Mikhail Ivanov

Spring 2021

475 Introduction to Combinatorics, Section 002

Syllabus
Midterm 1 , Solutions
Midterm 2 , Solutions
Final , Solutions
Slides
1 4 basic counting principles
2 k-permutations and k-combinations of sets
3 Permutations of multisets
4 Combinations of multisets and Probability
5 Pigeonhole principle I
6 Pigeonhole principle II
7 Generating permutations & inversions
8 Generating combinations
9 Partial orders and equivalence relations
10 Binomial coefficients I
11 Binomial coefficients II
12 Sperner Theorem and Multinomial Theorem
13 z choose k as a polynomial
14 More on posets
15 Inclusion-Exclusion formula and applications
16 Derangements
17 Permutations with restrictions I
19 Permutations with restrictions II
20 The Fibonacci sequence
21 Generating functions
22 Exponential Generating Functions
23 Linear recurrence relations I
24 Linear recurrence relations II
25 Linear recurrence relations III and The Catalan numbers
26 Catalan numbers II
27 Catalan numbers III
28 Stirling numbers of 2nd kind
29 Bell numbers and Stirling numbers of 1st kind
31 Partition numbers
32 Basic properties of graphs
33 Connected components and Eulerian Trails
35 Open Eulerian trails and Hamiltonian cycles
Slides_36_Knight's tour problems
Slides_37_Trees and Spanning Trees
Slides_38_The Shannon Switching Game
Slides_39_Review

461 College Geometry

Fall 2020

475 Introduction to Combinatorics, Section 003