Book:Rudolf Lidl/Applied Abstract Algebra

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Rudolf Lidl and Günter Pilz: Applied Abstract Algebra

Published $1997$, 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