Topics in Applied Abstract Algebra / Edition 1

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This book presents interesting applications of abstract algebra to practical real-world problems. Especially for those whose interest in algebra is not confined to abstract theory, the text makes the study of abstract algebra more exciting and meaningful. The book is appropriate as either a text for an applied abstract algebra course or as a supplemental text for a standard course in abstract algebra. While fully developed, the algebraic theory presented is just what is required for the applications discussed in the book.

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Product Details

  • ISBN-13: 9780534419110
  • Publisher: Cengage Learning
  • Publication date: 11/29/2004
  • Series: The Brooks/Cole Series in Advanced Mathematics
  • Edition description: New Edition
  • Edition number: 1
  • Pages: 336
  • Product dimensions: 5.40 (w) x 8.40 (h) x 1.00 (d)

Meet the Author

S. K. Jain is a Distinguished Professor of Mathematics at Ohio University. He is also the Director of the Center of Ring Theory and its Applications. Before joining the faculty at Ohio University, he was a Reader in Mathematics at the University of Delhi (1965-70). Dr. Jain has held visiting professor appointments at several institutions worldwide. His visiting positions include the Riverside, Santa Barbara and Berkeley campuses of the University of California, the Ohio State University in Columbus, North Carolina State University in Raleigh, University of Chicago, McMaster University in Hamilton and University of Frankfurt as well as the Indian Statistical Institute, and the Indian Institute of Technology. Dr. Jain has authored more than 100 research articles that have been published in professional journals. He was awarded the Outstanding Graduate Faculty Award, 1999- Ohio University. A life member of the Indian Mathematical Society, he is also a member of the American Mathematical Society and the Society for Industrial and Applied Mathematics. He has delivered Professional lectures at mathematical meetings all over the world and has been the organizer of conferences on many topics in Abstract Algebra. He is an executive editor of the East-West Journal of Mathematics and executive editor of the Journal of Algebra and its Applications, published by World Scientific Press. He has supervised 18 Ph.D. dissertations in noncommutative rings, modules, and applied linear algebra.
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Table of Contents

0. PRELIMINARY ALGEBRAIC CONCEPTS. Sets, Mappings, Relations, and Binary Operations. Groups and Semigroups. Cyclic Groups and Order of an Element. Subgroups of a Group. Quotient Groups and Homomorphisms. Applications of Groups in Number Theory. Rings and Fields. Finite Fields. 1. BOOLEAN ALGEBRAS AND SWITCHING CIRCUITS. Boolean Algebras. Switches and Logic Gates. Laws of Boolean Algebra. Boolean Polynomials and Boolean Functions. Switching Circuits and Gate Networks. Simplification of Circuits. Designing of Circuits. Bridge Circuits. 2. BALANCED INCOMPLETE BLOCK DESIGNS. Basic Definitions and Results. Incidence Matrix of a BIBD. Construction of BIBDs from Difference Sets. Construction of BIBDs using Quadratic Residues. Difference Set Families. Construction of BIBDs from Finite Fields. Construction of BIBDs from Nearrings. Planar Nearrings. Finite Integral Planar Nearrings and BIBDs. Finite Fields and Planar Nearrings. 3. ALGEBRAIC CRYPTOGRAPHY. Substitution Ciphers. Algebraic Enciphering Algorithms and Classical Cryptosystems. Block Ciphers and Advanced Encryption Standard. Public-key Cryptosystems. 4. CODING THEORY. Introduction to Error-correcting Codes. Linear Codes. Cyclic Codes. BHC Codes. 5. SYMMETRY GROUPS AND COLOR PATTERNS. Permutation Groups. Groups of Symmetries. Colorings and Color Patterns. Action of a Group on a Set. Burnside Theorem and Color Patterns. Polya's Theorem and Pattern Inventory. Generating Functions for Non-isomorphic Graphs. 6. WALLPAPER PATTERN GROUPS. Group of Symmetries of a Plane. Wallpaper Pattern Groups. Change of Basis in R2. Point Groups and Lattice Types. Equivalence of WP Groups. Classification of Point Groups. Classification of WP Groups. Sample Patterns.

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