Introduction to Enumerative Combinatorics

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Combinatorics is a branch of mathematics which deals with finite sets and their cardinalities. It is about counting certain objects having certain given properties. A typical question in combinatorics starts with the words "In how many ways" (we can do something). "In how many ways can we split 100 in a sum of distinct positive integers?", as an example. This online course is partially based on the course “Discrete Mathematics” for HSE bachelor students majoring in mathematics. The first half of the course (lectures 1 to 4) will be devoted to basic principles of enumeration. We will encounter basic combinatorial notions such as permutations, binomial coefficioents, Fibonacci and Catalan numbers, etc. In the second part of the course (lectures 4 to 8) we will be dealing with a very powerful method of solving combinatorial problems, namely generating functions. With their help we will study recurrence relations, partitions and variations of binomial coefficients -- the Gaussian binomial coefficients or q-binomial coefficients as they are sometimes called. The course consists of an introduction and eight lectures -- a lecture per week. Each lecture lasts for 1h30m approximately and is split into several shorter parts. Weeks 1-3 and 5-7 contain a quiz, whereas weeks 4 and 8 end by peer-graded assignements -- midterm and final exams. Do you have technical problems? Write to us: [email protected]