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 | :-) |

- 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.