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This book is written as an introduction to higher algebra for students with a background of a year of calculus. The first edition of this book emerged from a set of notes written in the 1970sfor a sophomorejunior level course at the University at Albany entitled "Classical Algebra." The objective of the course, and the book, is to give students enough experience in the algebraic theory of the integers and polynomials to appre ciate 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 congruence classes, Fermat's theorem, the Chinese remainder theorem; and then again for the ring of polynomials. Doing so leads to the study of simple field extensions, and, in particular, to an exposition of finite fields. Elementary properties of rings, fields, groups, and homomorphisms of these objects are introduced and used as needed in the development. Concurrently with the theoretical development, the book presents a broad variety of applications, to cryptography, errorcorrecting codes, Latin squares, tournaments, techniques of integration, and especially to elemen tary and computational number theory. A student who asks, "Why am I learning this?," willfind answers usually within a chapter or two. For a first course in algebra, the book offers a couple of advantages. • By building the algebra out of numbers and polynomials, the book takes maximal advantage of the student's prior experience in algebra and arithmetic. New concepts arise in a familiar context.
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From the reviews:
"The userfriendly 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 twosemester course and various suggestions for onesemester 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
 Table of contents (30 chapters)


Numbers
Pages 17

Induction
Pages 824

Euclid’s Algorithm
Pages 2546

Unique Factorization
Pages 4762

Congruences
Pages 6375

Table of contents (30 chapters)
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Bibliographic Information
 Bibliographic Information

 Book Title
 A Concrete Introduction to Higher Algebra
 Authors

 Lindsay N. Childs
 Series Title
 Undergraduate Texts in Mathematics
 Copyright
 1995
 Publisher
 SpringerVerlag New York
 Copyright Holder
 Springer Science+Business Media New York
 eBook ISBN
 9781441987020
 DOI
 10.1007/9781441987020
 Softcover ISBN
 9780387989990
 Series ISSN
 01726056
 Edition Number
 2
 Number of Pages
 XV, 522
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