Number Theory. What can I expect from such a course

[srfriggen]

I'm interested in taking a course in number theory as the material excites me very much, however, I'm not sure how such material would be taught. What can I expect from lectures, homework, exams, etc?



(on a somewhat related note, anyone here have any information regarding any special characteristics of the square roots of prime numbers? Of course they're all irrational, but, for example, do larger primes, or Mersenne primes exhibit different "behavior"? I can't seem to find any material on the web about such a question).

 

[mathwonk]

this question can only be answered by the instructor. when i last taught the course some 17 years ago, it was in three parts, which i made successfully more sophisticated. At first we did thing only requiring hands on tools like well ordering of integers, obtaining some of fermat's results such as his "little theorem" and his theorem characterizing sums of two squares. then we used some abstract algebra like finite abelian groups and studied quadratic reciprocity, and finally blew off the lid using complex analysis and group characters to prove dirichlet's theorem on primes in arithmetic progressions, as in serre's little book "a course in arithmetic".

other instructors might do something using elliptic curves for factorization algorithms, or coding. Its a big subject, amenable to many levels of sophistication, from none to lots.