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.Key features include:*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*Many examples and hundreds of problems are included, along with separate sections giving hints or complete solutions for most of the problems*The exposition proceeds from the particular to the general, often providing examples well before a theory that incorporates them; it includes blocks of problems that introduce additional topics and applications for further study*Applications to science and engineering, e.g., the fast Fourier transform, the theory of error-correcting codes, the use of Jordan canonical form in solving linear systems of ordinary differential equations, and constructions of interest in mathematical physics, appear in sequences of problems.Knapp, Anthony W. is the author of 'Basic Algebra and Advanced Algebra Set', published 2008 under ISBN 9780817645335 and ISBN 0817645330.