Discrete Structures with Contemporary Applications (Hardback) book cover

Discrete Structures with Contemporary Applications

By Alexander Stanoyevitch

© 2011 – Chapman and Hall/CRC

1,002 pages | 308 B/W Illus.

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Hardback: 9781439817681
pub: 2011-01-19
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Description

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.

Reviews

"… 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

Table of Contents

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

About the Author

Alexander Stanoyevitch is a professor at California State University–Dominguez Hills. He completed his doctorate in mathematical analysis at the University of Michigan, Ann Arbor, and has held academic positions at the University of Hawaii and the University of Guam. Dr. Stanoyevitch has taught many upper-level classes to mathematics and computer science students, has published several articles in leading mathematical journals, and has been an invited speaker at numerous lectures and conferences in the United States, Europe, and Asia. His research interests include areas of both pure and applied mathematics.

Subject Categories

BISAC Subject Codes/Headings:
COM046000
COMPUTERS / Operating Systems / General
MAT036000
MATHEMATICS / Combinatorics