to solve the proposed problems;
5. analyzing the available data to make statistical conclusions,
6. with the help of a large amount of data, applying the methods of descriptive statistics, obtain estimates of various characteristics,
?. ???????????/????????? ???????????????
7. analyzing the provided statistical data to creatively apply the knowledge gained.
3. Description
present the main methods of applied statistics,
teach how to apply statistical methods to solve practical problems,
give ideas from different sections of applied statistics.
4. Teaching and Learning Styles and Methods
● lectures,
● individual work,
● practical exercises.
5. Evaluation Methods and Criteria
The course is valued at a maximum of 20 points.
● Midterm exams and research work a total value 8 points (40%),
● Tests - maximum 3 points (15%),
● Final oral exam maximum 9 points (45%).
6. Basic Bibliography
  • ????????? ?. ?., “??????? ? ????????? ?????????????? ??????????’’, ???1, “??????????’’ ????., ?????, 2015:
  • Ивченко Г. И., Медведев Ю. И., “Математическая статистика’’, кн. дом “ Либроком’’, М., 2014.
  • Gibbons J. D., Chakraborti S., “Nonparametric Statistical Inference’’, Marcel Dekker inc., 2003.
  • Montgomery D. C., Runger G. C., Applied Statistics and Probability for Engineers, 6-th edit., J. Wiley and Sons, 2013.
  • Jay Devore “Probability and Statistics for Engineering and the Sciences ”, California, CENGADE, 2016.
7. Main sections of the course
Descriptive statistics. Point evaluations: properties, evaluation methods. Interval estimation, essential concepts of hypothesis testing, Neumann-Pearson test and its applications. Non-parametric methods: indicators of agreement, homogeneity and independence.
7th term
4 hours/week
Lect. 2 hours/week, pract. work 2 hours/week, individual work - 8 hours/week
OPTIONAL
0105/?44
1. Purpose of the Course
familiarize with the main methods of random processes, classic examples of random processes,
represent random processes with independent increments.
2. Educational Outcomes
?. ???????????? ??????? ? ???????????
1. present the main classes and characteristics of random processes,
2. build the simplest models of random processes,
?. ????????? ???????????? ???????????????
3. use the properties of Poisson and Wiener processes,
4. analyze existing problems and propose ways to solve them,
?. ???????????/????????? ???????????????
5. creatively apply the acquired knowledge.
3. Description
familiarize with the main methods of random processes, classic examples of random processes,
represent random processes with independent increments.
4. Teaching and Learning Styles and Methods
● lectures,
● individual work,
● practical exercises.
5. Evaluation Methods and Criteria
The course is valued at a maximum of 20 points.
● Midterm exams and research work a total value 8 points (40%),
● Tests - maximum 3 points (15%),
● Final oral exam maximum 9 points (45%).
6. Basic Bibliography
  • Миллер Б. М., Панков А. Р., “Теория случайных процессов в примерах и задачах”, физматлит, 2002.
  • Koralov. L., Sinai Y. G., “Theory of Probability and Random Processes”, Springer, 2007.
  • Булинский А. В., Ширяев А. Н., “ Теория случайных процессов”, 2005.
  • Sheldon M. Ross, “Introduction to Probability models”, 9-th edition, Elsevier, 2007.
  • Боровков А. А., “Теория вероятностей”, Наука, 2009.
7. Main sections of the course
Classification of random processes. Characteristics of a random process. Processes with independent increments, Poisson and Wiener processes. Continuous-time discrete Markov processes. Reproduction and destruction processes, branching processes. Stationary processes in the narrow and broad sense. The spectral representation of the correlation function of a stationary process.
7th term
4 hours/week
Lect. 4 hours/week, individual work – 8 hours/week
OPTIONAL
0112/?44
1. Purpose of the Course
introduce the classical theory of linear integral equations,
introduce the general theory of linear and nonlinear monotone operators acting on conic sections of Banach spaces,
present equations generated by Wiener-Hopf, Hammerstein and Urison type operators.
2. Educational Outcomes
?. ???????????? ??????? ? ???????????
1. to present the elements of the general theory of linear integral equations,
2. to use the methods of solving linear and nonlinear operator equations,
?. ????????? ???????????? ???????????????
4. to apply the received results of a theoretical nature in specific problems arising in applications,
5. to solve linear and non-linear integral equations with specific kernel functions.
3. Description
introduce the classical theory of linear integral equations,
introduce the general theory of linear and nonlinear monotone operators acting on conic sections of Banach spaces,
present equations generated by Wiener-Hopf, Hammerstein and Urison type operators.
4. Teaching and Learning Styles and Methods
● lectures,
● individual work,
● practical exercises.
5. Evaluation Methods and Criteria
The course is valued at a maximum of 20 points.
● Midterm exams and research work a total value 8 points (40%),
● Tests - maximum 3 points (15%),
● Participation- 1 point (5%),
● Final oral exam maximum 8 points (40%).
6. Basic Bibliography
  • Михлин С.Г. Лекции по линейным интегральным уравнениям. М.: ГИФМЛ, 1959 г.
  • Васильева А.Б., Тихонов Н.А. Интегральные уравнения. Изд. МГУ, 2009 г.
  • М. А. Красносельский. Положительные решения операторных уравнений. М., Изд. Физ .мат. лит. 1962г.
  • Л. Г. Арабаджян, Н. Б. Енгибарян, “Уравнения в свертках и нелинейные функциональные уравнения”, Итоги науки и техн. Сер. Мат. анал., 22 (1984), 175-244.
7. Main sections of the course
Elements of the classical theory of linear integral equations.
Conic Banach spaces. General questions in the theory of monotone operators acting on a
cone.
Problems of solvability of equations generated by Wiener-Hopf, Hammerstein and Urison
type operators.
The application of the obtained results in a number of fields of natural science.
6th term
2 hours/week
Lect. 2 hours/week, individual work - 4 hours/week
OPTIONAL
0104/?39
1. Purpose of the Course
Present the concept of an affine transformation, the equations of curves and surfaces, their characteristics, and classification.
Introduce the concepts of the projective plane and the projective line, as well as the equation of a line in the projective plane.
Study the groups of isometric and affine transformations of the plane (or space), and the group of projective transformations of the projective plane.
Clarify the concept of a multidimensional affine space, and present the notions of lines and hyperplanes in multidimensional affine spaces.
2. Educational Outcomes
?. ???????????? ??????? ? ???????????
1. Explain the concept of affine transformation.
2. Present the equations, characteristics, and classification of curves and surfaces.
3. Describe the groups of isometric and affine transformations of the plane (or space).
4. Clarify the concept of multidimensional affine space,
?. ????????? ???????????? ???????????????
5. Determine the canonical equations of curves and surfaces.
6. Identify the equation of a line in the projective plane.
7. Determine the canonical equations, foci, and centers of conic sections.
8. Find the canonical equations, axes, and centers of quadrics in three-dimensional space.
?. ???????????/????????? ???????????????
9. Analyze given problems and propose appropriate methods of solution.
3. Description
Present the concept of an affine transformation, the equations of curves and surfaces, their characteristics, and classification.
Introduce the concepts of the projective plane and the projective line, as well as the equation of a line in the projective plane.
Study the groups of isometric and affine transformations of the plane (or space), and the group of projective transformations of the projective plane.
Clarify the concept of a multidimensional affine space, and present the notions of lines and hyperplanes in multidimensional affine spaces.
4. Teaching and Learning Styles and Methods
● lectures,
● individual work.
5. Evaluation Methods and Criteria
The course is valued at a maximum of 20 points.
● tests - maximum 8 points (40%),
● participation 3 point (15%),
● Final exam - maximum 9 points (45%).
6. Basic Bibliography
  • Douglas F. Riddle , Analytic Geometry, 1995
  • Постников М. М., Лекции по геометрии. Аналитическая геометрия. М. УРСС, 2017
  • Смирнов Ю. М., Курс аналитической геометрии, УРСС, 2017.
  • П. С. Александров, Лекции по аналитической геометрии, ,,Наука,, М., 1998.
7. Main sections of the course
affine transformations, second degree curves and surfaces, projective plane, multidimensional affine spaces.
5th term
4 hours/week
Lect. 4 hours/week, individual work – 8 hours/week
OPTIONAL
0104/?42
1. Purpose of the Course
present the idea of matrices, the algorithm to make them canonical, the idea of zeroing polynomials, the Hamilton-Kelly theorem,
find the canonical forms of skew-symmetric, orthogonal matrices, the root subspaces of matrices, the relative basis to the subspace, the algorithm to make the matrix Jordanian, the algorithm to find the Jordanian basis, perform calculations with functions determined on matrices.
2. Educational Outcomes
?. ???????????? ??????? ? ???????????
1. to illustrate the Hamilton-Kelly theorem,
2. to represent the root subspaces of matrices,
3. to cover symmetric, skew-symmetric, orthogonal matrices, the Jordan form of the matrix and the Jordan basis,
?. ????????? ???????????? ???????????????
4. to find the canonical forms of symmetric, skew-symmetric, orthogonal matrices,
5. to perform calculations with functions determined on matrices,
6. to apply the Jordanian matrix transformation algorithm,
?. ???????????/????????? ???????????????
7. analyze existing problems and estimate what resources are needed to solve them.
3. Description
present the idea of matrices, the algorithm to make them canonical, the idea of zeroing polynomials, the Hamilton-Kelly theorem,
find the canonical forms of skew-symmetric, orthogonal matrices, the root subspaces of matrices, the relative basis to the subspace, the algorithm to make the matrix Jordanian, the algorithm to find the Jordanian basis, perform calculations with functions determined on matrices.
4. Teaching and Learning Styles and Methods
● lectures,
● individual work.
5. Evaluation Methods and Criteria
The course is valued at a maximum of 20 points.
● 2 midterm exams with a total value 8 points (40%),
● tests - maximum 3 points (15%),
● participation - 1 points (5%),
● Final oral exam - maximum 8 points (40%).
6. Basic Bibliography
  • Шафаревич И. Р., Ремизов А. О. Линейная алгебра и геометрия. М.Ф. 2009.
  • Ф.Р. Гантмахер, “Теория матриц”, М.:, Наука, 2010.
  • Joel N. Franklin,Matrix Theory, 2011.
  • Фаддеев Д. К. Лекции по алгебре. 5-е. СПб.: Лань, 2007.
7. Main sections of the course
Canonical forms of symmetric and skew-symmetric matrices. Сanonical appearance of matrices. The Hamilton-Kelly theorem. Root subspaces of matrices. The Jordanian version of the matrix.
5th term
4 hours/week
Lect. 4 hours/week, individual work - 8 hours/week
OPTIONAL
0112/?42
1. Purpose of the Course
introduce various proofs and generalizations of Weierstrass polynomial approximation theorems.
2. Educational Outcomes
?. ???????????? ??????? ? ???????????
1. formulate convergence criterions of bundle operators,
2. formulate the theorems of approximation with cubic averages,
3. formulate Weierstrass, Stone-Weierstrass and Muntz approximation theorems,
?. ????????? ???????????? ???????????????
4. apply the basic methods of approximation with polynomials,
5. do research work.
3. Description
introduce various proofs and generalizations of Weierstrass polynomial approximation theorems.
4. Teaching and Learning Styles and Methods
● lectures,
● practice work,
● individual work.
5. Evaluation Methods and Criteria
The course is valued at a maximum of 20 points.
● 2 midterm exams with a total value 8 points (40%),
● tests - maximum 2 points (10%),
● participation - 1 points (5%),
● Final oral exam - maximum 9 points (45%).
6. Basic Bibliography
  • Натансон И.П., Теория функций вещественной переменной.
  • Качмаж С., Штейнгауз Г., Ортогональные ряды.
  • ????????? ???????? ?????????? PDF ???????
7. Main sections of the course
Convergence of bundle operators, Weierstrass polynomial approximation theorems, Bernstein polynomials, Stone-Weierstrass theorem, independent systems and Gramm's matrix, mean square approximation, Munz's theorem.
6th term
2 hours/week
Lectures – 2 hours/week, Individual work- 4 hours/week
OPTIONAL
0112/?43
1. Purpose of the Course
introduce students to the basics of uniformly distributed sequences and ergodic theory.
2. Educational Outcomes
?. ???????????? ??????? ? ???????????
1. formulate an uniform distribution of sequences and criterions,
2. formulate the deviation of the sequence,
3. give estimates of trigonometric sums,
4. apply the preliminary knowledge of ergodic theory,
?. ????????? ???????????? ???????????????
5. check the uniform distribution of the sequence,
6. calculate the deviation of a finite sequence, solve problems,
7. apply the methods of ergodic theory when solving problems.
3. Description
introduce students to the basics of uniformly distributed sequences and ergodic theory.
4. Teaching and Learning Styles and Methods
● lectures,
● individual work.
5. Evaluation Methods and Criteria
The course is valued at a maximum of 20 points.
● Tests - maximum 8 points (40%),
● Individual work - maximum 3 points (15%),
● Final oral exam maximum 9 points (45%).
6. Basic Bibliography
  • Кейперс Л., Нидеррейтер Г., Равномерное распределение последовательностей.
  • Einsiedler M., Ward T., Ergodic Theory.
7. Main sections of the course
uniformly distributed sequences, Weyl's criterions, Feuer's criterion, sequence deviation, measure-preserving transformations, ergodic mappings, Poincaré's theorem, convergence theorems of ergodic means.
8th term
3 hours/week
Lect. 3 hours/week, individual work - 6 hours/week
OPTIONAL
0104/?45
1. Purpose of the Course
introduce the ideas, properties of the semi-group, group,
formulate the concepts of group order, element order, related class, normal subgroup, quotient group,
introduce the concepts and properties of ideal, ring, ratio ring.
2. Educational Outcomes
?. ???????????? ??????? ? ???????????
1. to explain the ideas, simplest properties of a semigroup, a group,
2. to present Lagrange's theorem, the main theorem of homomorphism, the concepts of element order, related class, normal subgroup, quotient group,
3. to present the main types and properties of rings, fields, the concept of ideal, quotient ring, to describe the simple elements of classical rings,
?. ????????? ???????????? ???????????????
4. to determine the order, inverse, co-solutions of the element of the group, homomorphism of the representation, find its core, the order of the quotient group,
5. to build a quotient ring, a finite field, determine the characteristic of the field,
?. ???????????/????????? ???????????????
6. to model the problems of the profession using algebraic methods.
3. Description
introduce the ideas, properties of the semi-group, group,
formulate the concepts of group order, element order, related class, normal subgroup, quotient group,
introduce the concepts and properties of ideal, ring, ratio ring.
4. Teaching and Learning Styles and Methods
● lectures,
● individual work,
● practical exercises.
5. Evaluation Methods and Criteria
The course is valued at a maximum of 20 points.
● Tests - maximum 8 points (40%),
● Participation- maximum 3 point (15%),
● Final oral exam maximum 9 points (45%).
6. Basic Bibliography
  • E.B.Vinberg, A Course in Algebra. 2003.
  • Кострикин А.И. Введение в алгебру. Ч. 2. М., Физико-математическая литература, 2004.
  • Фадеев Д.К. Лекции по алгебре , изд. ?Лань? 2007.
  • ????????? ?., ?????????? ????????????, ???, 2005:
  • ????????? ???., ?????????? ? ????? ??????????, 2023:
7. Main sections of the course
Groups and subgroups, parent sets, homogeneous groups, related classes, Lagrange's theorem, homomorphisms, basic types of rings, simple elements and finite fields.
8th term
10 weeks
individual work - 90 hours
OPTIONAL
0000\?48
1. Purpose of the Course
through practical work, to develop the professional skills and experience of the student, the ability to work independently in the professional field.
2. Educational Outcomes
?. ???????????? ??????? ? ???????????
1. work with computer programs,
2. develop mathematical models to solve a given problem.
?. ????????? ???????????? ???????????????
3. apply appropriate programming languages to solve a given problem.
?. ???????????/????????? ???????????????
4. manifest knowledge in individual and team work.
3. Description
through practical work, to develop the professional skills and experience of the student, the ability to work independently in the professional field.
4. Teaching and Learning Styles and Methods
1. Students are introduced to ways of doing research work ?
2. Students get to know the methods of teaching and conducting various exams in universities.
3. Applying, summarizing and presenting the acquired knowledge.
5. Evaluation Methods and Criteria
Practice is assessed in the form of a test. The internship is evaluated positively (verified) if the student participated in the internship, completed the tasks provided by the program, submitted the internship report within the specified period.
6. Basic Bibliography
  • Yerevan State University
  • American University of Armenia
  • Institute of Mathematics of the National Academy of Sciences of the Republic of Armenia
7. Main sections of the course
1. Students get acquainted with relevant problems and methods of analyzing and modeling them.
2. The manager gives an assignment: a professional project.
3. Students complete the assigned project.
8th term
3 hours/week
Lect. 3 hours/week, individual work – 6 hours/week
OPTIONAL
0112/?45
1. Purpose of the Course
introduce the concepts of Hermitian, symmetric, conjugate and self-conjugate operators in the Hilbert space, operators generated by differential expressions and their define domains,
introduce the basics of the spectral theory of Sturm-Liouville operators.
2. Educational Outcomes
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1. to formulate and prove theorems of completeness and uniqueness of eigenfunctions, theorems about eigenvalues and eigenfunctions of the differential operator, about their asymptotic behavior, according to theorems of analysis of eigenfunctions.
2. to explain the settings of inverse problems of spectral theory, in particular, to get acquainted with the theorems of uniqueness in inverse problems, constructive solutions of inverse problems,
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3. to build self-adjoint expansions of Sturm-Louville operators,
4. to use the obtained results in Schr?dinger-type linear equations arising in quantum mechanics.
3. Description
introduce the concepts of Hermitian, symmetric, conjugate and self-conjugate operators in the Hilbert space, operators generated by differential expressions and their define domains,
introduce the basics of the spectral theory of Sturm-Liouville operators.
4. Teaching and Learning Styles and Methods
● lectures,
● individual work,
● practical exercises.
5. Evaluation Methods and Criteria
The course is valued at a maximum of 20 points.
● Midterm exams with total value 8 points (40%),
● Participation- maximum 3 point (15%),
● Final oral exam maximum 9 points (45%).
6. Basic Bibliography
  • Naimark M. A. Linear differential operators(in Russian). Izdat . ’’Nauka’’, Moscow, 1969. Second edition, revised and augmented . With an appendix by V. E. Ljance.
  • Freiling G. Yurko V. Inverse Sturm-Liouville problems and their applications. Nova Science Publishers, Inc., Huntington, NY, 2001.
  • Yurko V. A. Introduction to theory of inverse spectral problems. (in Russian), Moscow, Fizmatlit, 2007.
  • Canonical Dirak operator, T.Harutyunyan, Y. Ashrafyan (??????????????)?
7. Main sections of the course
Cauchy's problem. Boundary problem. Transformation operator. Asymptotics of eigenvalues. Asymptotics of normalizing constants. Analysis by eigenfunctions.
8th term
3 hours/week
Lect. 3 hours/week, individual work - 6 hours/week
OPTIONAL
0104/?45
1. Purpose of the Course
provide the formulas and axioms of the calculation of propositions and predicates, give the tables of logical connections, the expression of Boolean functions by means of logical connections,
present Post's and G?del's theorems about the completeness of propositional and predicate calculus, Maltsev's theorem about the compactness of formulas of the 1st order predicate calculus.
2. Educational Outcomes
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1. present the formulas and axioms of the theory of propositions and predicates, explain the tables of logical connections, the expression of Boolean functions through logical connections,
2. present Maltsev's theorem on the compactness of 1st-order predicate calculus formulas,
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3. to determine the truth or logical consistency of the formulas of the theory of propositions and predicates,
4. find the norms of a certain Boolean function, simplify contact schemes, build nodes (models), build non-standard analysis elements,
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5. to model the problems of the profession using algebraic methods.
3. Description
provide the formulas and axioms of the calculation of propositions and predicates, give the tables of logical connections, the expression of Boolean functions by means of logical connections,
present Post's and G?del's theorems about the completeness of propositional and predicate calculus, Maltsev's theorem about the compactness of formulas of the 1st order predicate calculus.
4. Teaching and Learning Styles and Methods
● lectures,
● individual work,
● practical exercises.
5. Evaluation Methods and Criteria
The course is valued at a maximum of 20 points.
· Midterm exams with total value 8 points (40%)
· Participation- maximum 3 point (15%)
· Final oral exam maximum 9 points (45%) .
6. Basic Bibliography
  • Мендельсон Э., Введение в математическую логику, 2009.
  • Колмогоров А. Н., Драгалин А. Г., Математическая логика. М., 2004.
  • Лавров И. А., Максимова Л. Л. Задачи по теории множеств, математической логике и теории алгоритмов. М., Физматлит, 2005.
  • Клини С. К., Математическая логика. - М.: Мир, 2003. 480 с.
  • E.B.Vinberg, A Course in Algebra. 2003.
7. Main sections of the course
Elements of the calculus of propositions, completeness of the calculus of propositions, Post's theorem, elements of the calculus of predicates and non-contradiction, calculus of predicates G?del's theorem on completeness, Maltsev's theorem on compactness.
8th term
4 hours/week
Lect. 3 hours/week, individual work - 6 hours/week
OPTIONAL
0105/?45
1. Purpose of the Course
introduce the basics of random geometric element’s research,
to present the probabilistic methods of image recovery, the method of factorization.
2. Educational Outcomes
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1. present different types of isoperimetric inequalities and their applications, build adequate geometric probabilistic models,
2. represent invariant dimensional views of k - planes ( k ?. ????????? ???????????? ???????????????
3. explain convex bodies in probabilistic ways,
4. apply knowledge in processes of random geometric elements.

3. Description
introduce the basics of random geometric element’s research,
to present the probabilistic methods of image recovery, the method of factorization.
4. Teaching and Learning Styles and Methods
● lectures,
● individual work,
● practical exercises.
5. Evaluation Methods and Criteria
The course is valued at a maximum of 20 points.
● Midterm exams with total value 8 points (40%),
● Tests - maximum 3 point (15%),
● Final oral exam maximum 9 points (45%).
6. Basic Bibliography
  • Rolf Schneider, Wolfgang Weil, “Stochastic and Integral Geometry”, Springer, 2008.
  • Luis A. Santalo, “Integral Geometry and Geometric probability”, Cambridge University Press, Cambridge, 2004.
  • Martin Haenggi, “Stochastic Geometry for Wireless Networks”, Cambridge University Press, 2013.
  • Rémi Langevin, “Integral geometry from Buffon to geometers of today”, France, 2015.
  • Sayandev Mukherjee, “Analytical Modeling of Heterogeneous Cellular Networks”, Cambridge University Press, 2014.
7. Main sections of the course
Fixed measurable appearances for different spaces and different transformation sets. Models of Poisson hyperplane processes. Combinatorial formulas for different k-planes (k
8th term
3 hours/week
Lect. 3 hours/week, individual work - 6 hours/week
OPTIONAL
0105/?45
1. Purpose of the Course
familiarize with the basics of image restoration and tomography,
form a stereological way of thinking.
2. Educational Outcomes
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1. getting the necessary theoretical knowledge to apply in different types of stochastic models,
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2. use appropriate stochastic models to solve the proposed tomographic problems,
3. by analyzing the available data, build the appearance of the distribution function of the projection surfaces,
4. effectively use the openly views of covariograms,
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5. creatively apply stochastic methods by analyzing the proposed problem.
3. Description
familiarize with the basics of image restoration and tomography,
form a stereological way of thinking.
4. Teaching and Learning Styles and Methods
● lectures,
● individual work,
● practical exercises.
5. Evaluation Methods and Criteria
The course is valued at a maximum of 20 points.
● Tests with total value 8 points (40%),
● Individual work - maximum 3 point (15%),
● Final oral exam maximum 9 points (45%).
6. Basic Bibliography
  • Baddeley A. J., Jensen E. B. V. “Stereology for statisticians”, Chapman & Hall, 2005.
  • Bene? V., Rataj J. “Stochastic Geometry”, Selected topics, Kluwer, Dordrecht, 2004.
  • Gardner R. J., “Geometric Tomography”, 2nd ed., Cambridge University Press, Cambridge, 2006
  • Baddeley A. T., Bárány I., Schneider R., Weil W., “Stochastic Geometry”, Lecture Notes in Mathematics, vol. 1892, Springer, Berlin, 2007.
  • Rolf Schneider, Wolfgang Weil, “Stochastic and Integral Geometry”, Springer, 2008.
  • Martin Haenggi, “Stochastic Geometry for Wireless Networks”, Cambridge University Press, 2013.
  • Rémi Langevin, “Integral geometry from Buffon to geometers of today”, France, 2015.
  • Sayandev Mukherjee, “Analytical Modeling of Heterogeneous Cellular Networks”, Cambridge University Press, 2014.
7. Main sections of the course
Radon's transformation and its properties. Definition and properties of covariogram. Isoperimetric inequality. Chord's length distribution function. The distribution function of the chord's length in a fixed direction.
8th term
2 hours/week
Lect. 2 hours/week, individual work - 4 hours/week
OPTIONAL
0112/?08
1. Purpose of the Course
introduce students to the general theory of nonlinear partial differential equations and model problems arising in various branches of physics.
the existence and uniqueness of solutions for Cauchy-type and boundary value problems for different classes of nonlinear PDEs, as well as qualitative properties of the constructed solutions.
2. Educational Outcomes
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1. Present solvability theorems for Cauchy and boundary value problems of nonlinear PDEs.
2. Apply variational and iterative methods for solving nonlinear equations
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3. Apply theoretical results to concrete nonlinear model problems arising in practice.
3. Description
introduce students to the general theory of nonlinear partial differential equations and model problems arising in various branches of physics.
the existence and uniqueness of solutions for Cauchy-type and boundary value problems for different classes of nonlinear PDEs, as well as qualitative properties of the constructed solutions.
4. Teaching and Learning Styles and Methods
● lectures,
● individual work.
5. Evaluation Methods and Criteria
The course is valued at a maximum of 20 points.
? tests - maximum 6 points (30%),
? individual work - maximum 4 points (20%),
? participation - maximum 1 point (5%),
? Final exam - maximum 9 points (45%).
6. Basic Bibliography
  • M. O. Korpusov, A. G. Sveshnikov. Non-linear functional analysis and mathematical modelling in physics: methods of studying non-linear operators. URSS, Moscow, 2011, 1-474.
  • H. Fujita. On the blowing up of solutions of the Cauchy problem for ut = ?u + u 1+α. J. Fac. Sci. Univ. Tokyo Sect. I., 13 (1966), 109-124.
  • A. Z. Fino, M. Ruzhansky, B. T. Torebek. Fujita-type results for the degenerate parabolic equations on the Heisenberg groups. Nonlinear Differential Equations and Applications. 31:2 (2024), 1-37.
  • M.A. Krasnosel'skii, G.M. Vainikko, Approximate Solution of Operator Equations . Springer; 1st edition, 1972, 496-pages.
  • K. Hayakawa. On nonexistence of global solutions of some semilinear parabolic differential equations. Proc. Japan Acad. 49(7) (1973), 503-505.
7. Main sections of the course
· Elements of the general theory of nonlinear monotone operators; concepts of classical, weak, and relaxed solutions of nonlinear equations; the concept of solution blow-up within Fujita’s theory.
· Questions of uniqueness and asymptotic behavior of constructed solutions.
Applications of obtained results in several fields of physics, in particular:
nonlinear heat conduction processes, diffusion processes, mathematical theory of spatio-temporal spread of epidemics, kinetic theory of gases, etc.

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