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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. Contents:Algebraic structuresCryptographyNumber theoretic algorithmsPolynomial time primality testElliptic curvesCombinatorics on wordsAutomataDiscrete infinite groups

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"This extremely reader-friendly textbook covers a broad range of practical topics in the intersection of abstract algebra and computer science. [...] Each chapter ends with a well-chosen set of approachable problems, valuable to instructors and students alike. [...] Overall, authors Diekert, Kufleitner, Rosenberger, and Hertrampf have given us an excellent book on a fascinating area of mathematical practice. I warmly recommend it to readers interested in these topics."
James A. Swenson in: MAA November 2017 https://www.maa.org/press/maa-reviews/discrete-algebraic-methods

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Volker Diekert, Manfred Kufleitner and Ulrich Hertrampf, Stuttgart, Germany; Gerhard Rosenberger, Hamburg, Germany.

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