Applied Discrete Structures by Al Doerr and Ken Levasseur is a free open content textbook in discrete mathematics. Originally published in 1984 & 1989 by Pearson, the book has been updated to include references to Mathematica and Sage, the open source computer algebra system.
Contents:
Front Matter: Contents and Introduction
Chapter 1: Set Theory I
Chapter 2: Combinatorics
Chapter 3: Logic
Chapter 4: More on Sets
Chapter 5: Introduction to Matrix Algebra
Chapter 6: Relations and Graphs
Chapter 7: Functions
Chapter 8: Recursion and Recurrence Relations
Chapter 9: Graph Theory
Chapter 10: Trees
Chapter 11: Algebraic Systems
Chapter 12: More Matrix Algebra
Chapter 13: Boolean Algebra
Chapter 14: Monoids and Automata
Chapter 15: Group Theory and Applications
Chapter 16: An Introduction to Rings and Fields
Solutions to Odd-Numbered Exercises
Ken Levasseur (Faculty)
Just a few other comments on our text:
It was originally published as Applied Discrete Structures for Computer Science, first by SRA and then by MacMillan. Pearson owned the copyright in 2010, but the released it to us at no cost, to our surprise.
The 1980's version featured Pascal, and we've replaced it with Mathematica and Sage.