Graduate course statistics

Area	2000/01	2001/02	2002/03	2003/04	2004/05	Total
Measure theory and integration	507	507	507	507	507	5
Functional analysis	510	---	510	510,512	510	5
Complex analysis	---	508	508	508,509	508,509	6
Applied analysis	550,604D	550	550,551	550	550,601D,605E	9
Algebra	501	501,502	501	501	501,502	7
Topology	527	527	527,528,530,603D	527,528	527,528	10
Algebraic geometry	502	532	502,602H	502,532,533	533	8
Differential geometry, including geometric PDE	525	602	525,526	525,526,602	525,526	9
Number theory	---	---	537,538	537,539A,540,620D	537,620D	8
Combinatorics	523	---	---	---	503,610D	3
ODE	---	---	---	---	514	1
PDE (other than DG or numerical)	---	554	519	516,517,519,520	520,606,611D	9
Numerical methods (including numerical PDE)	---	---	---	521,607E	521,607E	4
Dynamical systems	---	552	---	---	552	2
Probability	544	418,544,608D	544,545,608D	544,545,608D,609	544,545,608D,608E	15
Mathematical biology	560	---	---	560	561	3
Mathematical finance	605D,608D	607D	605D(I+II)	605D,605F,607D	605D,606E	10
Mathematical modelling of applied problems	605	605D	---	605E	606D	4
Total	14	15	22	34	33	:-)

Comments:

This table is based on the grad course booklets distributed to the department each September, and (for 2004-05) on the course list on the dept web page. Any courses whose descriptions are missing from there will likely not be listed here, either.
The courses are classified according to what was actually being taught, rather than just the title. For example, when Math 502 (Algebra II) was taught as a basic course in algebraic geometry, it is listed as such.
Each course is listed in only one category. For courses that might belong equally to more than one area, I tried to pick the more "specific" one - for example, "numerical methods in PDE" are listed as "numerical methods", but "numerical methods in math finance" - as "math finance". I apologize for any remaining inaccuracies.
501 ([Abstract] Algebra) and 508 (Complex analysis) cover quite well the syllabus of the comprehensive exams in these areas, so they are good courses to take for students preparing for the exams. There are no graduate level courses covering the real analysis and linear algebra portions of the exams. 507 (Measure Theory and Integration, aka. Real analysis) includes some but not all of the real analysis material. I guess 550 (Applied analysis) is the essential course to take for students in applied math. but I do not know enough about it to offer any advice.
The current version of Math 510 (Functional Analysis) is actually a mixture of point-set topology, real analysis, and just enough functional analysis to hint at what you will be missing. (I will try to change it this year.) We have had no courses in harmonic analysis - selected topics are being included in applied and PDE courses as needed.
In addition to the 15 "regular" probability courses listed above, there were also 4 additional summer graduate courses in probability in 2004 and 2005.
Other departments may offer courses appropriate for some of our students, especially in applied math. I have made no effort to include these. But I would be quite interested to find out how many of our students do indeed take courses in other departments.