Enumerative combinatorics deals with finite sets and their cardinalities. In other words, a typical problem of enumerative combinatorics is to find the number of ways a certain pattern can be formed. In the first part of our course we will be dealing with elementary combinatorial objects and notions: permutations, combinations, compositions, Fibonacci and Catalan numbers etc. In the second part of the course we introduce the notion of generating functions and use it to study recurrence relations and partition numbers. The course is mostly self-contained. However, some acquaintance with basic linear algebra and analysis (including Taylor series expansion) may be very helpful. Do you have technical problems? Write to us: coursera@hse.ru
Chain rule. Inverse function theorem
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Avis
DP
Apr 21, 2017
Very good gourse, I persoally enjoyed the lectures in which the relatipnship with other areas of mathematics were discussed.
CX
Feb 12, 2018
by far the best math course I had (and I've taken many) on coursera
À partir de la leçon
Generating functions, continued. Generating function of the Catalan sequence
In this lecture we discuss further properties of formal power series. In particular, we prove an analogue of the binomial theorem for an arbitrary rational exponent. We apply this technique to computing the generating function of the sequence of Catalan numbers.
Enseigné par
Evgeny Smirnov
Associate Professor
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