Languages and Machines
by C. D. H. Cooper
Publisher: Macquarie University 2008
This is a text on discrete mathematics that discusses the mathematics behind computing science. It includes chapters on logic, set theory and strings and languages. There are some chapters on finite-state machines, some chapters on Turing machines and computability, and a couple of chapters on codes.
Download or read it online for free here:
(multiple PDF files)
by Rupinder Sekhon - Connexions
Applied Finite Mathematics covers topics including linear equations, matrices, linear programming (geometrical approach and simplex method), the mathematics of finance, sets and counting, probability, Markov chains, and game theory.
by Vladlen Koltun - Stanford University
Contents: Sets and Notation; Induction; More Proof Techniques; Divisibility; Prime Numbers; Modular Arithmetic; Relations and Functions; Mathematical Logic; Counting; Binomial Coefficients; Inclusion-Exclusion Principle; Pigeonhole Principle; etc.
by A.F. Pixley - Harvey Mudd College
This text is an introduction to a selection of topics in discrete mathematics: Combinatorics; The Integers; The Discrete Calculus; Order and Algebra; Finite State Machines. The prerequisites include linear algebra and computer programming.
Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous. This book will help you think well about discrete problems: problems where tools like calculus fail because there's no continuity.