Rudolf Lidl Livres

Focusing on the theory of finite fields, this book offers a comprehensive introduction that highlights its applications in combinatorics, coding theory, cryptology, and switching circuits. It is structured in two parts: the first covers fundamental concepts, while the second explores significant applications, especially in information theory and algebraic coding. With numerous worked examples and exercises, the text caters to advanced undergraduates and graduate students from various disciplines, making it accessible even to non-specialists interested in this vital area of modern algebra.

Focusing exclusively on the theory of finite fields, the book delves into the mathematical structures and properties that define these fields. It explores their applications in various areas, including coding theory and cryptography. With a systematic approach, the text provides in-depth explanations, examples, and exercises to enhance understanding, making it a valuable resource for students and researchers interested in advanced algebra and number theory.

Accessible to junior and senior undergraduate students, this survey contains many examples, solved exercises, sets of problems, and parts of abstract algebra of use in many other areas of discrete mathematics. Although this is a mathematics book, the authors have made great efforts to address the needs of users employing the techniques discussed. Fully worked out computational examples are backed by more than 500 exercises throughout the 40 sections. This new edition includes a new chapter on cryptology, and an enlarged chapter on applications of groups, while an extensive chapter has been added to survey other applications not included in the first edition. 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.

Frontmatter -- Vorbemerkung -- Inhalt -- 1. Grundlagen -- 2. Algebraische Strukturen -- 3. Halbgruppen -- 4. Gruppen -- 5. Ringe und Körper -- 6. Boolesche Algebra -- Literatur -- Symbolverzeichnis -- Namen- und Sachverzeichnis -- Backmatter