Dewey Class 
512 
Title 
A Concrete Introduction to Higher Algebra ([EBook]) / by Lindsay Childs. 
Author 
Childs, Lindsay N. 
Other name(s) 
SpringerLink (Online service) 
Publication 
New York, NY : Springer US , 1979. 
Physical Details 
XIV, 340 p. : online resource. 
Series 
Undergraduate texts in mathematics 01726056 
ISBN 
9781468400656 
Summary Note 
This book is written as an introduction to higher algebra for students with a background of a year of calculus. The book developed out of a set of notes for a sophomorejunior level course at the State University of New York at Albany entitled Classical Algebra. In the 1950s and before, it was customary for the first course in algebra to be a course in the theory of equations, consisting of a study of polynomials over the complex, real, and rational numbers, and, to a lesser extent, linear algebra from the point of view of systems of equations. Abstract algebra, that is, the study of groups, rings, and fields, usually followed such a course. In recent years the theory of equations course has disappeared. Without it, students entering abstract algebra courses tend to lack the experience in the algebraic theory of the basic classical examples of the integers and polynomials necessary for understanding, and more importantly, for ap preciating the formalism. To meet this problem, several texts have recently appeared introducing algebra through number theory.: 
Contents note 
I INTEGERS  1 Numbers  2 Induction; the Binomial Theorem  3 Unique Factorization into Products of Primes  4 Primes  5 Bases  6 Congruences  7 Congruence Classes  8 Rings and Fields  9 Matrices and Vectors  10 Secret Codes, I  11 Fernjat’s Theorem, I: Abelian Groups  12 Repeating Decimals, I  13 Error Correcting Codes, I  14 The Chinese Remainder Theorem  15 Secret Codes, II  II POLYNOMIALS  1 Polynomials  2 Unique Factorization  3 The Fundamental Theorem of Algebra  4 Irreducible Polynomials in ?[x]  5 Partial Fractions  6 The Derivative of a Polynomial  7 Sturm’s Algorithm  8 Factoring in ?[x], I  9 Congruences Modulo a Polynomial  10 Fermat’s Theorem, II  11 Factoring in ?;[x], II: Lagrange Interpolation  12 Factoring in ?p[x]  13 Factoring in ?[x], III: Mod m  III FIELDS  1 Primitive Elements  2 Repeating Decimals, II  3 Testing for Primeness  4 Fourth Roots of One in ?p  5 Telephone Cable Splicing  6 Factoring in ?[x], IV: Bad Examples Modp  7 Congruence Classes Modulo a Polynomial: Simple Field Extensions  8 Polynomials and Roots  9 Error Correcting Codes, II  10 Isomorphisms, I  11 Finite Fields are Simple  12 Latin Squares  13 Irreducible Polynomials in ?p[x]  14 Finite Fields  15 The Discriminant and Stickelberger’s Theorem  16 Quadratic Residues  17 Duplicate Bridge Tournaments  18 Algebraic Number Fields  19 Isomorphisms, II  20 Sums of Two Squares  21 On Unique Factorization  Exercises Used in Subsequent Chapters  Comments on the Starred Problems  References. 
System details note 
Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users) 
Internet Site 
http://dx.doi.org/10.1007/9781468400656 
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