Course No.：21603Z
Period：10
Credits：0.5
Course Category：Lecture
Primary Coverage：
Talk 1. Basic Counting. In the first lecture we review the basic techniques and results in enumeration, including the twelve-fold way, set and integer partitions, and the famous Catalan family.
Talk 2. All about Permutations. Perhaps the most basic sequences in discrete mathematics are permutations. We describe several representations of permutations: as words, functions, union of cycles, and various labeled trees; and discuss the combinatorial properties and statistics of them.
Talk 3. Linear Algebra in Graph Theory. We show how to use linear algebra to obtain combinatorial properties of discrete structures. In particular, how to understand the eiganvalues of a matrix coming from a graph or digraph. Applications in enumeration will be discussed.
Talk 4. Linear Algebraic in Combinatorics. This is a survey on the fundamental ideas and results of enumerative combinatorics. I will present various algebraic tools, including formal power series, reflection principle, sieve methods, and factorization in free monoids.
Talk ５. Probabilistic Methods in Combinatorics
The probabilistic method is a powerful tool in graph theory and combinatorics, which proves the existence of a configuration by creating a suitable probability space and by showing a positive probability that the random configuration meets the desired criteria. In this talk I will present some basic techniques of probabilistic combinatorics, along with applications in computer science, discrete geometry, and number theory.
Author：Huafei Yan
