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
Syllabus
Midterm 1
,
Solutions
Midterm 2
,
Solutions
Final
,
Solutions
Slides
Slides_1_4 basic counting principles
Slides_2_k-permutations and k-combinations of sets
Slides_3_Permutations of multisets
Slides_4_Combinations of multisets and Probability
Slides_5_Pigeonhole principle first examples
Slides_6_Pigeonhole principle advanced
Slides_8_Generating permutations & inversions
Slides_9_Generating combinations
Slides_10_Partial orders and equivalence relations
Slides_11_Binomial coefficients
Slides_12_Properties of Binomial Coefficients
Slides_13_Sperner Theorem and Multinomial Theorem
Slides_14_x choose k as a polynomial
Slides_15_More on posets
Slides_16_Inclusion-Exclusion formula and applications
Slides_17_Derangements
Slides_18_Permutations with restrictions
Slides_19_Some combinatorial number theory
Slides_20_Fibonacci sequence
Slides_21_Generating functions
Slides_22_Exponential Generating Functions
Slides_23_Linear recurrence relations I
Slides_24_Linear recurrence relations II
Slides_25_Recurrence relations
Slides_26_Catalan numbers I
Slides_27_Catalan numbers II
Slides_28_Stirling numbers of 2nd kind
Slides_29_Bell numbers and Stirling numbers of 1st kind
Slides_30_Partition numbers
Slides_31_Basic Properties of Graphs
Slides_32_Connected components and Eulerian Trails
Slides_33_Open Eulerian trails
Slides_34_Review of Midterm Exam 2 and Enumerative combinatorics
Slides_35_Hamiltonian paths and cycles and Bipartite Graphs
Slides_36_Knight's tour problems
Slides_37_Trees and Spanning Trees
Slides_38_The Shannon Switching Game
Slides_39_Review