Discrete Algebraic Methods
Subtitle: Arithmetic, Cryptography, Automata and Groups
By: Volker Diekert, Manfred Kufleitner, Gerhard Rosenberger, Ulrich Hertrampf
Series: De Gruyter Textbook; De Gruyter textbook
Publisher: De Gruyter
Published: 2016
Place of publication: Berlin; Boston
Language: eng; ger
Number of pages: 354
ISBN-13: 9783110416329; 9783110413335; 9783110413328
Subjects: Pre-Calculus; Cryptography; Reference; Textbooks; Algebraische Methode; Diskrete Mathematik; Algorithms; Computer science; Mathematics; MATHEMATICS; Essays; Ordered algebraic structures
Description: From basic algebraic structures to cryptography, arithmetic with elliptic curves, and automata - this textbook contains a modern introduction to discrete algebraic methods as required by mathematicians and computer scientists in the age of the internet. It lays foundations for theoretical computer science and is suitable for master students with a basic background in mathematics.

The idea behind this book is to provide the mathematical foundations for assessing modern developments in the Information Age. It deepens and complements the basic concepts, but it also considers instructive and more advanced topics. The treatise starts with a general chapter on algebraic structures; this part provides all the necessary knowledge for the rest of the book. The next chapter gives a concise overview of cryptography. Chapter 3 on number theoretic algorithms is important for developping cryptosystems, Chapter 4 presents the deterministic primality test of Agrawal, Kayal, and Saxena. The account to elliptic curves again focuses on cryptographic applications and algorithms. With combinatorics on words and automata theory, the reader is introduced to two areas of theoretical computer science where semigroups play a fundamental role. The last chapter is devoted to combinatorial group theory and its connections to automata.
Notes: Includes bibliographical references and index.

In English.
Table of contents: title: Frontmatter --; title: Preface --; title: Contents --; title: 1. Algebraic structures --; title: 2. Cryptography --; title: 3. Number theoretic algorithms --; title: 4. Polynomial time primality test --; title: 5. Elliptic curves --; title: 6. Combinatorics on words --; title: 7. Automata --; title: 8. Discrete infinite groups --; title: Solutions to exercises --; title: Bibliography --; title: Index.