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Algebra II: Textbook for Students of Mathematics de Alexey L. Gorodentsev

Algebra II: Textbook for Students of Mathematics

Autor Alexey L. Gorodentsev
en Limba Engleză Hardback – 21 feb 2017
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.

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Specificații

ISBN-13: 9783319508528
ISBN-10: 3319508520
Pagini: 370
Ilustrații: XV, 370 p. 155 illus., 2 illus. in color.
Dimensiuni: 155 x 235 x 27 mm
Greutate: 0.72 kg
Ediția:1st ed. 2017
Editura: Springer International Publishing
Colecția Springer
Locul publicării:Cham, Switzerland

Cuprins

§1Tensor Products.- §2 Tensor Algebras.- §3 Symmetric Functions.- §4 Calculus of Arrays, Tableaux, and Diagrams.- §5 Basic Notions of Representation Theory.- §6 Representations of Finite Groups in Greater Detail.- §7 Representations of Symmetric Groups.- §8 sl_2-Modules.- §9 Categories and Functors.- §10 Extensions of Commutative Rings.- §11 Affine Algebraic Geometry.- §12 Algebraic Manifolds.- §13 Algebraic Field Extensions.- §14 Examples of Galois Groups.- References.- Hints to Some Exercises.- Index.

Recenzii

“This is the second of a two-volume set of books offering a ‘Russian-style’ intensive introduction to abstract algebra. … Each chapter contains both ‘exercises’ that are imbedded in the text, and ‘problems’ that are collected at the end of each chapter. … In summary, this book, like its predecessor, seems to have been written for mathematicians … .” (Mark Hunacek, MAA Reviews, March, 2017) 
“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) 

Notă biografică

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.

Textul de pe ultima copertă

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.

Caracteristici

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