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A Course in Algebra
E B Vinberg
Price
2025.00
ISBN
9780821848586
Language
English
Pages
528
Format
Paperback
Dimensions
180 x 240 mm
Year of Publishing
2009
Territorial Rights
Restricted
Imprint
American Mathematical Society
Catalogues

This is a comprehensive textbook on modern algebra written by an internationally renowned specialist. It covers material traditionally found in advanced undergraduate and basic graduate courses and presents it in a lucid style. The author includes almost no technically difficult proofs, and reflecting his point of view on mathematics, he tries wherever possible to replace calculations and difficult deductions with conceptual proofs and to associate geometric images to algebraic objects. The effort spent on the part of students in absorbing these ideas will pay off when they turn to solving problems outside of this textbook.

Another important feature is the presentation of most topics on several levels, allowing students to move smoothly from initial acquaintance with the subject to thorough study and a deeper understanding. Basic topics are included, such as algebraic structures, linear algebra, polynomials, and groups, as well as more advanced topics, such as affine and projective spaces, tensor algebra, Galois theory, Lie groups, and associative algebras and their representations. Some applications of linear algebra and group theory to physics are discussed.

The book is written with extreme care and contains over 200 exercises and 70 figures. It is ideal as a textbook and also suitable for independent study for advanced undergraduates and graduate students.

E. B. Vinberg, Moscow State University, Russia
Chapter 1. Algebraic Structures
Chapter 2. Elements of Linear Algebra
Chapter 3. Elements of Polynomial Algebra
Chapter 4. Elements of Group Theory
Chapter 5. Vector Spaces
Chapter 6. Linear Operators
Chapter 7. Affine and Projective Spaces
Chapter 8. Tensor Algebra
Chapter 9. Commutative Algebra
Chapter 10. Groups
Chapter 11. Linear Representations and Associative Algebras
Chapter 12. Lie Groups
Answers to Selected Exercises
Bibliography
Index
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