Back to Combinatorics and Probability

## Combinatorics and Probability, University of California San Diego

4.6
202 ratings
40 reviews

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 `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....

### Top reviews

By ZB

Oct 13, 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.

By CZ

Sep 11, 2018

The final project is hard for me cuz I don't have Python experience. and the logic is a little bit complicated. That's not for absolutely beginners!

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40 Reviews

By Remy E. Francis

Feb 07, 2019

Sometimes difficult to follow along with the accent for material that I already found new and challenging. Needed to supplement with Khan Academy and other sources.

By Michael Khor Hock Eu

Jan 22, 2019

Prof Vlad has really great examples!

By Ziqi Yuan

Dec 31, 2018

Great! Challenging final project but worth trying!

By Serhat Giydiren

Dec 22, 2018

Excellent, thanks.

By Bryan W Berry

Nov 27, 2018

Much stronger than the first course in this series. I very much enjoyed Vladimir and Alexander's lectures. The weakest part, unfortunately, were Alexander Shen's weeks. I must credit him, however, for being very responsive on the forum.

By Miguel Diaz

Nov 26, 2018

Super interesting the topic about combinatorics

By Vijay Ram

Nov 24, 2018

While I imagine Alexander Shen to be a great person and a math genius, he seems entirely unprepared for the lectures. He speaks well, I can understand his accent, but his lack of preparation and poor slides make a difficult situation terrible. The other instructors do a much better job, but I also wish there were more tests of our knowledge.

Oct 13, 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.

By Saptarshi Manna

Oct 10, 2018

Concepts are presented in such a way that a novice can understand easily. For an advanced learner, there are concepts that are lit from a different perspective. Not all the instructors are equally competent. Sometimes you have to watch the videos twice to get the full understanding. But that's worth of your time. Overall enjoyable. Programming practices are also good and of intermediate quality.

By Charalampos Rafail Poulikidis

Oct 09, 2018

Most of the courses of this specialisation (not only on prob) are VERY hard to follow. Instructors lack of passion while teaching and they just reading the script from the slides. Whatever I passed and learned was from random sources at the internet.

To the instructors: Take a blackboard and start solving the problems by hand. By reading a long queue of numbers from slides for 10min, the student can't follow at all. This is not a simple presentation, this is math topics. You can't just pass a slide full of numbers and some sentences thinking that the student can comprehend all that stuff.

On the other hand, on the 3rd party quizzes has been made a magnificent job.