Re: Sage AMS short course
Noam Elkies
> I just wrote a "Sage & Elliptic Curves" AMS Short course proposal,
> [...] The actual proposal is due January 7, 2010.
That's not much time left!
I have no context of other short-course proposals to compare this to
(nor other short courses, since I so rarely attend the annual Joint
Meetings); but this looks very promising. What's the audience --
that is, who is going to be reading this proposal? I see that you
already asked the chair of the short course committee whether
this is "in the right spirit" so I expect you'll get some sense of
the answer. The audience might affect some details of editing;
e.g. a relative outsider might wonder about the appearance of
three kinds of algebra at the bottom of page 1 (plain "algebra",
then "commutative algebra", then "exact linear algebra"), but
somebody closer to the field will know what you mean (though even then
you might make the first instance something like "basic algebra").
Conversely, readers who have already seen the congruent number problem
(if only by reading Wiles' description of BSD for the Clay megabuck prize)
will not be at all surprised that it's basically a problem about
elliptic curves.
BTW: is that now really the oldest suriving open math problem?
It's unquestionably *one* of the oldest -- Dickson cites an
Arabic manuscript from 972(!) that asks an equivalent question,
and scholarship since Dickson might have pushed it further back --
but it might not even be the oldest problem in number theory:
perhaps one can find an explicit earlier statement of the problem of the
infinitude of even perfect numbers or of the existence of an odd one.
(And if I remember right there was also a problem in Diophantus that
reduces to the solution of y^2=x^6+x^2+1 in rationals, and this
genus-2 problem was finally solved only a few years ago.) Anyway,
unless you're quite sure of the status of the congruent-number problem,
you may want to write "one of the oldest" rather than "the oldest".
Besides that I note some transparent typos and the like:
@ "algebraic and analysis" --> "algebra and analysis" (or
"algebraic and analytic <something>").
@ "a Python-based interfaces" -- either singular "interface",
or plural but without "a", depending on what you want to say.
@ "general and advanced" -- better "elementary and advanced"
(if I'm right that this is the contrast you want to draw).
@ "education, studying and research" -- what's the difference
between the first two? Perhaps you mean "self-study" for the second,
but that's also self-education.
@ "in a web-browser or the command-line" -- at least the first of these
two hyphens shouldn't be there.
@ Maybe change "Counting points" (in item 3 of "Topics covered...") to
"How to count points" to parallel the grammar of the other six items.
@ In item 4, "Torsion points" should not be capitalized.
@ top of page 3: the name is Schoof, not Schoff.
Good luck (and happy 2010),
--NDE
William Stein
> William Stein writes:
>
>> I just wrote a "Sage & Elliptic Curves" AMS Short course proposal,
>> [...] The actual proposal is due January 7, 2010.
>
> That's not much time left!
>
> I have no context of other short-course proposals to compare this to
> (nor other short courses, since I so rarely attend the annual Joint
> Meetings); but this looks very promising.
This one appears to be the canonical example:
http://www.ams.org/meetings/shcourse-09.html
I think it is the oldest -- Coates described it as such last time I
saw him. I've been looking and looking and I can't find any specific
older problems in mathematics. That said, I might call it "perhaps
the oldest" or "possibly the oldest".
Regarding the Diophantus problem above, you're right, that was solved
by Joe Wetherell as his Ph.D. thesis, when he was at Berkeley with me
back in 1997. I'm not sure if that problem was stated so clearly as
a problem though by Diophantus.
> Besides that I note some transparent typos and the like:
>
> @ "algebraic and analysis" --> "algebra and analysis" (or
> "algebraic and analytic <something>").
>
> @ "a Python-based interfaces" -- either singular "interface",
> or plural but without "a", depending on what you want to say.
>
> @ "general and advanced" -- better "elementary and advanced"
> (if I'm right that this is the contrast you want to draw).
>
> @ "education, studying and research" -- what's the difference
> between the first two? Perhaps you mean "self-study" for the second,
> but that's also self-education.
>
> @ "in a web-browser or the command-line" -- at least the first of these
> two hyphens shouldn't be there.
>
> @ Maybe change "Counting points" (in item 3 of "Topics covered...") to
> "How to count points" to parallel the grammar of the other six items.
>
> @ In item 4, "Torsion points" should not be capitalized.
>
> @ top of page 3: the name is Schoof, not Schoff.
>
> Good luck (and happy 2010),
Thanks!!
Also, any chance *you* would be interested -- at least in principle --
in doing one of the lecture sequences? "Elliptic curves of large
rank" would fill a major gap in the program, and I can help with
Sage-enhancing whatever you come up with (so you won't have to know
anything in particular about Sage).
-- William
Noam Elkies
> older problems in mathematics.
What's the oldest statement of the two perfect-number problems?
They're at least strongly implicit in the classical Greek works,
but I have no idea if Descartes' 1638 mentioned in the Mathworld
entry for OddPerfectNumber is the first explicit statement.
> Regarding the Diophantus problem above, you're right, that was solved
> by Joe Wetherell as his Ph.D. thesis, when he was at Berkeley with me
> back in 1997.
Thanks, I did not remember the specific reference.
> I'm not sure if that problem was stated so clearly as a problem though
> by Diophantus.
As I recall the paper specifically said it was, even though
Diophantus was content to find the single example (x,y)=(1/2,9/8)
(Diophantus didn't count x=0 and x=-1/2, let alone points at infinity),
and didn't (ever?) ask to describe all solutions.
>> Besides that I note some transparent typos and the like: [...]
>> Good luck (and happy 2010),
> Thanks!!
You're welcome!
> Also, any chance *you* would be interested -- at least in principle --
> in doing one of the lecture sequences? "Elliptic curves of large
> rank" would fill a major gap in the program, and I can help with
> Sage-enhancing whatever you come up with (so you won't have to know
> anything in particular about Sage).
Hm, I could be, though I think "elliptic surfaces" would be both
more honest (assuming canonical heights etc. are implemented by then)
-- none of my own work on high-rank curves was done in Sage, except
to the extent that gp etc. were accessed via a Sage distribution --
and closer to the other topics. I could still note high-rank curves
as one application, since every rank record is obtained by
specialization from an elliptic surface (or possibly an elliptic curve
over P^n for some n>1).
NDE