Algebra I Textbook for Students of Mathematics 1st edition by Alexey Gorodentsev 3319452852 9783319452852

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Product details:

ISBN-10 :  3319452852 

ISBN-13 :  9783319452852

Author: Alexey L. Gorodentsev 

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.  

Algebra I Textbook for Students of Mathematics 1st Table of contents:

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. Descriptions 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

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Tags: Algebra, Students, Mathematics, Alexey Gorodentsev