Combinatorics and Probability

Introduction to Discrete Mathematics for Computer Science,

Counting is one of the basic mathematically related tasks we encounter on a day to day basis. The main question here is the following. If we need to count something, can we do anything better than just counting all objects one by one? Do we need to create a list of all phone numbers to ensure that there are enough phone numbers for everyone? Is there a way to tell that our algorithm will run in a reasonable time before implementing and actually running it? All these questions are addressed by a mathematical field called Combinatorics. In this course we discuss most standard combinatorial settings that can help to answer questions of this type. We will especially concentrate on developing the ability to distinguish these settings in real life and algorithmic problems. This will help the learner to actually implement new knowledge. Apart from that we will discuss recursive technique for counting that is important for algorithmic implementations. One of the main `consumersâ€™ of Combinatorics is Probability Theory. This area is connected with numerous sides of life, on one hand being an important concept in everyday life and on the other hand being an indispensable tool in such modern and important fields as Statistics and Machine Learning. In this course we will concentrate on providing the working knowledge of basics of probability and a good intuition in this area. The practice shows that such an intuition is not easy to develop. In the end of the course we will create a program that successfully plays a tricky and very counterintuitive dice game. As prerequisites we assume only basic math (e.g., we expect you to know what is a square or how to add fractions), basic programming in python (functions, loops, recursion), common sense and curiosity. Our intended audience are all people that work or plan to work in IT, starting from motivated high school students. Do you have technical problems? Write to us: [email protected]

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Rating 4.4★ based on 51 ratings 7 weeks 6 weeks, 3-5 hours/week Oct 12 (last week) \$79 University of California San Diego, National Research University Higher School of Economics via Coursera Alexander S. Kulikov, Vladimir Podolskii On all desktop and mobile devices English Programming Mathematics Computer Science Algorithms Math And Logic

What people are saying

alexander shen

I love Professor Alexander Shen, because he makes me happy.

The weakest part, unfortunately, were Alexander Shen's weeks.

bit more

This one is a bit more 'mathy' than the first one, it has a good pace and the exercises are really cool I think the level could have been a bit more advanced.

However, I felt some of the videos could do with a bit more editing (with the typos and etc.).

final project

Challenging final project but worth trying!

The final project is hard for me cuz I don't have Python experience.

nice introduction

I completely recommend it Probability section was little weak It is better to read slides and do not watch the videos A very nice introduction to probability and combinatorics.

Hard to understand lecturer This course is a nice introduction to probability and give good ideas to make proof of combinatorics (the week 2 was the best), all of this give it in a nice an intuitive way.

probability theory

although I have learnt probability theory both in undergraduate and postgraduate level, it still gives me some inspiration toward probability theory.

Some paradoxes examples help me to understand the probability theory better and clearer.

lot more

Furthermore, for some of the weeks (week 4 say), there were a lot more material comparing to others (week 6 say).

Good first course in probability/combinatorics at the university level; last assignment had a lot more coding than other assignments, a lot more overall great course and it was exactly what I was looking for.

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