Günter Pilz - Böcker

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).

This is a survey, accessible to junior/senior undergraduate students and containing many examples, solved exercises, and sets of problems, of some parts of abstract algebra that are of use in many other areas of discrete mathematics. Three major themes are particularly relevant to computer science, Boolean algebras and switching circuits, finite fields and algebraic coding, and semigroups and automata. The topics of the book can be studied independently of each other, although the book is a mathematics book, the authors have made great efforts to address the needs of the users of the techniques that are being discussed. There is a special emphasis on fully worked out computational examples. More than 500 exercises accompany the 40 sections. This new edition includes major changes to the first edition: corrections and improvements to the first four chapters, a new chapter on Cryptology, and an enlarged chapter on Applications of Groups. An extensive chapter has been added to survey other (mostly recent) applications, many of which were not included in the first edition, nor are commonly found in undergraduate texts.The book assumes knowledge of the material covered in a course on linear algebra and, preferably, a first course in (abstract) algebra covering the basics of groups, rings, and fields.