Good discrete mathematics notes?

Question

Good morning,

Do you know of a good resource for discrete mathematics notes, lectures and/or videos?

I found the classes + notes given to be lacking at my university...

Topics covered thus far:

• Logic theory
• Graph theory (walks, paths, cycles, circuits, forests, planar, Eulerian, Hamiltonian, minimal spanning tree, Prim's, Kruskell's, Four Color Theorem)
• Set theory (union, compliment, universal sets; equivalency relations, equivalency classes, matrices, 1-1, invertible, onto, congruences)
• Number theory (natural, real and integer sets)
• Proofs (strong induction, weak induction, well ordering, Euclid's algorithm)
• GCFs and GCDs, permutations, unordered permutations (choose)
• Binomial theorem (Pascal's triangle; finding coefficients)
• Modulo arithmetic
• Powers and prime numbers (with gcd and mod: Fermat's little theorem)

Thanks for all suggestions,

Alec Taylor

Answer 1

Stanley's Enumerative Combinatorics. It's actually one of the top books in combinatorics. A new second edition of his book is available (for now) in PDF on his web page:

http://www-math.mit.edu/~rstan/ec/ec1.pdf

It might be a little more advanced than what you're wanting. And, there's no graph theory in it.

Answer 2

Try Discrete mathematics, a set of notes by William Chen. Here are the chapter headings:

Chapter 1: LOGIC AND SETS
Chapter 2: RELATIONS AND FUNCTIONS
Chapter 3: THE NATURAL NUMBERS
Chapter 4: DIVISION AND FACTORIZATION
Chapter 5: LANGUAGES
Chapter 6: FINITE STATE MACHINES
Chapter 7: FINITE STATE AUTOMATA
Chapter 8: TURING MACHINES
Chapter 9: GROUPS AND MODULO ARITHMETIC
Chapter 10: INTRODUCTION TO CODING THEORY
Chapter 11: GROUP CODES
Chapter 12: PUBLIC KEY CRYPTOGRAPHY
Chapter 13: PRINCIPLE OF INCLUSION-EXCLUSION
Chapter 14: GENERATING FUNCTIONS
Chapter 15: NUMBER OF SOLUTIONS OF A LINEAR EQUATION
Chapter 16: RECURRENCE RELATIONS
Chapter 17: GRAPHS
Chapter 18: WEIGHTED GRAPHS
Chapter 19: SEARCH ALGORITHMS
Chapter 20: DIGRAPHS

Answer 3

I have nothing but nice things to say about Diestel's GTM "Graph Theory". You can view the whole book online here - http://diestel-graph-theory.com/basic.html

Of course, this only really addresses the graph theory from your question above, and much of it is probably at a higher level than you're asking for. Still worth plugging as an excellent resource.

Answer 4

For some combinatorics and graph theory, I highly recommend Tom Trotter's book, compiled from a set of lecture notes during a pair of semesters in which he taught (by a graduate student at the time, Mitch Keller) and freely available at his website.