About this Course

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Intermediate Level
Approx. 111 hours to complete
English
Subtitles: English, Arabic
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.
Intermediate Level
Approx. 111 hours to complete
English
Subtitles: English, Arabic

Offered by

National Research University Higher School of Economics logo

National Research University Higher School of Economics

Syllabus - What you will learn from this course

Week
1

Week 1

11 hours to complete

Introduction

11 hours to complete
2 videos (Total 9 min), 5 readings
2 videos
Introduction7m
5 readings
About the University10m
Course Overview10m
Grading and Logistics10m
Suggested Readings10h
About the Instructor10m
11 hours to complete

Permutations and binomial coefficients

11 hours to complete
7 videos (Total 78 min)
7 videos
Permutations10m
k-permutations8m
Merry-go-rounds and Fermat’s little theorem 18m
Merry-go-rounds and Fermat’s little theorem 211m
Binomial coefficients14m
The Pascal triangle16m
1 practice exercise
Quiz 210h
Week
2

Week 2

12 hours to complete

Binomial coefficients, continued. Inclusion and exclusion formula.

12 hours to complete
7 videos (Total 87 min)
7 videos
Balls in boxes and multisets 110m
Balls in boxes and multisets 26m
Integer compositions11m
Principle of inclusion and exclusion: two examples12m
Principle of inclusion and exclusion: general statement9m
The derangement problem19m
1 practice exercise
Quiz 310h
Week
3

Week 3

14 hours to complete

Linear recurrences. The Fibonacci sequence

14 hours to complete
11 videos (Total 105 min), 1 reading, 1 quiz
11 videos
Fibonacci numbers and the Pascal triangle7m
Domino tilings8m
Vending machine problem10m
Linear recurrence relations: definition7m
The characteristic equation8m
Linear recurrence relations of order 211m
The Binet formula11m
Sidebar: the golden ratio9m
Linear recurrence relations of arbitrary order8m
The case of roots with multiplicities12m
1 reading
Spoilers! Solutions for quizzes 2, 3, and 4.2h
1 practice exercise
Quiz 410h
Week
4

Week 4

14 hours to complete

A nonlinear recurrence: many faces of Catalan numbers

14 hours to complete
7 videos (Total 73 min), 2 readings, 1 quiz
7 videos
Recurrence relation for triangulations11m
The cashier problem9m
Dyck paths5m
Recurrence relations for Dyck paths9m
Reflection trick and a formula for Catalan numbers12m
Binary trees15m
2 readings
Solutions10m
!!!Solutions for the older version of the Middterm10m

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