On 6/14/14, 6:22 PM, William Stein wrote:
On Sat, Jun 14, 2014 at 6:12 PM,  <jeanbigbo...@gmail.com> wrote:
Dima writes:
"there is nothing wrong with using a bit of pure mathematics for
applied problems; e.g. cryptographers do this all the time... "

Agreed.  My formal education was from a time when fields, groups, and such
were not common undergraduate fare.

They are still not common undergraduate fare, in the US at least.
Most math major seniors I've encountered at Univ of Washington know
almost nothing about groups, rings and fields.     I personally did an
undergrad math minor without once ever hearing about groups, rings or
fields -- then I ran into a misfiled book [1] in the programming
section of a bookstore about abstract algebra, and was instantly
hooked.

I've seen it catching on in some universities especially in physics departments. Since there is now a fairly solid pipeline between physics and quantitative finance, I've met economics and business students who are expected to know this material or get familiar with it very quickly.

I went through a good sequence of courses in calculus, vector analysis, differential equations, and some real/complex analysis. The deeper mathematical topics were offered but I didn't have the time to take those courses.

Abstract algebra is a really beautiful and powerful
collection of ideas and ways of thinking about mathematics.  It's also
assumed in a lot of Sage documentation.

[1] http://www.amazon.com/Abstract-Algebra-David-M-Burton/dp/0697067610

I'll add this to the list.

I've found Nicholas Wheeler's course notes from Reed College to be very helpful in learning or relearning various parts of mathematics/mathematical physics. He uses Mathematica when he uses a CAS. Since I don't have a license for it, I'm diving into Sage.

http://academic.reed.edu/physics/faculty/wheeler/documents/index.html




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