Book:Rudolf Lidl/Applied Abstract Algebra

This book is part of Springer's Undergraduate Texts in Mathematics series.

Subject Matter

 * Abstract Algebra

Contents

 * Preface
 * List of Symbols


 * 1 Lattices
 * 1 Properties and Examples of Lattices
 * 2 Distributive Lattices
 * 3 Boolean Algebras
 * 4 Boolean Polynomials
 * 5 Ideals, Filters, and Equations
 * 6 Minimal Forms of Boolean Polynomials
 * Notes


 * 2 Applications of Lattices
 * 7 Switching Circuits
 * 8 Applications of Switching Circuits
 * 9 More Applications of Boolean Algebras
 * Notes


 * 3 Finite Fields and Polynomials
 * 10 Some Group Theory
 * 11 Rings and Polynomials
 * 12 Fields
 * 13 Finite Fields
 * 14 Irreducible Polynomials over Finite Fields
 * 15 Factorization of Polynomials over Finite Fields
 * Notes


 * 4 Coding Theory
 * 16 Introduction to Coding
 * 17 Linear Codes
 * 18 Cyclic Codes
 * 19 Special Cyclic Codes
 * 20 Decoding BCH Codes
 * Notes


 * 5 Cryptology
 * 21 Classical Cryptosystems
 * 22 Public Key Cryptosystems
 * 23 Discrete Logarithms and Other Ciphers
 * Notes


 * 6 Applications of Groups
 * 24 Fast Adding
 * 25 Pólya's Theory of Enumeration
 * 26 Image Understanding
 * 27 Symmetry Groups
 * Notes


 * 7 Further Applications of Algebra
 * 28 Semigroups
 * 29 Semigroups and Automata
 * 30 Semigroups and Formal Languages
 * 31 Semigroups and Biology
 * 32 Semigroups and Sociology
 * 33 Linear Recurring Sequences
 * 34 Fast Fourier Transforms
 * 35 Latin Squares
 * 36 Block Designs
 * 37 Hadamard Matrices, Transforms, and Networks
 * 38 Gröbner Bases for Algebraic and Differential Equations
 * 39 Systems Theory
 * 40 Abstract Data Types
 * Notes


 * Bibliography
 * Index