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?

  • $\begingroup$ Continued fractions and their application to music could be an interesting one (just as an example) $\endgroup$
    – Sp3000
    Jun 17 '13 at 16:31
  • $\begingroup$ Induction, congruence classes/linear congruences, Chinese remainder theorem, Euler's Theorem, some sets/functions, groups/permutations, group theory (like langrange's theorem) $\endgroup$
    – user67258
    Jun 17 '13 at 16:34
  • 2
    $\begingroup$ 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...? $\endgroup$
    – DonAntonio
    Jun 17 '13 at 16:59
  • $\begingroup$ 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. $\endgroup$
    – 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.


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