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. 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 a separate 90-page section giving hints or complete solutions for most of the problems.
Preliminaries about the Integers, Polynomials, and Matrices.- Vector Spaces over ?, ?, and ?.- Inner-Product Spaces.- Groups and Group Actions.- Theory of a Single Linear Transformation.- Multilinear Algebra.- Advanced Group Theory.- Commutative Rings and Their Modules.- Fields and Galois Theory.- Modules over Noncommutative Rings.