Concrete Abstract Algebra: From Numbers to Groebner Bases

Description

Concrete Abstract Algebra develops the theory of abstract algebra from numbers to Groebner bases, whilst taking in all the usual material of a traditional introductory course. In addition there is a rich supply of topics like cryptography, factoring algorithms for integers, quadratic residues, finite fields, factoring algorithms for polynomials and systems of non-linear equations. A special feature is that Groebner bases do not appear as an isolated example. They are fully integrated as a subject that can be successfully taught in an undergraduate context. Lauritzen's approach to teaching abstract algebra is based on an extensive use of examples, applications and exercises. The basic philosophy is that inspiring, non-trivial applications and examples give motivation and ease the learning of abstract concepts. This book is built on several years of experience teaching introductory abstract algebra at Aarhus, where the emphasis on concrete and inspiring examples has improved student performance significantly. Solutions to the exercises are available to lecturers from solutions@cambridge.org.

'I highly recommend this book ... If you are looking for a solid introduction to the topic of abstract algebra, this is the book for you.' Computing Reviews 'A very useful book, which emphazises the relation between number theory and algebra offering also a very comprehensible introduction to a relatively new branch of algebra.' Monatshefte fur Mathematik '... this textbook is absolutely self-contained, with the prerequisites kept to a minimum. The exposition is perfectly lucid, rigorous, detailed and user-friendly, which makes the book also suitable for private study. In summary, this is a highly interesting and original textbook on basic abstract algebra, with many topical extras and didactic novelties. It is perfectly suited for beginners in the field...' Werner Kleinert, Zentralblatt MATH 'Unlike many books on abstract algebra, this one is written in a very lively style, with emphasis on illuminating examples and applications. This makes the book a valuable addition to undergraduate literature on this topical subject.' EMS Newsletter