A Course in Algebra (Graduate Studies in Mathematics, Vol. 56) (Graduate Studies in Mathematics, V. 56)

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. 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 E.b. Vinberg. Includes Bibliographical References (p. 501-502) And Index. When you are introduced to people, at first you only learn their names and faces. Introductory book on undergraduate algebra meant for a two year course.