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Applied abstract algebra with Maple and MATLAB. 3rd edition. (English) Zbl 1348.00002

Textbooks in Mathematics. Boca Raton, FL: CRC Press (ISBN 978-1-4822-4823-4/hbk; 978-1-4822-4827-2/ebook). xvi, 539 p. (2016).
In this book (a third edition) the use of the mathematical software systems Maple and MATLAB about several topics (mainly combinatorics, graph theory, coding theory, and cryptography) is included. The study of fundamentals of abstract algebra is combined with many proper (and understable) examples and practical tasks. Any chapter of the book is organized as follows: firstly the corresponding general theory is given. After that the Maple and MATLAB materials (connected to the topic of this chapter) are presented and separated into different sections. In the end of any chapter the number of theoretical and computer exercises are included. Beginning with a review of groups and finite fields the authors go on considering block designs, classical error-correcting codes (coding theory, Chapters 2, 3, 4, and 5), Vigenere, RSA, and ElGamal ciphers, AES (cryptography, Chapters 6, 7, 8, 9, and 10), Polya and graph theory (combinatorial counting techniques, Chapters 11 and 12); finally dealing with a new topic (Chapter 13) which is focused on the mathematical models of Western music. Several other parts of the book were also updated. This edition also contains more than 100 new exercises.
The book can be very useful for students as a course on linear and abstract algebra as well as a basic course on coding theory and cryptography. Also, it can be used for training of participants in competitions with practical usage of mathematical software systems. The aim to integrate mathematical theory with Maple and MATLAB implementations is achieved.

MSC:

00A05 Mathematics in general
94-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to information and communication theory
94Bxx Theory of error-correcting codes and error-detecting codes
05-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to combinatorics
94A60 Cryptography
05B05 Combinatorial aspects of block designs
11T71 Algebraic coding theory; cryptography (number-theoretic aspects)
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