LIBERO WebOPAC Catalogue Display (W561)

Catalogue Information
Field name	Details
Dewey Class	512
Title	Applied Abstract Algebra ([EBook] /) / by Rudolf Lidl, Günter Pilz.
Author	Lidl, Rudolf
Added Personal Name	Pilz, Günter author.
Other name(s)	SpringerLink (Online service)
Publication	New York, NY : : Springer US, , 1984.
Physical Details	XVIII, 545 p. : online resource.
Series	Undergraduate texts in mathematics 0172-6056
ISBN	9781461564652
Summary Note	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. Cer 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 pre 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 mathe 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).:
Contents note	1 Lattices -- § 1. Properties of Lattices -- §2. Boolean Algebras -- §3. Minimal Forms of Boolean Polynomials -- Notes -- 2 Applications of Lattices -- §1. Switching Circuits -- §2. Propositional Logic -- §3. Further Applications -- Notes -- 3 Finite Fields and Polynomials -- §1. Rings and Fields -- §2. Finite Fields -- §3. Irreducible Polynomials over Finite Fields -- §4. Factorization of Polynomials over Finite Fields -- §5. The Nullspace of a Matrix (Appendix to §4) -- Notes -- 4 Coding Theory -- §1. Linear Codes -- §2. Cyclic Codes -- §3. Special Cyclic Codes -- Notes -- 5 Further Applications of Fields and Groups -- §1. Combinatorial Applications -- §2. Algebraic Cryptography -- §3. Linear Recurring Sequences -- §4. Fast Adding -- §5. Polya’s Theory of Enumeration -- Notes -- 6 Automata -- § 1. Semiautomata and Automata -- §2. Description of Automata; Examples -- §3. Semigroups -- §4. Input Sequences -- §5. The Monoid of a (Semi-) Automaton and the (Semi-) Automaton of a Monoid -- §6. Composition and Decomposition -- §7. Minimal Automata -- Notes -- 7 Further Applications of Semigroups -- §1. Formal Languages -- §2. Semigroups in Biology -- §3. Semigroups in Sociology -- 8 Solutions to the Exercises -- 1 -- 2 -- 3 -- 4 -- 5 -- 6 -- 7 -- A. Some Fundamental Concepts -- B. Computer Programs -- Author Index.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-1-4615-6465-2
Links to Related Works	Subject References: Algebra . Mathematics . Authors: Lidl, Rudolf . Pilz, Günter . Corporate Authors: SpringerLink (Online service) . Series: Undergraduate texts in mathematics . Classification: 512 .

Catalogue Display

Applied Abstract Algebra

Reviews