Algebra and Number Theory - A Selection of Highlights (2nd, revised Edition)

This second edition gives a thorough introduction to the vast field of Abstract Algebra with a focus on its rich applications. It is among the pioneers of a new approach to conveying abstract algebra starting with rings and fields, rather than with groups. Our teaching experience shows that examples of groups seem rather abstract and require a certain formal framework and mathematical maturity that would distract a course from its main objectives. Our philosophy is that the integers provide the most natural example of an algebraic structure that students know from school. A student who goes through ring theory first, will attain a solid background in Abstract Algebra and be able to move on to more advanced topics. The centerpiece of our book is the development of Galois Theory and its important applications, such as the solvability by radicals and the insolvability of the quintic, the fundamental theorem of algebra, the construction of regular n-gons and the famous impossibilities: squaring the circling, doubling the cube and trisecting an angle. However, our book is not limited to the foundations of abstract algebra but concludes with chapters on applications in Algebraic Geometry and Algebraic Cryptography.

General

Imprint:	De Gruyter
Country of origin:	Germany
Series:	De Gruyter Textbook
Release date:	September 2023
First published:	2023
Authors:	Benjamin Fine • Anja Moldenhauer • Gerhard Rosenberger • Annika Schürenberg • Leonard Wienke
Dimensions:	240 x 170mm (L x W)
Pages:	390
Edition:	2nd, revised Edition
ISBN-13:	978-3-11-078998-0
Categories:	Books
LSN:	3-11-078998-1
Barcode:	9783110789980

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