Chapman and Hall/CRC
1,002 pages | 308 B/W Illus.
Reflecting many of the recent advances and trends in this area, Discrete Structures with Contemporary Applications covers the core topics in discrete structures as well as an assortment of novel applications-oriented topics. The applications described include simulations, genetic algorithms, network flows, probabilistic primality tests, public key cryptography, and coding theory.
A modern and comprehensive introduction to discrete structures
With clear definitions and theorems and carefully explained proofs, this classroom-tested text presents an accessible yet rigorous treatment of the material. Numerous worked-out examples illustrate key points while figures and tables help students grasp the more subtle and difficult concepts. "Exercises for the Reader" are interspersed throughout the text, with complete solutions included in an appendix. In addition to these, each section ends with extensive, carefully crafted exercise sets ranging from routine to nontrivial; answers can be found in another appendix. Most sections also contain computer exercises that guide students through the process of writing their own programs on any computing platform.
Accommodates various levels of computer implementation
Although the book highly encourages the use of computing platforms, it can be used without computers. The author explains algorithms in ordinary English and, when appropriate, in a natural and easy-to-understand pseudo code that can be readily translated into any computer language. A supporting website provides an extensive set of sample programs.
"… this textbook is excellent. The author clearly had put a lot of effort in presenting the topics clearly and as engaging as possible. His many years of teaching and mentoring clearly show. The more I read it through the more I like the book, especially how the exercises are so carefully selected and presented. For this reason alone, this book is worth keeping and using. …
The topics covered should provide enough materials for two or even three semester courses.
I heartily recommend this textbook and have been using it both in preparing teaching materials and in educating myself. …
The level of difficulty makes this book suitable for undergraduate and beginning graduate students of mathematics and computer science."
—IACR Book Reviews, September 2014
"…this is the most physically readable textbook that I have seen in a long time. The print is clear and large … 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 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, MAA Reviews, March 2011
Logic and Sets
Relations and Functions, Boolean Algebra, and Circuit DesignRelations and Functions
Equivalence Relations and Partial Orderings
Boolean Algebra and Circuit Design
The Integers, Induction, and RecursionMathematical Induction
Some Topics in Elementary Number Theory
Number SystemsRepresentations of Integers in Different Bases
Modular Arithmetic and Congruences
Floating Point Arithmetic
Public Key Cryptography
Counting Techniques, Combinatorics, and Generating FunctionsFundamental Principles of Counting
Permutations, Combinations, and the Binomial Theorem
Discrete Probability and SimulationIntroduction to Discrete Probability
Random Numbers, Random Variables, and Basic Simulations
Complexity of AlgorithmsSome Algorithms for Searching and Sorting
Growth Rates of Functions and the Complexity of Algorithms
Graphs, Trees, and Associated AlgorithmsGraph Concepts and Properties
Paths Connectedness, and Distances in Graphs
Graph Traversal and Optimization Problems
Graph Traversal Problems
Tree Growing and Graph Optimization Algorithms
Randomized Search and Optimization Algorithms
Randomized Search and Optimization: An Overview
Appendix A: Pseudo Code Dictionary
Appendix B: Solutions to all Exercises for the Reader
Appendix C: Answers/Brief Solutions to Odd Numbered Exercises