About this Course
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Beginner Level

Approx. 21 hours to complete

Suggested: 6 weeks, 3-5 hours/week ...

English

Subtitles: English, Greek, Chinese (Simplified)

Skills you will gain

Random VariableProbability InterpretationsProbabilityCombinatorics

100% online

Start instantly and learn at your own schedule.

Flexible deadlines

Reset deadlines in accordance to your schedule.

Beginner Level

Approx. 21 hours to complete

Suggested: 6 weeks, 3-5 hours/week ...

English

Subtitles: English, Greek, Chinese (Simplified)

Learners taking this Course are

  • Machine Learning Engineers
  • Risk Managers
  • Software Engineers
  • Data Scientists
  • Security Engineers

Syllabus - What you will learn from this course

Week
1
3 hours to complete

Basic Counting

12 videos (Total 54 min), 4 readings, 9 quizzes
12 videos
Rule of Sum3m
How Not to Use the Rule of Sum3m
Convenient Language: Sets4m
Generalized Rule of Sum3m
Number of Paths4m
Rule of Product3m
Back to Recursive Counting3m
Number of Tuples5m
Licence Plates3m
Tuples with Restrictions5m
Permutations9m
4 readings
Slides1m
Slides1m
Listing All Permutations5m
Slides1m
8 practice exercises
Rule of Sum in Programming4m
Numbers Divisible by 2 or 38m
Operations with Sets10m
Generalized Rule of Sum18m
Rule of Product in Programming10m
Applications of the Rule of Product12m
Tuples5m
Counting with Restrictions20m
Week
2
3 hours to complete

Binomial Coefficients

8 videos (Total 76 min), 4 readings, 6 quizzes
8 videos
Number of Games in a Tournament10m
Combinations8m
Pascal's Triangle9m
Symmetries4m
Row Sums10m
Binomial Theorem12m
Practice Counting13m
4 readings
Generating Combinatorial Objects: Code10m
Slides10m
Slides10m
Slides10m
6 practice exercises
Number of Segments and Diagonals20m
Forming Sport Teams15m
Number of Iterations of Nested For Loops4m
Sum of the First Six Rows of Pascal's Triangle2m
Expanding (3a-2b)^k20m
Practice Counting10m
Week
3
3 hours to complete

Advanced Counting

8 videos (Total 36 min), 3 readings, 8 quizzes
8 videos
Salad5m
Combinations with Repetitions7m
Distributing Assignments Among People3m
Distributing Candies Among Kids3m
Numbers with Fixed Sum of Digits4m
Numbers with Non-increasing Digits2m
Splitting into Working Groups4m
3 readings
Salads10m
Slides1m
Slides1m
8 practice exercises
Salads10m
Combinations with Repetitions10m
Distributing Assignments Among People10m
Distributing Candies Among Kids15m
Numbers with Fixed Sum of Digits15m
Numbers with Non-increasing Digits7m
Splitting into Working Groups10m
Problems in Combinatorics45m
Week
4
5 hours to complete

Probability

17 videos (Total 126 min), 4 readings, 11 quizzes
17 videos
Galton Board6m
Natural Sciences and Mathematics6m
Rolling Dice7m
More Probability Spaces10m
Not Equiprobable Outcomes4m
More About Finite Spaces6m
Mathematics for Prisoners7m
Not All Questions Make Sense10m
What Is Conditional Probability?7m
How Reliable Is The Test?8m
Bayes' Theorem8m
Conditional Probability: A Paradox7m
Past and Future8m
Independence8m
Monty Hall Paradox8m
`Our Position'6m
4 readings
Slides
Slides
Slides
Slides
10 practice exercises
Concentration for Galton Board10m
Computing Probabilities for Two Dice12m
Computing Probabilities: More Examples12m
Fair Decisions and Imperfect Coins20m
Inclusion-Exclusion Formula10m
Computing Conditional Probabilities16m
Prisoner, King and Conditional Probabilities10m
More Conditional Probabilities8m
More About Independence20m
Monty Hall Gone Crazy20m
4.6
57 ReviewsChevron Right

33%

got a tangible career benefit from this course

50%

got a pay increase or promotion

Top reviews from Combinatorics and Probability

By PRAug 3rd 2019

Had loads of fun during most part of the course. Frequent quizzes keep the learner on toes. Thoroughly enjoyed the final programming quiz to implement a dice game.

By ZBOct 13th 2018

I really enjoyed taking this course. The teaching was pretty good and some of the quiz questions will challenge you if you haven't done Combinatorics before.

Instructors

Avatar

Alexander S. Kulikov

Visiting Professor
Department of Computer Science and Engineering
Avatar

Vladimir Podolskii

Associate Professor
Computer Science Department

About University of California San Diego

UC San Diego is an academic powerhouse and economic engine, recognized as one of the top 10 public universities by U.S. News and World Report. Innovation is central to who we are and what we do. Here, students learn that knowledge isn't just acquired in the classroom—life is their laboratory....

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...

About the Introduction to Discrete Mathematics for Computer Science Specialization

Discrete Math is needed to see mathematical structures in the object you work with, and understand their properties. This ability is important for software engineers, data scientists, security and financial analysts (it is not a coincidence that math puzzles are often used for interviews). We cover the basic notions and results (combinatorics, graphs, probability, number theory) that are universally needed. To deliver techniques and ideas in discrete mathematics to the learner we extensively use interactive puzzles specially created for this specialization. To bring the learners experience closer to IT-applications we incorporate programming examples, problems and projects in our courses....
Introduction to Discrete Mathematics for Computer Science

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 enroll in the course, you get access to all of the courses in the Specialization, and you earn a certificate when you complete the work. 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.

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