Discrete structures with contemporary applications / Alexander Stanoyevitch.

Enhanced descriptions from Syndetics:

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 provided by Syndetics

• 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 notes provided by Syndetics

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.