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Undergraduate Algebra is a text for the standard undergraduate algebra course. It concentrates on the basic structures and results of algebra, discussing groups, rings, modules, fields, finite fields, Galois Theory, and other topics. The author has also included a chapter on groups of matrices which is unique in a book at this level. Throughout the book, the author has attempted to strike a balance between abstraction and concrete results, providing illustrative examples to reinforce the general theory. Numerous exercises, ranging from the computational to the theoretical, are contained herein.For the third edition, the author has included material on linear algebra in combination with group theory, and also material on polynomials.

Tabla de contenidos provista por Syndetics

• Foreword
• The Integers
• Groups
• Rings
• Polynomials
• Vector Spaces and Modules
• Some Linear Groups
• Field Theory
• Finite Fields
• The Real and Complex Numbers
• Sets
• Appendix
• Index

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CHOICE Review

Lang is a distinguished mathematician and a prolific writer, and this is his fifth work in the well-regarded Springer series of undergraduate texts in mathematics. Paired with Lang's Introduction to Linear Algebra (1986), this book is an attractive choice for use in an introductory abstract algebra course for bright and well-prepared undergraduates. The topics covered include an emphasis on field theory, Galois theory, and special features of finite fields that provide needed background for coding theory. Lang writes with grace and with considerable reliance on the reader or instructor to fill in gaps, to see connections, and to contribute substantially to the learning process. He consistently allows the relatively mature reader to see the new mathematics in overview and to see examples, details, and proofs as supporting rather than overwhelming the main lines of the material. Although this is primarily a textbook, many undergraduate libraries will wish to have it (along with Lang's other works in the Springer series) for use as complementary sources for undergraduate mathematics courses.-J. Cunningham, Susquehanna University