Modern Algebra With Applications

Blending the theoretical with the practical in the instruction of modern algebra "There is no other book of comparable content available. Because of its detailed coverage of applications generally neglected in the literature, it is a desirable addition to undergraduate mathematics and computer science libraries." –Choice Modern algebra guides are often structured from the point of view of the subject’s intrinsic interest, offering only vague promises of practical applications in later courses or more sophisticated texts. William Gilbert’s classic Modern Algebra with Applications, however, incorporates the applications of modern algebra throughout its authoritative treatment of the subject, not only effectively holding his readers’ interest but also creating a more seamless method of instruction. The book covers the full complement of group, ring, and field theory typically contained in a standard modern algebra course. Numerous examples are included in each chapter, and answers to odd-numbered exercises are appended in the back. Chapter topics include: Boolean Algebras, Groups, Quotient Groups, Symmetry Groups in Three Dimensions, Polya-Burnside Method of Enumeration, Monoids and Machines, Rings and Fields, Polynomial and Euclidean Rings, Quotient Rings, Field Extensions, Latin Squares, Geometrical Constructions, Error-Correcting Codes. Modern Algebra with Applications remains an ideal companion to upper undergraduate and graduate level algebra courses.