About this Course
9,024 recent views

100% online

Start instantly and learn at your own schedule.

Flexible deadlines

Reset deadlines in accordance to your schedule.

Intermediate Level

Approx. 35 hours to complete

Suggested: 8 weeks, 8-10 hours per week...

English

Subtitles: English, Arabic
User
Learners taking this Course are
  • Data Scientists
  • Machine Learning Engineers
  • Data Engineers
  • Financial Analysts
  • Software Engineers
User
Learners taking this Course are
  • Data Scientists
  • Machine Learning Engineers
  • Data Engineers
  • Financial Analysts
  • Software Engineers

100% online

Start instantly and learn at your own schedule.

Flexible deadlines

Reset deadlines in accordance to your schedule.

Intermediate Level

Approx. 35 hours to complete

Suggested: 8 weeks, 8-10 hours per week...

English

Subtitles: English, Arabic

Syllabus - What you will learn from this course

Week
1
11 hours to complete

Introduction

1 video (Total 8 min), 4 readings
1 video
4 readings
Course Overview10m
Grading and Logistics10m
Suggested Readings10h
About the Instructor10m
11 hours to complete

Permutations and binomial coefficients

7 videos (Total 78 min), 1 quiz
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
12 hours to complete

Binomial coefficients, continued. Inclusion and exclusion formula.

7 videos (Total 87 min), 1 quiz
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
14 hours to complete

Linear recurrences. The Fibonacci sequence

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
14 hours to complete

A nonlinear recurrence: many faces of Catalan numbers

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
4.6
26 ReviewsChevron Right

Top reviews from Introduction to Enumerative Combinatorics

By RAMar 30th 2018

Excellent selection of material and presentation; TAs were of great help as well. The techniques taught in this course will be a nice addition to my algorithms analysis toolbox.

By RRAug 22nd 2017

Great lectures and content. I really enjoyed it. However, the solutions exercises could be clearer and in more detail. Thank you!

Instructor

Avatar

Evgeny Smirnov

Associate Professor
Faculty of Mathematics

About National Research University Higher School of Economics

National Research University - Higher School of Economics (HSE) is one of the top research universities in Russia. Established in 1992 to promote new research and teaching in economics and related disciplines, it now offers programs at all levels of university education across an extraordinary range of fields of study including business, sociology, cultural studies, philosophy, political science, international relations, law, Asian studies, media and communicamathematics, engineering, and more. Learn more on www.hse.ru...

Frequently Asked Questions

  • Once you enroll for a Certificate, you’ll have access to all videos, quizzes, and programming assignments (if applicable). Peer review assignments can only be submitted and reviewed once your session has begun. If you choose to explore the course without purchasing, you may not be able to access certain assignments.

  • When you purchase a Certificate you get access to all course materials, including graded assignments. Upon completing the course, your electronic Certificate will be added to your Accomplishments page - from there, you can print your Certificate or add it to your LinkedIn profile. If you only want to read and view the course content, you can audit the course for free.

More questions? Visit the Learner Help Center.