Autor: Alexey L. Gorodentsev
ISBN-13: 9783319452845
Veröffentl: 01.01.2017
Einband: Book
Seiten: 564
Gewicht: 1027 g
Format: 246x169x40 mm
Sprache: Englisch

Algebra I

Textbook for Students of Mathematics, Originaltitel:Algebra. Uchebnik dlya studentov-matematikov. Chast' 1
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Notations and Abbreviations.- 1 Set-Theoretic and Combinatorial Background.- 2 Integers and Residues.- 3 Polynomials and Simple Field Extensions.- 4 Elementary Functions and Power Series Expansions.- 5 Ideals, Quotient Rings, and Factorization.- 6 Vectors.- 7 Duality.- 8 Matrices.- 9 Determinants.- 10 Euclidean Spaces.- 11 Projective Spaces.- 12 Groups.- 13 Description of Groups.- 14 Modules over a Principal Ideal Domain.- 15 Linear Operators.- 16 Bilinear Forms.- 17 Quadratic Forms and Quadrics.- 18 Real Versus Complex.- 19 Hermitian Spaces.- 20 Quaternions and Spinors.- References.- Hints to Selected Exercises.- Index.
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.
Autor: Alexey L. Gorodentsev
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.

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Autor: Alexey L. Gorodentsev
ISBN-13:: 9783319452845
ISBN: 3319452843
Erscheinungsjahr: 01.01.2017
Verlag: Springer-Verlag GmbH
Gewicht: 1027g
Seiten: 564
Sprache: Englisch
Sonstiges: Buch, 246x169x40 mm, 10 schwarz-weiße und 40 farbige Abbildungen, Bibliographie