About this Course

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Learner Career Outcomes

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Shareable Certificate
Earn a Certificate upon completion
100% online
Start instantly and learn at your own schedule.
Flexible deadlines
Reset deadlines in accordance to your schedule.
Beginner Level
Approx. 14 hours to complete
Russian
Subtitles: Russian

Learner Career Outcomes

12%

got a tangible career benefit from this course

14%

got a pay increase or promotion
Shareable Certificate
Earn a Certificate upon completion
100% online
Start instantly and learn at your own schedule.
Flexible deadlines
Reset deadlines in accordance to your schedule.
Beginner Level
Approx. 14 hours to complete
Russian
Subtitles: Russian

Offered by

Moscow Institute of Physics and Technology logo

Moscow Institute of Physics and Technology

Syllabus - What you will learn from this course

Content RatingThumbs Up96%(6,613 ratings)Info
Week
1

Week 1

6 hours to complete

Инвариант

6 hours to complete
11 videos (Total 66 min), 3 readings, 2 quizzes
11 videos
МФТИ1m
О первой неделе3m
Пятнашки вводная5m
Пятнашки историческая часть3m
Кучки бумажек7m
Шахматная доска9m
Вода и молоко5m
Решение пятнашек ч. 111m
Решение пятнашек ч. 214m
Шоколадка3m
3 readings
МФТИ10m
Решения10m
Решения дополнительных задач10m
2 practice exercises
Задачи4h
Задачи10m
Week
2

Week 2

2 hours to complete

Формула Эйлера

2 hours to complete
10 videos (Total 57 min), 3 readings, 2 quizzes
10 videos
О футбольном мяче и бублике8m
Многогранники и многоугольники на мяче и бублике6m
Теорема Эйлера9m
Леонард Эйлер историческая часть4m
Из чего можно склеить футбольный мяч?8m
Замощения плоскости6m
Нерешенные задачи о замощениях плоскости7m
Заключение31s
Марджори Райс историческая часть3m
3 readings
Доказательство теоремы Эйлера10m
Решения10m
Решения10m
2 practice exercises
Задачи14m
Задачи4m
Week
3

Week 3

1 hour to complete

Бесконечность

1 hour to complete
9 videos (Total 60 min), 1 reading, 1 quiz
9 videos
Гармонический ряд8m
Ряд из обратных квадратов7m
Убывающая геометрическая прогрессия8m
Сколь угодно долгое падение сушины9m
Конечные и бесконечные множества, подмножества, взаимно-однозначное соответствие10m
Множество всех подмножеств, теорема Кантора8m
Заключение, самоподобие и бесконечность1m
Георг Кантор историческая часть2m
1 reading
Решения10m
1 practice exercise
Задачи14m
Week
4

Week 4

1 hour to complete

Непрерывность

1 hour to complete
11 videos (Total 60 min), 1 reading, 1 quiz
11 videos
Задача про карты разного масштаба и теорема Брауэра о неподвижной точке9m
Теорема Борсука-Улама и задача о температуре на Земле5m
Задача о шарнире в поезде Москва - Санкт-Петербург. Теорема о промежуточном значении6m
Задача Н. Н. Константинова о возах7m
Определение предела 16m
Определение предела 25m
Задача о винной бочке и перестановка пределов6m
Разрывные функции: целая и дробная части числа5m
Заключение35s
Лёйтзен Эгберт Ян Брауэр историческая часть2m
1 reading
Решения10m
1 practice exercise
Задачи14m

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Frequently Asked Questions

  • Access to lectures and assignments depends on your type of enrollment. If you take a course in audit mode, you will be able to see most course materials for free. To access graded assignments and to earn a Certificate, you will need to purchase the Certificate experience, during or after your audit. If you don't see the audit option:

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