About this Course

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Intermediate Level
Approx. 111 hours to complete
English
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

Offered by

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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), 6 readings
2 videos
Introduction7m
6 readings
About the University10m
Rules on the academic integrity in the course10m
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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