Fundamentals of Number Theory

Fundamentals of Number Theory

3.0 1
by William J. LeVeque
     
 

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ISBN-10: 0486689069

ISBN-13: 9780486689067

Pub. Date: 02/07/1996

Publisher: Dover Publications

This excellent textbook introduces the basics of number theory, incorporating the language of abstract algebra. A knowledge of such algebraic concepts as group, ring, field, and domain is not assumed, however; all terms are defined and examples are given — making the book self-contained in this respect.
The author begins with an introductory chapter on

Overview

This excellent textbook introduces the basics of number theory, incorporating the language of abstract algebra. A knowledge of such algebraic concepts as group, ring, field, and domain is not assumed, however; all terms are defined and examples are given — making the book self-contained in this respect.
The author begins with an introductory chapter on number theory and its early history. Subsequent chapters deal with unique factorization and the GCD, quadratic residues, number-theoretic functions and the distribution of primes, sums of squares, quadratic equations and quadratic fields, diophantine approximation, and more. Included are discussions of topics not always found in introductory texts: factorization and primality of large integers, p-adic numbers, algebraic number fields, Brun's theorem on twin primes, and the transcendence of e, to mention a few.
Readers will find a substantial number of well-chosen problems, along with many notes and bibliographical references selected for readability and relevance. Five helpful appendixes — containing such study aids as a factor table, computer-plotted graphs, a table of indices, the Greek alphabet, and a list of symbols — and a bibliography round out this well-written text, which is directed toward undergraduate majors and beginning graduate students in mathematics. No post-calculus prerequisite is assumed. 1977 edition.

Product Details

ISBN-13:
9780486689067
Publisher:
Dover Publications
Publication date:
02/07/1996
Series:
Dover Books on Mathematics Series
Pages:
288
Sales rank:
352,804
Product dimensions:
5.62(w) x 8.20(h) x 0.57(d)

Related Subjects

Table of Contents

Contents

Chapter 1 Introduction,
Chapter 2 Unique Factorization and the GCD,
Chapter 3 Congruences and the Ring Zm,
Chapter 4 Primitive Roots and the Group Um,
Chapter 5 Quadratic Residues,
Chapter 6 Number-Theoretic Functions and the Distribution of Primes,
Chapter 7 Sums of Squares,
Chapter 8 Quadratic Equations and Quadratic Fields,
Chapter 9 Diophantine Approximation,
Bibliography,
Appendix,
Factor Table,
Computer-Plotted Graphs,
Table of Indices,
Greek Alphabet,
List of Symbols,
Index,

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Fundamentals of Number Theory 3 out of 5 based on 0 ratings. 1 reviews.
Guest More than 1 year ago
LeVeque covers certain topics in great detail, and others can be quite vague. One must have prior knowledge on modular aritmetic in order to get started with this text. The Euclidean Algorithm is explained from origins to applicability in nearly every single proof. LeVeque's best feature is in descripitons of Rings in modulus Z and their respecive domains and their respective theorems, congruences, etc. If you are weak in this area I recommend this text for that area of Number Theory.