Math592 Seminar on Mathematics: Philosophy and Methodology
Fall Semester, 2006
Instructor: Anatoly Libgober
Office: SEO 413
Phone: 312-413-2138
Office Hours: MW 11 a.m. or by appointment.
Texts:
1.Mathematics: Frontiers and Perspectives, V.Arnold, M.Atiyah, P.Lax,
B.Mazur, Editors, AMS 2000.
2. H.Bass, Mathematics, Mathematicians and
Mathematics Education, Bull. AMS, 2005, vol. 42, p.417-430.
3.
Y.Manin, George Cantor and his heritage. math.AG/0209244.
4.I.Stewart and D.Tall, The foundations of mathematics, Oxford University
Press, 1977.
5.F.Klein, Elementary Mathematics from Advanced View Point, Dover,NY, 1953.
6.G.Polya, How to solve it, Princeton University Press, 1953.
Hours: The seminar meets Thursday at 5-8 p.m.
in TH 321.
Description
This is seminar for DA and masters students aiming to explore
some fundamental issues in contemporary mathematics and ways to present it
to students with various backgrounds. Particular focus
will be on developing skills for enchancing breadth
of understanding mathematics. The seminar will inlcude
presentations and discussions of various articles (from
sources listed above; the list of text will be expanded
if needed). Students are expected actively
participate by writing and presenting several
papers on material of their and other students
of the seminar interest. Solving problems illustrating
the issues which are discussed also will be
important part of the course.
Grading and Homework
Grades will be based on oral and written presentations
of papers and solution of assigned problems.
Other Sources
1.American Mathemamatical Monthly, MAAA various issues.
2. P.Sarnak, Riemann Hypothesis