This free online discrete mathematics textbook is broken down into four basic concepts – Counting and Listing, Functions, Decision Trees and Recursion, and Basic Concepts in Graph Theory.

It was written in 2010 by Edward S. Bender and S. Gill Williamson – faculty members from the Department of Computer Science and Engineering at the University of California San Diego. Discrete math is useful for students hoping to pursue the fields of computer science, engineering, biology, sociology, economics and operations research. The authors have opted to present their material in the “powerful and universal language of mathematics.” Their discrete mathematics textbook was designed for sophomores who have taken a course in Java programming or are con-currently taking a course in Java and who have already taken an introductory course in discrete mathematics that would cover topics such as Arithmetic, Logic and Numbers.

## Table of Contents for *Lists, Decisions and Graphs*

- Basic Counting and Listing
- 1. Lists with Repetitions
- 2. Lists Without Repetition
- 3. Sets
- 4. Probability and Basic Counting
- Functions
- 1. Some Basic Terminology
- 2. Permutations
- 3. Other Combinatorial Aspects of Functions
- 4. Functions and Probability
- Decision Trees and Recursion
- 1. Basic Concepts of Decision Trees
- 2. Recursive Algorithms
- 3. Decisions Trees and Conditional Probability
- 4. Inductive Proofs and Recursive Equations
- Basic Concepts in Graph Theory
- 1. What is a Graph?
- 2. Digraphs, Paths and Subgraphs
- 3. Trees
- 4. Rates of Growth and Analysis of Algorithms

View this Free Online Material at the source:

Lists, Decisions and Graphs