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Algebra I

Textbook for Students of Mathematics

Authors: Gorodentsev, Alexey L.

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  • Challenging amount of material thoughtfully organized for deep and fast learning
  • Large collection of exercises equipped with hints and a lot of problems for independent solution
  • Simple modern explanation of subjects usually omitted in basic courses, such as representations of the symmetric group, geometry of algebraic varieties, meaty aspects of the category theory etc
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eBook $54.99
price for USA in USD
  • ISBN 978-3-319-45285-2
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $69.99
price for USA in USD
Softcover $69.99
price for USA in USD
About this Textbook

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.

 


About the authors

A.L. Gorodentsev is professor at the Independent University of Moscow and  at the Faculty of Mathematics at the National Research University „Higher School of Economics“. 

He is working in the field of algebraic and symplectic geometry, homological algebra and representation theory connected with geometry of algebraic and symplectic varieties.

He is one of the first developers of the “Helix Theory” and semiorthogonal decomposition technique for studying the derived categories of coherent sheaves.

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)


Table of contents (20 chapters)

Table of contents (20 chapters)

Buy this book

eBook $54.99
price for USA in USD
  • ISBN 978-3-319-45285-2
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $69.99
price for USA in USD
Softcover $69.99
price for USA in USD
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Bibliographic Information

Bibliographic Information
Book Title
Algebra I
Book Subtitle
Textbook for Students of Mathematics
Authors
Copyright
2016
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing AG
eBook ISBN
978-3-319-45285-2
DOI
10.1007/978-3-319-45285-2
Hardcover ISBN
978-3-319-45284-5
Softcover ISBN
978-3-319-83257-9
Edition Number
1
Number of Pages
XX, 564
Number of Illustrations
37 b/w illustrations, 42 illustrations in colour
Topics