Algebra I

Textbook for Students of Mathematics

By: Alexey L. Gorodentsev

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Paperback | 4 July 2018

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586 Pages

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23.5 x 15.5 x 3.02

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This book is the first volume of an intensive "Russian-style" two-year graduate course in abstract algebra, and introduces readers to the basic algebraic structures - fields, rings, modules, algebras, groups, and categories - and explains the main principles of and methods for working with them.

The course covers substantial areas of advanced combinatorics, geometry, linear and multilinear algebra, representation theory, category theory, commutative algebra, Galois theory, and algebraic geometry - topics that are often overlooked in standard undergraduate courses.

This textbook is based on courses the author has conducted at the Independent University of Moscow and at the Faculty of Mathematics in the Higher School of Economics. The main content is complemented by a wealth of exercises for class discussion, some of which include comments and hints, as well as problems for independent study.

Industry Reviews

"The book weaves together a great deal of classical material with a modern approach. ... the book consists of the large number of exercises ... which the author assigns for homework and the problems for independent study provided at the end of each chapter; a student who works through these will be well rewarded. ... instructors would find it more suitable for a graduate course in which the students are already familiar with the more elementary parts of the material." (John D. Dixon, zbMATH 1359.15001, 2017)

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