About this Course

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Learner Career Outcomes

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50%

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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. 20 hours to complete
English
Subtitles: English, Greek, Chinese (Simplified)

Skills you will gain

Random VariableProbability InterpretationsProbabilityCombinatorics

Learner Career Outcomes

33%

got a tangible career benefit from this course

50%

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. 20 hours to complete
English
Subtitles: English, Greek, Chinese (Simplified)

Offered by

University of California San Diego logo

University of California San Diego

National Research University Higher School of Economics logo

National Research University Higher School of Economics

Syllabus - What you will learn from this course

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Week
1

Week 1

3 hours to complete

Basic Counting

3 hours to complete
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

Week 2

4 hours to complete

Binomial Coefficients

4 hours to complete
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 Loops30m
Sum of the First Six Rows of Pascal's Triangle30m
Expanding (3a-2b)^k20m
Practice Counting30m
Week
3

Week 3

3 hours to complete

Advanced Counting

3 hours to complete
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

Week 4

5 hours to complete

Probability

5 hours to complete
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

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About the Introduction to Discrete Mathematics for Computer Science Specialization

Discrete Mathematics is the language of Computer Science. One needs to be fluent in it to work in many fields including data science, machine learning, and software engineering (it is not a coincidence that math puzzles are often used for interviews). We introduce you to this language through a fun try-this-before-we-explain-everything approach: first you solve many interactive puzzles that are carefully designed specifically for this online specialization, and then we explain how to solve the puzzles, and introduce important ideas along the way. We believe that this way, you will get a deeper understanding and will better appreciate the beauty of the underlying ideas (not to mention the self confidence that you gain if you invent these ideas on your own!). To bring your experience closer to IT-applications, we incorporate programming examples, problems, and projects in the specialization....
Introduction to Discrete Mathematics for Computer Science

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