First Course in Algebra and Number Theory - 1st Edition - ISBN: 9780127431505, 9781483270371

First Course in Algebra and Number Theory

1st Edition

Authors: Edwin Weiss
eBook ISBN: 9781483270371
Imprint: Academic Press
Published Date: 1st January 1971
Page Count: 560
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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


Preface

I. 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 Problems

II. 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 Problems

III. 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 Problems

IV. 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 Problems

Selected Answers and Comments

Subject Index

Details

No. of pages:
560
Language:
English
Copyright:
© Academic Press 1971
Published:
Imprint:
Academic Press
eBook ISBN:
9781483270371

About the Author

Edwin Weiss

Affiliations and Expertise

Department of Mathematics, Boston University