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Elsevier

First Course in Algebra and Number Theory

  • 1st Edition - January 1, 1971
  • Latest edition
  • Author: Edwin Weiss
  • Language: English

First Course in Algebra and Number Theory presents the basic concepts, tools, and techniques of modern algebra and number theory. It is designed for a full year course at the… Read more

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Description

First Course in Algebra and Number Theory presents the basic concepts, tools, and techniques of modern algebra and number theory. It is designed for a full year course at the freshman or sophomore college level. The text is organized into four chapters. The first chapter is concerned with the set of all integers - positive, negative, and zero. It investigates properties of Z such as division algorithm, Euclidean algorithm, unique factorization, greatest common divisor, least common multiple, congruence, and radix representation. In chapter 2, additional axioms about Z were introduced and some of their consequences are discussed. The third chapter sets up terminologies about polynomials, solutions or roots of polynomial equations, and factorization of polynomials. Finally, chapter 4 studies logically simpler algebraic systems, known as "groups", algebraic objects with a single operation. The book is intended for students in the freshman and sophomore levels in college.

Table of contents

PrefaceI. Elementary Number Theory 1-1. Divisibility 1-2. The Division Algorithm 1-3. The Greatest Common Divisor 1-4. Unique Factorization 1-5. A Convenient Notation 1-6. Linear Diophantine Equations 1-7. Congruence 1-8. Radix Representation Miscellaneous ProblemsII. Rings and Domains 2-1. Rings: Elementary Properties 2-2. Examples 2-3. Ordered and Well-Ordered Domains 2-4. Computation Rules 2-5. Characterization of the Integers Miscellaneous ProblemsIII. Congruences and Polynomials 3-1. Linear Congruences 3-2. Units and Fields 3-3. Polynomials and Polynomial Functions 3-4. Factorization in F[X] 3-5. Roots Of Polynomials 3-6. Solving Polynomials In Zm[x] 3-7. Quadratic Reciprocity Miscellaneous ProblemsIV. Groups 4-1. Basic Facts And Examples 4-2. Subgroups and Cosets 4-3. Cyclic Groups 4-4. Normal Subgroups; Factor Groups; Homomorphisms 4-5. Permutation Groups 4-6. The Group Z*m Miscellaneous ProblemsSelected Answers and CommentsSubject Index

Product details

  • Edition: 1
  • Latest edition
  • Published: May 10, 2014
  • Language: English

About the author

EW

Edwin Weiss

Affiliations and expertise
Department of Mathematics, Boston University

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