Librería Portfolio

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