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Publisher:

Chapman & Hall/CRC

Publication Date:

2011

Number of Pages:

982

Format:

Hardcover

Price:

99.95

ISBN:

9781439817681

Category:

Textbook

[Reviewed by , on ]

Charles Ashbacher

03/11/2011

In a world of increasingly thick mathematics textbooks, this one is no exception. However, the reason for that thickness is exceptional: this is the most physically readable textbook that I have seen in a long time. The print is clear and large; it is one-and-one-half times the size of the text in another math book that I am reading. This is excellent, for eyestrain should not be a consequence of studying mathematics.

In terms of content, the material is fairly standard for the discrete mathematics course containing topics in a computer science path, as one can see from the table of contents.

The text is readable, there are many examples and in many cases proofs of the theorems are included. A large number of exercises are provided and split into two categories, the traditional math problem and exercises to be performed on a computer. The computer exercises require the writing of code and where appropriate algorithms in pseudocode are listed. Solutions to the odd numbered exercises are included in an appendix.

The two most important courses in the computer science major are the first programming and discrete math classes. Each establishes a foundation of skills that will be repeatedly used throughout the major field of study and this book is an excellent text for the development of the needed skills in math.

Charles Ashbacher splits his time between consulting with industry in projects involving math and computers, teaching college classes and co-editing The Journal of Recreational Mathematics. In his spare time, he reads about these things and helps his daughter in her lawn care business.

**Logic and Sets**

Logical Operators

Logical Quantifiers

Sets

**Relations and Functions, Boolean Algebra, and Circuit Design**Relations and Functions

Equivalence Relations and Partial Orderings

Boolean Algebra and Circuit Design

**The Integers, Induction, and Recursion**Mathematical Induction

Recursion

Some Topics in Elementary Number Theory

**Number Systems**Representations of Integers in Different Bases

Modular Arithmetic and Congruences

Matrices

Floating Point Arithmetic

Public Key Cryptography

**Counting Techniques, Combinatorics, and Generating Functions**Fundamental Principles of Counting

Permutations, Combinations, and the Binomial Theorem

Generating Functions

**Discrete Probability and Simulation**Introduction to Discrete Probability

Random Numbers, Random Variables, and Basic Simulations

**Complexity of Algorithms **Some Algorithms for Searching and Sorting

Growth Rates of Functions and the Complexity of Algorithms

**Graphs, Trees, and Associated Algorithms**Graph Concepts and Properties

Paths Connectedness, and Distances in Graphs

Trees

**Graph Traversal and Optimization Problems**

Graph Traversal Problems

Tree Growing and Graph Optimization Algorithms

Network Flows

**Randomized Search and Optimization Algorithms**

Randomized Search and Optimization: An Overview

Genetic Algorithms

**Appendix A: Pseudo Code Dictionary Appendix B: Solutions to all Exercises for the Reader Appendix C: Answers/Brief Solutions to Odd Numbered Exercises**

** **

**References **

**Index**

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