I need to teach a course in elementary number theory next academic year. What topics should be included on a first course in this area? What is best order of doing things? The students have a minimum background in proof but this is a second year undergraduate module. I am looking for applications which will motivate the student in this subject. Are there good resources on elementary number theory?

  • Continued fractions and their application to music could be an interesting one (just as an example) – Sp3000 Jun 17 '13 at 16:31
  • Induction, congruence classes/linear congruences, Chinese remainder theorem, Euler's Theorem, some sets/functions, groups/permutations, group theory (like langrange's theorem) – user67258 Jun 17 '13 at 16:34
  • 2
    I find this question odd as usually courses at undergraduate level are determined according to the students' assumed interests and the departament's goals: are these mathematics students? Is the department strong in number theory? Has this first course to serve as a basis for continuation in algebraic number theory and/or close subjects or must it stand by itself and be only a "gentle" introduction to the subject...? – DonAntonio Jun 17 '13 at 16:59
  • The goal is to highlight rigour but not to put off students. There is no continuation course and I think your description of a gentle introduction is a true reflection of what we want to achieve. – matqkks Jun 17 '13 at 21:41

The best thing would be to follow David M. Burton's book 'Elementary Number Theory'.

You could do much worse than to use Underwood Dudley, Elementary Number Theory; it’s $35$ years old, but it’s very readable, it has all of the traditional topics, and it’s available in an inexpensive Dover paperback edition and an even more inexpensive Kindle edition.

Your Answer

By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service, privacy policy and cookie policy, and that your continued use of the website is subject to these policies.

Not the answer you're looking for? Browse other questions tagged or ask your own question.