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AuthorLidl, Rudolf. author
TitleApplied Abstract Algebra [electronic resource] / by Rudolf Lidl, Gรผnter Pilz
ImprintNew York, NY : Springer US, 1984
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Descript XVIII, 545p. 175 illus. online resource


There is at present a growing body of opinion that in the decades ahead discrete mathematics (that is, "noncontinuous mathematics"), and therefore parts of applicable modern algebra, will be of increasing importance. Cerยญ tainly, one reason for this opinion is the rapid development of computer science, and the use of discrete mathematics as one of its major tools. The purpose of this book is to convey to graduate students or to final-year undergraduate students the fact that the abstract algebra encountered preยญ viously in a first algebra course can be used in many areas of applied mathematics. It is often the case that students who have studied mathematics go into postgraduate work without any knowledge of the applicability of the structures they have studied in an algebra course. In recent years there have emerged courses and texts on discrete matheยญ matics and applied algebra. The present text is meant to add to what is available, by focusing on three subject areas. The contents of this book can be described as dealing with the following major themes: Applications of Boolean algebras (Chapters 1 and 2). Applications of finite fields (Chapters 3 to 5). Applications of semigroups (Chapters 6 and 7)


1 Lattices -- ยง 1. Properties of Lattices -- ยง2. Boolean Algebras -- ยง3. Minimal Forms of Boolean Polynomials -- Notes -- 2 Applications of Lattices -- ยง1. Switching Circuits -- ยง2. Propositional Logic -- ยง3. Further Applications -- Notes -- 3 Finite Fields and Polynomials -- ยง1. Rings and Fields -- ยง2. Finite Fields -- ยง3. Irreducible Polynomials over Finite Fields -- ยง4. Factorization of Polynomials over Finite Fields -- ยง5. The Nullspace of a Matrix (Appendix to ยง4) -- Notes -- 4 Coding Theory -- ยง1. Linear Codes -- ยง2. Cyclic Codes -- ยง3. Special Cyclic Codes -- Notes -- 5 Further Applications of Fields and Groups -- ยง1. Combinatorial Applications -- ยง2. Algebraic Cryptography -- ยง3. Linear Recurring Sequences -- ยง4. Fast Adding -- ยง5. Polyaโ{128}{153}s Theory of Enumeration -- Notes -- 6 Automata -- ยง 1. Semiautomata and Automata -- ยง2. Description of Automata; Examples -- ยง3. Semigroups -- ยง4. Input Sequences -- ยง5. The Monoid of a (Semi-) Automaton and the (Semi-) Automaton of a Monoid -- ยง6. Composition and Decomposition -- ยง7. Minimal Automata -- Notes -- 7 Further Applications of Semigroups -- ยง1. Formal Languages -- ยง2. Semigroups in Biology -- ยง3. Semigroups in Sociology -- 8 Solutions to the Exercises -- 1 -- 2 -- 3 -- 4 -- 5 -- 6 -- 7 -- A. Some Fundamental Concepts -- B. Computer Programs -- Author Index

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