Book:Rudolf Lidl/Applied Abstract Algebra
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Rudolf Lidl and Günter Pilz: Applied Abstract Algebra
Published $\text {1997}$, Springer
- ISBN 978-0387982908
This book is part of Springer's Undergraduate Texts in Mathematics series.
Subject Matter
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