Book:Rudolf Lidl/Applied Abstract Algebra

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

• 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