A Concrete Introduction to Higher Algebra by L N Childs

A Concrete Introduction to Higher Algebra by L N Childs

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 sophomore-junior 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, error-correcting 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.

Lindsay N. Childs is Professor Emeritus at the University of Albany where he earned recognition as a much-loved mentor of students, and as an expert in Galois field theory. Capping his tenure at Albany, he was named a Collins Fellow for his extraordinary devotion to the University at Albany and the people in it over a sustained period of time. Post University of Albany, Professor Childs has taught a sequence of online courses whose content evolved into this book. Lindsay Childs is author of A Concrete Introduction to Higher Algebra, published in Springer's Undergraduate Texts in Mathematics series, as well as a monograph, Taming Wild Extensions: Hopf Algebras and Local Galois Module Theory (American Mathematical Society), and more than 60 research publications in abstract algebra.

SKU	Unavailable
ISBN 13	9780387903330
ISBN 10	038790333X
Title	A Concrete Introduction to Higher Algebra
Author	L N Childs
Series	Undergraduate Texts In Mathematics
Condition	Unavailable
Binding Type	Hardback
Publisher	Springer
Year published	1992-10-01
Number of pages	338
Cover note	Book picture is for illustrative purposes only, actual binding, cover or edition may vary.