Basic Algebra and Advanced Algebra Set

Basic Algebra and Advanced Algebra systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or applied, aspiring or established. Together, the two books give the reader a global view of algebra and its role in mathematics as a whole, presenting the subject matter in a forward-looking way that takes into account its historical development.
Three prominent themes recur and blend together at times: the analogy between integers and polynomials in one variable over a field, the interplay between linear algebra and group theory, and the relationship between number theory and geometry. The exposition proceeds from the particular to the general, often providing examples well before a theory that incorporates them. The presentation includes blocks of problems that introduce additional topics and applications to science and engineering to guide further study. Many examples and hundreds of problems are included, along with separate sections giving hints or complete solutions for most of the problems.

Summary

Basic Algebra and Advanced Algebra systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or applied, aspiring or established. Together, the two books give the reader a global view of algebra and its role in mathematics as a whole, presenting the subject matter in a forward-looking way that takes into account its historical development.

Three prominent themes recur and blend together at times: the analogy between integers and polynomials in one variable over a field, the interplay between linear algebra and group theory, and the relationship between number theory and geometry. The exposition proceeds from the particular to the general, often providing examples well before a theory that incorporates them. The presentation includes blocks of problems that introduce additional topics and applications to science and engineering to guide further study. Many examples and hundreds of problems are included, along with separate sections giving hints or complete solutions for most of the problems.

Product details

• Authors: Anthony W Knapp, Anthony W. Knapp
• Publisher: Springer, Basel
• Languages: English
• Product format: Book
• Released: 13.12.2007
• EAN: 9780817645335
• ISBN: 978-0-8176-4533-5
• No. of pages: 1454
• Dimensions: 155 mm x 235 mm x 84 mm
• Weight: 2608 g
• Illustrations: XLVI, 1454 p. 2 volume-set.
• Series: Cornerstones; Cornerstones
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Arithmetic, algebra; Algebra, A, Group Theory, Mathematics and Statistics, Linear Algebra, Commutative algebra, Commutative rings, Commutative Rings and Algebras, Rings (Algebra), Groups & group theory, Group Theory and Generalizations, Matrix theory, Linear and Multilinear Algebras, Matrix Theory, Field Theory and Polynomials, Field theory (Physics), Associative rings, Associative Rings and Algebras, algebraic geometry;algebraic number theory;matrix theory, Groups and group theory