Re: Heuristics for number theory?

Larry Hammick wrote:
>
> What was the content of your course? Proving that pi is irrational
> is rather untypical in a first course in NT. What else went on?
> And was this course intended for math majors only, or did it
> aim at students of information technology? That would have
> an influence on the instructor's choice of problems, I expect.
> LH
>

The course content so far has consisted of modular
arithmetic/divisibility/primality/etc., primality testing, quadratic
reciprocity, RSA, continued fractions (with lots of corresponding
algebraic/transcendental/irrational stuff mixed in), elliptic curves,
diophantine equations, arithmetical functions, moebius inversion,
asymptotics, probably lots of other things I can't remember off the top
of my head.

Part of the problem, as I see it, is there is no underlying theme. It
practically doesn't matter what order you study things in because
they're unrelated. In most subjects there is the satisfying feeling of
building up but in number theory each new chapter is like "ok, forget
everything from the last chapter, now we're going to concentrate on
THIS type of problem!" (of course the modular arithmetic stuff and
important things like Euler's phi more or less stick- but these are
covered in algebra courses or even freshman discrete math (albeit not
in anywhere near such excruciating, unnecessary and painful detail))

The course is more or less aimed at math majors, I suppose. There are
only 4 or 5 students who regularly attend (9 altogether but most never
show up). Of those 4, 2 are math majors, 1 is a grad student
linguistics major, 1 is a community college math teacher taking the
course for fun, and 1 is an electrical engineer type major.

M. Toede

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