Overview
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
Includes supplementary material: sn.pub/extras
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Table of contents (14 chapters)
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Front Matter
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Back Matter
Keywords
About this book
This book is the second volume of an intensive “Russian-style” two-year undergraduate 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.
Reviews
“This textbook contains fourteen chapters furnished with a lot of examples, counterexamples and numerous exercises, some of which are provided with commentary and hints, as well as problems for independent solution that were assigned as homework. … This textbook is self-contained, well written and recommended to undergraduate, graduate and Ph. D. students and it might be very useful for advanced algebra lectures as well.” (Marek Golasiński, zbMATH, Vol. 1365.13001, 2017)
Authors and Affiliations
About the author
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.
Bibliographic Information
Book Title: Algebra II
Book Subtitle: Textbook for Students of Mathematics
Authors: Alexey L. Gorodentsev
DOI: https://doi.org/10.1007/978-3-319-50853-5
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing AG 2017
Hardcover ISBN: 978-3-319-50852-8Published: 22 February 2017
Softcover ISBN: 978-3-319-84507-4Published: 13 July 2018
eBook ISBN: 978-3-319-50853-5Published: 12 February 2017
Edition Number: 1
Number of Pages: XV, 370
Number of Illustrations: 153 b/w illustrations, 2 illustrations in colour
Topics: Algebra