Back to Combinatorics and Probability
University of California San Diego

Combinatorics and Probability

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 online 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 ‘consumers’ 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.

Status: Combinatorics
Status: Probability Distribution
BeginnerCourse23 hours

Featured reviews

JC

5.0Reviewed Sep 8, 2020

It's a perfect introduction to combinatorics and probability, short, fun, and easy to understand. I would like to see more puzzles, those are extremely fun and interesting

FF

4.0Reviewed Jul 31, 2020

Great course. The final Project unclear had instructions on how to provide input. I spent a lot of time trying to troubleshoot it even though I already have a correct solution

JY

4.0Reviewed Mar 1, 2018

Awesome course, good topics. Easy to get help. Some topics weren't that clear at first, but you'll eventually understand.

PR

5.0Reviewed Aug 2, 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.

SS

5.0Reviewed Jul 16, 2020

Great lessons, great instructors, literacy slides, this course has everything. I'm so proud to complete two out of five courses in this specialization!

ZB

5.0Reviewed Oct 12, 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.

TK

5.0Reviewed May 18, 2020

I lacked confidence in permutations and combinations since my high school, but now i am enjoying solving combinatorial problems. Thanks to professors

JC

5.0Reviewed Sep 1, 2020

Difficult topics discussed in easy to understand ways and uses fun and interesting problems/exercises to test your understanding.

KB

5.0Reviewed Dec 25, 2019

Great course, lots of good info, not too long. Some of the coding assignments and quizzes are challenging, but the staff respond very quickly to questions in the forums.

CW

5.0Reviewed Jul 8, 2021

the dainty old dude was the worst lecturer who rambled non-coherent nonsense. the younger folks were much better verbal communicators. overall great course!

KF

5.0Reviewed May 28, 2020

Amazing course, gave me geometrical intuitions some times that made understanding a whole lot easier. The explanation was quite clear.

SP

5.0Reviewed Feb 26, 2021

Special thanks to Prof. Vladimir Podolskii and Prof. Alexander S. Kulikov for their amazing explanations and diligent visuals of the concepts as well as problem sets. You Rock!

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