Discrete Mathematics And Algebraic Structures

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Fundamental Structures of Algebra and Discrete Mathematics

Introduces and clarifies the basic theories of 12 structural concepts, offering a fundamental theory of groups, rings and other algebraic structures. Identifies essentials and describes interrelationships between particular theories. Selected classical theorems and results relevant to current research are proved rigorously within the theory of each structure. Throughout the text the reader is frequently prompted to perform integrated exercises of verification and to explore examples.
Discrete Mathematics and Algebraic Structures

Author: Larry J. Gerstein
language: en
Publisher: W H Freeman & Company
Release Date: 1987-01-01
Provides a brief but substantial introduction to ideas, structures and techniques in discrete mathematics and abstract algebra. It addresses many of the common mathematical needs of students in mathematics and computer science at undergraduate level.
Discrete Mathematics

Conveying ideas in a user-friendly style, this book has been designed for a course in Applied Algebra. The book covers graph algorithms, basic algebraic structures, coding theory and cryptography. It will be most suited for senior undergraduates and beginning graduate students in mathematics and computer science as also to individuals who want to have a knowledge of the below-mentioned topics. Provides a complete discussion on several graph algorithms such as Prims algorithm and Kruskals algorithm for sending a minimum cost spanning tree in a weighted graph, Dijkstras single source shortest path algorithm, Floyds algorithm, Warshalls algorithm, Kuhn-Munkres Algorithm. In addition to DFS and BFS search, several applications of DFS and BFS are also discussed. Presents a good introduction to the basic algebraic structures, namely, matrices, groups, rings, fields including finite fields as also a discussion on vector spaces and linear equations and their solutions. Provides an introduction to linear codes including cyclic codes. Presents a description of private key cryptosystems as also a discussion on public key cryptosystems such as RSA, ElGamal and Miller-Rabin. Finally, the Agrawal-KayalSaxena algorithm (AKS Algorithm) for testing if a given positive integer is prime or not in polynomial time is presented- the first time in a textbook. Two distinguished features of the book are: Illustrative examples have been presented throughout the book to make the readers appreciate the concepts described. Answers to all even-numbered exercises in all the chapters are given.