Discrete Structures with Contemporary Applications

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

Biography

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.

"… 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