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Discrete Mathematics

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Author(s): Professor Arthur T. Benjamin, The Teaching Company
Series: The Great Courses: Science & Mathematics
Publisher: n/a
Year: 2009

Language: English
Pages: 160

1
What Is Discrete Mathematics?
2
Basic Concepts of Combinatorics
3
The 12-Fold Way of Combinatorics
4
Pascal's Triangle and the Binomial Theorem
5
Advanced Combinatorics—Multichoosing
6
The Principle of Inclusion-Exclusion
7
Proofs—Inductive, Geometric, Combinatorial
8
Linear Recurrences and Fibonacci Numbers
9
Gateway to Number Theory—Divisibility
10
The Structure of Numbers
11
Two Principles—Pigeonholes and Parity
12
Modular Arithmetic—The Math of Remainders

13
Enormous Exponents and Card Shuffling
14
Fermat's "Little" Theorem and Prime Testing
15
Open Secrets—Public Key Cryptography
16
The Birth of Graph Theory
17
Ways to Walk—Matrices and Markov Chains
18
Social Networks and Stable Marriages
19
Tournaments and King Chickens
20
Weighted Graphs and Minimum Spanning Trees
21
Planarity—When Can a Graph Be Untangled?
22
Coloring Graphs and Maps
23
Shortest Paths and Algorithm Complexity
24
The Magic of Discrete Mathematics