A Concrete Introduction to Higher Algebra (Undergraduate Texts in Mathematics). Questo articolo non è disponibile.A Concrete Introduction to Higher Algebra (Undergraduate Texts in Mathematics)

This is an introduction to higher algebra for students with a background of a year of calculus. The book aims to give these students enough experience in the algebraic theory of the integers and polynomials to appreciate the basic concepts of abstract algebra. The main theoretical thread is to develop algebraic properties of the ring of integers: unique factorization into primes; congruences and congrunce classes; Fermat's theorem; the Chinese remainder theorem; and for the ring of polynomials. Concurrently with the theoretical development, the book presents a broad variety of applications, to cryptography, error-correcting codes, Latin squares, tournaments, techniques of integration and especially to elementary and computational number theory. Many of the recent advances in computational number theory are built on the mathematics which is presented in this book. Thus the book may be used as a first course in higher algebra, as originally intended, but may also serve as an introduction to modern computational number theory, or to applied algebra.

From the reviews:

"The user-friendly exposition is appropriate for the intended audience. Exercises often appear in the text at the point they are relevant, as well as at the end of the section or chapter. Hints for selected exercises are given at the end of the book. There is sufficient material for a two-semester course and various suggestions for one-semester courses are provided. Although the overall organization remains the same in the second edition¿Changes include the following: greater emphasis on finite groups, more explicit use of homomorphisms, increased use of the Chinese remainder theorem, coverage of cubic and quartic polynomial equations, and applications which use the discrete Fourier transform." MATHEMATICAL REVIEWS