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Number Theory: A Historical Approach, by John J. Watkins
Download PDF Number Theory: A Historical Approach, by John J. Watkins
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The natural numbers have been studied for thousands of years, yet most undergraduate textbooks present number theory as a long list of theorems with little mention of how these results were discovered or why they are important. This book emphasizes the historical development of number theory, describing methods, theorems, and proofs in the contexts in which they originated, and providing an accessible introduction to one of the most fascinating subjects in mathematics.
Written in an informal style by an award-winning teacher, Number Theory covers prime numbers, Fibonacci numbers, and a host of other essential topics in number theory, while also telling the stories of the great mathematicians behind these developments, including Euclid, Carl Friedrich Gauss, and Sophie Germain. This one-of-a-kind introductory textbook features an extensive set of problems that enable students to actively reinforce and extend their understanding of the material, as well as fully worked solutions for many of these problems. It also includes helpful hints for when students are unsure of how to get started on a given problem.
- Uses a unique historical approach to teaching number theory
- Features numerous problems, helpful hints, and fully worked solutions
- Discusses fun topics like Pythagorean tuning in music, Sudoku puzzles, and arithmetic progressions of primes
- Includes an introduction to Sage, an easy-to-learn yet powerful open-source mathematics software package
- Ideal for undergraduate mathematics majors as well as non-math majors
- Digital solutions manual (available only to professors)
- Sales Rank: #874014 in Books
- Published on: 2013-12-26
- Original language: English
- Number of items: 1
- Dimensions: 10.10" h x 1.30" w x 7.20" l, 2.60 pounds
- Binding: Hardcover
- 592 pages
Review
"An excellent contribution to the list of elementary number theory textbooks. Number theory, it is true, has as rich a history as any branch of mathematics, and Watkins has done terrific work in integrating the stories of the people behind this subject with the traditional topics of elementary number theory. There is more than enough material here for a one-semester course, and while this is standard for textbooks at this level, the added historical and biographical material--which cover mathematical developments and people well into the 20th century--are well worth the increased weight of the text."--Mark Bollman, MAA Reviews
From the Back Cover
"I know of no other book at this easily accessible level that combines extensive coverage of the mathematics with so many interesting biographical facts and anecdotes."--Thomas W. Cusick, University at Buffalo, State University of New York
"This is a very nice introductory text on number theory. It has a good selection of topics, lots of nice history, and many exercises. There is a lot to like here."--David A. Cox, Amherst College
"Watkins has advanced an outstanding and engaging treatise on the elementary theory of numbers. I expect it to be extremely valuable in inspiring young minds to think deeply about mathematics, and intend to use this text in my own courses on the topic."--Alex Kontorovich, Yale University
About the Author
John J. Watkins is professor emeritus of mathematics at Colorado College. His books include Across the Board: The Mathematics of Chessboard Problems (Princeton), Topics in Commutative Ring Theory (Princeton), Graphs: An Introductory Approach, and Combinatorics: Ancient and Modern.
Most helpful customer reviews
16 of 17 people found the following review helpful.
very nice text for non-majors
By Christine
This text is quite a nice introduction to number theory requiring mostly high school mathematics and some calculus in a few places. Quite suitable for students who want to get a sense of mathematics but are not committed to its study. The historical elements situate the mathematics in their time and convey effectively human aspects of the doing of mathematics as opposed to conveying the substance without a sense of the process.
Further, the Kindle version is very excellent since it's a print replica (a wrapped version of a PDF) of the text which means that the eBook form will faithfully preserve the mathematical typesetting precisely as set for printing. This is unlike the completely unsatisfactory results of so many of the mathematical and physics texts which are delivered via the ordinary Kindle format, that suffer from images for equations that don't scale with the font sizing and so on. Kudos to whoever decided on print replica for this text. May others take notice!
3 of 6 people found the following review helpful.
Beautiful
By Eva
This is a beautiful book and it is a very interesting story. A good read for a math nerd like myself!!
1 of 3 people found the following review helpful.
Five Stars
By Thomas R. Schulte
Great book and excellent service!
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