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MAT202: Introduction to Discrete Mathematics
TJ Yusun
Contents
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Contents
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Front Matter
Welcome Message
About This Resource
Feedback and Acknowledgements
Colophon
1
Review of MAT102
Sets and Functions
Logic and Proof Techniques
Integers and Divisibility
2
Counting Techniques
The Basic Counting Principles
Permutations and Combinations
Binomial Coefficients
The Balls in Bins Formula
Combinatorial Arguments
Summary
Exercises
3
Pigeonhole and Inclusion-Exclusion
The Pigeonhole Principle
Principle of Inclusion-Exclusion
Application: Derangements
Exercises
4
Congruence Modulo \(n\)
Equivalence Relations
Congruences and their Properties
Solving Congruences
Euler's Theorem
The Chinese Remainder Theorem
Exercises
5
Graph Theory
Modeling with Graphs
Basic Definitions
Eulerian Graphs
Isomorphisms and Subgraphs
Connectedness and Trees
Bipartite Graphs
Hamiltonian Graphs
Exercises
Back Matter
A
How to Read and Write Mathematics
Introduction to
L
a
T
e
X
Reading Mathematics
Writing Mathematics, Part I
Writing Mathematics, Part II
B
Notation
C
List of Results
D
List of Examples and Exercises
References
Authored in PreTeXt
MAT202: Introduction to Discrete Mathematics
TJ Yusun
Department of Mathematical and Computational Sciences
University of Toronto Mississauga
Mississauga, ON, Canada
tj.yusun@utoronto.ca
August 21, 2023
Welcome Message
About This Resource
Feedback and Acknowledgements
Colophon