Discrete Structures with Contemporary Applications

Discrete Structures with Contemporary Applications

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Hardback
$104.95
ISBN 9781439817681
Cat# K10918
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Features

  • Covers many recent applications of discrete mathematics, including simulations, genetic algorithms, and public key cryptography
  • Presents algorithms in pseudo code
  • Offers sample programs via the author’s website
  • Illustrates difficult concepts with over 300 figures

Pedagogical Features

  • Follows the recommendations of the ACM
  • Introduces several supplementary topics that can form an excellent basis for student projects
  • Includes a wide variety of examples and exercises, with solutions in the appendices
  • Incorporates computer exercises that teach students how to write their own programs

Solutions manual available upon qualifying course adoption.

Summary

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.

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

Author Bio(s)

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.

Editorial Reviews

…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

Downloads Updates

Resource OS Platform Updated Description Instructions
Platform type December 20, 2010 Author site click on http://www.csudh.edu/math/astanoyevitch/discrete.html

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