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George E. Andrews

Number Theory (Dover Books on Mathematics) 1st Edition

by George E. Andrews (Author)

(404)

Part of: Dover Books on Mathematics (303 books)

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Written by a distinguished mathematician and teacher, this undergraduate text uses a combinatorial approach to accommodate both math majors and liberal arts students. In addition to covering the basics of number theory, it offers an outstanding introduction to partitions, plus chapters on multiplicativity-divisibility, quadratic congruences, additivity, and more.

Although mathematics majors are usually conversant with number theory by the time they have completed a course in abstract algebra, other undergraduates, especially those in education and the liberal arts, often need a more basic introduction to the topic. In this book, the author solves the problem of maintaining the interest of students at both levels by offering a combinatorial approach to elementary number theory. Among the topics covered in this accessible, carefully designed introduction are:

Multiplicativity-divisibility, including the fundamental theorem of arithmetic
Combinatorial and computational number theory
Congruences, arithmetic functions, primitive roots and prime numbers
Later chapters offer lucid treatments of quadratic congruences, additivity (including partition theory), and geometric number theory

Of particular importance in this text is the author's emphasis on the value of numerical examples in number theory and the role of computers in obtaining such examples. Exercises provide opportunities for constructing numerical tables with or without a computer. Students can then derive conjectures from such numerical tables, after which relevant theorems will seem natural and well-motivated.

Dover is widely recognized for a magnificent mathematics list featuring such world-class theorists as Paul J. Cohen (Set Theory and the Continuum Hypothesis), Alfred Tarski (Undecidable Theories), Gary Chartrand (Introductory Graph Theory), Hermann Weyl (The Concept of a Riemann Surface), Shlomo Sternberg (Dynamical Systems), and multiple works by C. R. Wylie in geometry, plus Stanley J. Farlow's Partial Differential Equations for Scientists and Engineers.

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ISBN-10

9780486682525
ISBN-13

978-0486682525
Edition

1st
Publisher

Dover Publications
Publication date

October 12, 1994
Part of series

Dover Books on Mathematics
Language

English
Dimensions

5.5 x 0.75 x 8.75 inches
Print length

288 pages

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Elementary Number Theory: Second Edition (Dover Books on Mathematics)
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From the Publisher

Where Patterns Meet Proof: A Hands-On Intro to Number Theory

Combinatorial Approach Keeps It Intuitive – Makes abstract concepts feel natural through patterns, examples, and thoughtful structure.
Covers Core and Advanced Topics – Includes divisibility, congruences, arithmetic functions, primitive roots, quadratic congruences, and partition theory.
Learn by Exploring Patterns – Numerical examples and computational exercises encourage students to make conjectures and discover theorems organically.

Editorial Reviews

About the Author

The Holy Grail of Number Theory
George E. Andrews, Evan Pugh Professor of Mathematics at Pennsylvania State University, author of the well-established text Number Theory (first published by Saunders in 1971 and reprinted by Dover in 1994), has led an active career discovering fascinating phenomena in his chosen field — number theory. Perhaps his greatest discovery, however, was not solely one in the intellectual realm but in the physical world as well.

In 1975, on a visit to Trinity College in Cambridge to study the papers of the late mathematician George N. Watson, Andrews found what turned out to be one of the actual Holy Grails of number theory, the document that became known as the "Lost Notebook" of the great Indian mathematician Srinivasa Ramanujan. It happened that the previously unknown notebook thus discovered included an immense amount of Ramanujan's original work bearing on one of Andrews' main mathematical preoccupations — mock theta functions. Collaborating with colleague Bruce C. Berndt of the University of Illinois at Urbana-Champaign, Andrews has since published the first two of a planned three-volume sequence based on Ramanujan's Lost Notebook, and will see the project completed with the appearance of the third volume in the next few years.

In the Author's Own Words:
"It seems to me that there's this grand mathematical world out there, and I am wandering through it and discovering fascinating phenomena that often totally surprise me. I do not think of mathematics as invented but rather discovered." — George E. Andrews

Product details

ASIN ‏ : ‎ 0486682528
Publisher ‏ : ‎ Dover Publications
Publication date ‏ : ‎ October 12, 1994
Edition ‏ : ‎ 1st
Language ‏ : ‎ English
Print length ‏ : ‎ 288 pages
ISBN-10 ‏ : ‎ 9780486682525
ISBN-13 ‏ : ‎ 978-0486682525
Item Weight ‏ : ‎ 10.4 ounces
Dimensions ‏ : ‎ 5.5 x 0.75 x 8.75 inches
Part of series ‏ : ‎ Dover Books on Mathematics
Best Sellers Rank: #125,818 in Books (See Top 100 in Books)
- #14 in Number Theory (Books)
- #141 in Mathematics (Books)
Customer Reviews:
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Customers say

Customers find this number theory book excellent for self-study and as a reference for basic classes, with problems that range from easy to moderate in difficulty. They consider it good value for money. The readability receives mixed feedback, with some customers finding it challenging to read.

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26 customers mention content, 23 positive, 3 negative

Customers find the book excellent for self-study and as a reference for basic number theory classes, with one customer noting it serves as a great introduction to the subject.

Good book. It may help to be familiar with proof by induction before reading this book....Read more

It is a great book to get day by day closer to this fascinating theory, even for us the begginersRead more

...I found it to be one of the best textbooks I've used so far....Read more

The book is good, formatting of exercises is kinda lameRead more

12 customers mention difficulty level, 9 positive, 3 negative

Customers find the book's problems easy to moderate in difficulty, with one customer noting that no background beyond very basic set theory is assumed.

Easy to understand and the information builds gradually from one topic to the next....Read more

Great book easy to follow if you think paradigicly great for review to those adept with mathematics and also useful for those still learningRead more

...A notable drawback is the presentation of proofs; many lack intermediate steps, requiring considerable time and effort to fully understand them.Read more

Number theory is both easy and difficult. This book does a good job of highlighting some of these aspects in a clear and straightforward way....Read more

7 customers mention value for money, 7 positive, 0 negative

Customers find the book offers good value, with one mentioning it's a great cheap number theory book.

...is the correct one (they both are, I guess) but, since the books are so inexpensive, I would suggest try each or using both....Read more

...but I can say with certainty that the first nine chapters are worth the effort.Read more

...Dover typically publishes comprehensive texts at reasonable prices....Read more

...Still the price of this book is quite low to have access to all of this big range of mathematics to pick and choose what is most interesting to any...Read more

9 customers mention readability, 6 positive, 3 negative

Customers have mixed opinions about the readability of the book, with some finding it challenging and not easy to read, while others appreciate its concise and clear presentation.

...The exercises were numerous, challenging and illuminating....Read more

Definitely not an easy read, but it was lots of fun and I liked it.Read more

Good presentation, easy to digest text on a very 'mundane' subject of number theory .Read more

...This book does a good job of highlighting some of these aspects in a clear and straightforward way....Read more

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