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Fundamentals of Number Theory
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 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.
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 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.
- GenresMathematicsNumber Theory
288 pages, Paperback
First published December 1, 1977
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Displaying 1 - 3 of 3 reviews
April 15, 2025
An excellent introduction. The subject material is properly balanced with examples, history and motivation. There is a clear sense of flow and purpose in the text itself, which distinguishes it from the modern dry and unreadable "textbooks", which are often little more than lists of definitions and theorems.
As it's a bit dated, so you won't find the most recent results in there, but it is supposed to cover the fundamentals. And the classical style of mathematical writing (almost always found in Dover Books - a publisher to remember) makes it a pleasure to read.
As it's a bit dated, so you won't find the most recent results in there, but it is supposed to cover the fundamentals. And the classical style of mathematical writing (almost always found in Dover Books - a publisher to remember) makes it a pleasure to read.
March 11, 2011
This a great book on Number Theory for one who knows math but not Number Theory. The subject is covered at the undergraduate level.
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June 12, 2013thank you
Displaying 1 - 3 of 3 reviews