How and what to teach on a first year elementary number theory course.

[matqkks]

In the late 80’s and early 90’s there was the idea of ‘calculus reform’ and some emphasis and syllabus changed. The order of doing things in calculus also changed with the advantage of technology.
Similarly in linear algebra there was a linear algebra curriculum study group which produced some really good ways of teaching linear algebra and also highlighted curriculum changes. This was produced in the January 1993 College Mathematics Journal.
Has any similar work been covered in number theory. I am looking for what are the important topics to cover and any work or research on the teaching of number theory.

 

[dkotschessaa]

I don't know if any similar work has been done, but I think it's a shame that such a wonderful topic, which requires no knowledge of calculus, set theory, or any other advanced mathematics, isn't offered more frequently in a first year form.

However, I did get some exposure to number theory through early math history, and I think that's a great place to start. The greeks were doing number theory long before any of the above branches of math were discovered. Proofs about triangular and square numbers and such are fairly easy to construct for a first year student. Pythagorean triples, etc.

-Dave K

 

[romsofia]

I would say for ELEMENTARY number theory the big topics to cover are (in no order of course): Chinese reminder theorem, modular arithmetic, Pythagorean triples, prime numbers, and the Euclidean algorithm (matrix method as well!).
Another cool topic you could try to introduce is the "art" of cryptography. You could do some caser ciphers and then move onto basic examples of RSA encryption.
Good luck!