This book communicates the spirit of mathematics by means of simple ideas and problems, emphasizing exploration rather than drill. Its accessible approach encourages appreciation of mathematics and is ideal for readers with weak backgrounds, yet is interesting enough to involve anyone. Counting. Probability. Statistics. Geometry. Logic. Exponential Growth. Averages. Natural Numbers. Changing Bases. Clock Arithmetic. Secret Writing. Infinite Sets. Number Theory Selections. For anyone who needs to learn or review basic math concepts.

Mathematics for the Liberal Arts Student

Science & Math

Wisner, Robert J.

Walker, Carol L.

Brewer, James W.

Mathematics

Pearson College Div

Emphasizing the fact that solid mathematics leads to solid applications, this book builds a mathematical foundation that includes topics in number theory and the theory of infinite fields. It includes time-locked versions of Scientific Notebook and MuPAD that will help professionals quickly get up to speed. Chapter topics cover integers and computer algebra, codes, Euclidean algorithm, ciphers, error control codes, Chinese remainder theorem, theorems of Fermat and Euler, public key ciphers, finite fields, error-correcting codes, advanced encryption standard, and polynomial algorithms and fast fourier transforms. For data security officers.

Applied Algebra: Codes, Ciphers, and Discrete Algorithms

Computers & Technology

Hardy, Darel W.

Computer Science

Using mathematical tools from number theory and finite fields, Applied Algebra: Codes, Ciphers, and Discrete Algorithms, Second Edition presents practical methods for solving problems in data security and data integrity. It is designed for an applied algebra course for students who have had prior classes in abstract or linear algebra. While the content has been reworked and improved, this edition continues to cover many algorithms that arise in cryptography and error-control codes. New to the Second Edition <ul>
<li>A CD-ROM containing an interactive version of the book that is powered by Scientific Notebook®, a mathematical word processor and easy-to-use computer algebra system</li> <li>New appendix that reviews prerequisite topics in algebra and number theory</li> <li>Double the number of exercises</li> </ul> Instead of a general study on finite groups, the book considers finite groups of permutations and develops just enough of the theory of finite fields to facilitate construction of the fields used for error-control codes and the Advanced Encryption Standard. It also deals with integers and polynomials. Explaining the mathematics as needed, this text thoroughly explores how mathematical techniques can be used to solve practical problems. About the Authors Darel W. Hardy is Professor Emeritus in the Department of Mathematics at Colorado State University. His research interests include applied algebra and semigroups. Fred Richman is a professor in the Department of Mathematical Sciences at Florida Atlantic University. His research interests include Abelian group theory and constructive mathematics. Carol L. Walker is Associate Dean Emeritus in the Department of Mathematical Sciences at New Mexico State University. Her research interests include Abelian group theory, applications of homological algebra and category theory, and the mathematics of fuzzy sets and fuzzy logic.

Applied Algebra: Codes, Ciphers and Discrete Algorithms, Second Edition (Discrete Mathematics and Its Applications)

Richman, Fred

Chapman and Hall/CRC

Type-2 fuzzy sets extend both ordinary and interval-valued fuzzy sets to allow distributions, rather than single values, as degrees of membership. Computations with these truth values are governed by the truth value algebra of type-2 fuzzy sets. The Truth Value Algebra of Type-2 Fuzzy Sets: Order Convolutions of Functions on the Unit Interval explores the fundamental properties of this algebra and the role of these properties in applications. Accessible to anyone with a standard undergraduate mathematics background, this self-contained book offers several options for a one- or two-semester course. It covers topics increasingly used in fuzzy set theory, such as lattice theory, analysis, category theory, and universal algebra. The book discusses the basics of the type-2 truth value algebra, its subalgebra of convex normal functions, and their applications. It also examines the truth value algebra from a more algebraic and axiomatic view.

The Truth Value Algebra of Type-2 Fuzzy Sets: Order Convolutions of Functions on the Unit Interval (Chapman & Hall/CRC Monographs and Research Notes in Mathematics)

Harding, John

Walker, Elbert A.

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Books by Walker, Carol L.