Courses:

Combinatorial Analysis >> Content Detail



Study Materials



Readings

Amazon logo When you click the Amazon logo to the left of any citation and purchase the book (or other media) from Amazon.com, MIT OpenCourseWare will receive up to 10% of this purchase and any other purchases you make during that visit. This will not increase the cost of your purchase. Links provided are to the US Amazon site, but you can also support OCW through Amazon sites in other regions. Learn more.

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

 








© 2017 Coursepedia.com, by Higher Ed Media LLC. All Rights Reserved.