Discovering Number Theory

Discovering Number Theory is a textbook by John Jones and Jeff Holt published by W. H. Freeman and Company.

Requests for examination copies of the materials should go directly to the publisher. Visit this W.H. Freeman page and you should find a link which you can use to request a copy of the book.

W.H. Freeman is starting a web page with materials for the book. It is in the process of being updated.

Development of these course materials was supported by the NSF under grant Revitalizing Undergraduate Number Theory.


Course Basics

The basic operation of the course is as follows. (This is also explained in the first day handout below.)

Version/Format Information

The Mathematica files require at least version 3.0.

Maple V worksheets require at least version R4. We also provide versions for R5, R5.1, and Maple 6.


The book, as purchased in the store contains an introduction to the course, all prelabs, all homework problems, a cd-rom with the electronic notebooks for Maple, Mathematica, and Web. The book also contains printouts of the electronic notebooks.

Now, here are the chapters and topics. Sections marked as Going Farther are expository (as opposed to discovery oriented). Some are in the lab, and some are in chapter summaries.

  1. Divisibility and Factorization
  2. The Euclidean Algorithm and Linear Diophantine Equations
  3. Congruences
  4. Applications of Congruences
  5. Solving Linear Congruences
  6. Primes of Special Forms
  7. Chinese Remainder Theorem
  8. Multiplicative Orders
  9. The Euler phi-function
  10. Primitive Roots
  11. Quadratic Congruences
  12. Representation Problems
  13. Continued Fractions

John Jones
Last modified: Wed Sep 13 10:55:14 MST 2000