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Combinatorial Analysis >> Content Detail



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Readings

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The readings are assigned in the required textbook: Amazon logo Bona, M. A Walk through Combinatorics. 1st ed. Singapore, SG: World Scientific Publishing Company, 2002. ISBN: 9810249012.


Lec #TopicsReadings
1Introduction

Pigeonhole Principle
Chapter 1
2Mathematical InductionChapter 2
3PermutationsChapter 3
4Binomial TheoremChapter 4
5Compositions

Integer Partitions
Chapter 5
6Set Partitions
7Cycles in Permutations

Stirling Numbers
Chapter 6
8Exam 1
9Inclusion-exclusion PrincipleChapter 7
10Inclusion-exclusion (cont.)

Mobius Inversion
11Recurrence Relations
12Generating FunctionsChapter 8
13Generating Functions (cont.)
14Catalan Numbers
15Generating Functions (cont.)
16Exam 2
17Graphs

Eulerian Walks

Hamiltonian Cycles
Chapter 9
18Trees

Counting Trees
Chapter 10
19Matrix-tree Theorem
20Matrix-tree Theorem (cont.)
21Matrix-tree Theorem and Eulerian Digraphs
22Bipartite Graphs and MatchingsChapter 11
23Planar Graphs

Polyhedra

Maps
Chapter 12
24Chromatic Polynomials
25Exam 3
26Polya Counting

Ramsey Theory

Probabilistic Method

 








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