Re: Heuristics for number theory?

On Mon, 11 Apr 2005 21:53:53 +0000 (UTC),
jdolan@xxxxxxxxxxxxxxxxxxxxxxxx (James Dolan) wrote:

>in article <1113199301.672446.298590@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
>stephen white <mildredtoede@xxxxxxxxx> wrote:
>
>|People say some of the stuff becomes more digestable when you look at
>|it from some higher algebraic / complex analysis / analytic number
>|theory viewpoint..... so why bother with an elementary number theory
>|class at all? I feel I've gained virtually nothing from this class,
>|and the problems have been more frustrating than all my other classes
>|combined.
>
>i guess that it's a matter of taste, but i have to strongly agree with
>this. i'm not an expert in number theory, but i've found that looking
>at number theory from some of these supposedly "higher" viewpoints (in
>my case especially focusing on the galois-theory viewpoint and its
>geometric interpretation) makes large parts of number theory
>surprisingly easy to understand and beautiful, in contrast to the
>overwhelming ugliness found in most "elementary" introductions to the
>subject.

This is an area I want to learn about after completing the courses
I'm doing at the moment (which include one based on Apostol's book
on analytic number theory). I've been to some lectures on Galois
theory, and although the ideas haven't really stuck yet (euphemism
for the fact that I have a head like a sieve ... no pun intended),
it's an area I can probably revise fairly quickly. (I'm part-way
through Artin's book, but have had to leave off because of lack
of time; I've also got several other books on Galois theory I can
look at when time permits.)

Are there any texts you would particularly recommend? I've had
the book by Pierre Samuel sitting on my shelves for years, and
was more or less intending to use that to learn from initially.

I don't know what "geometrical interpretation" you're referring to:
can you expand on that, for the benefit of the [even] less expert?

--
Angus Rodgers
(angus_prune@ eats spam; reply to angusrod@)
Contains mild peril
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