Algebra I : Textbook for Students of Mathematics / by Alexey L. Gorodentsev.

Format:

Book

Author/Creator:

Gorodentsev, Alexey L., Author.

Language:

English

Subjects (All):

Algebra.

Local Subjects:

Algebra.

Physical Description:

1 online resource (XX, 564 p. 79 illus., 42 illus. in color.)

Edition:

1st ed. 2016.

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2016.

Summary:

This book is the first 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.

Contents:

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.

Notes:

Includes bibliographical references and index.

Description based on publisher supplied metadata and other sources.

ISBN:

3-319-45285-1

OCLC:

1066197180