*Core* and *Advanced* Graduate Courses: Definitions and Schedules

The 8000 level courses appearing in the tables below constitute the current working definition of the term *core graduate course. *A graduate course not appearing on this list will be called an *advanced graduate course.* Please refer to the full list of Mathematics courses 4000 and above.

To increase the predictability and the enrollment for core graduate courses, we will stay with the prescribed Fall/Spring schedule for core graduate courses. Advanced graduate courses may be offered on a less predictable basis.

Advanced graduate courses include three sub-classes:

*Topics*courses (title includes the word "Topics"). Examples include 8102, 8302, ...*Seminar*courses (title includes the word "Seminar"). Examples include 9187, 9287, ...*Other*advanced courses (title does not include either of the words "Topics" or "Seminar") . Examples include 8642, 8680, 8629, 8670...

It is allowable to list a Topics or Seminar course multiple times on your program of study assuming it is *not a duplicate course* covering the same topic. Topics and Seminar courses generally have subtitles describing the topic, to list two courses on the program of study it is sufficient that the subtitles are (significantly) different *even if the course numbers are the same*. On your transcript, only the course number and title appear. On your program of study, you should try to list the course number, the abbreviated title *and the subtitle. * For example:

- 8102 Topics: Lie Algebras
- 9487 Seminar: Morse Theory

This is a professional research degree designed to prepare students for various advanced professional careers, including college teaching and research.

**Year 0** courses include basic advanced undergraduate material, which incoming Ph.D. students are required to master before engaging in graduate coursework. Well prepared incoming students can petition to skip some or all of the Year 0 courses. The Director of Graduate Studies will administer an informal exam to see if the students are sufficiently ready to skip Year 0 courses.

Fall | Spring |
---|---|

Advanced Calculus of One Real Variable 7700 |
Advanced Multivariable Calculus 7900 |

Topology 8655 |
Complex Variables 7940 |

Abstract Algebra 7720 |
Advanced Linear Algebra 7920 |

**Year 1** courses will train students to develop a common solid foundation on basic graduate mathematics. The Ph.D. student is required to pass all 6 courses, and to pass qualifying exams in Algebra and Real Analysis. The qualifying exams will be given in May of each year, shortly after finals week. There will be an opportunity to retake a qualifying exam in August just before the beginning of the Fall semester. The Analysis qualifying exams will be from topics from Real Analysis I and Real Analysis II. The Algebra qualifying exams will be from topics from Algebra I and Algebra II. Extremely well prepared students, with the permission of their initial adviser and the Director of Graduate studies, may take one or both qualifying exams in August before they start their first semester. If they pass, then with the permission of their initial adviser and the Director of Graduate studies they may skip the corresponding courses in Year 1.

Fall | Spring |
---|---|

Real Analysis I 8420 |
Real Analysis II 8411 |

Algebra I 8410 |
Algebra II 8411 |

Complex Analysis 8425 |
Differentiable Manifolds 8430 |

**Year 2** and above are the post-qual core courses. Every Ph.D. student must complete at least six of the post-qual core courses. (Note that the parity of the year is determined by the beginning of the AY. For example, Spring 2016 occurs in the beginning of AY 2015, and so would be considered to be in an odd year.)

EVEN YEAR | ODD YEAR | ||
---|---|---|---|

Fall | Spring | Fall | Spring |

Harmonic Analysis I 8630 |
Harmonic Analysis II 8631 |
Harmonic Analysis I 8630 |
Harmonic Analysis II 8631 |

PDE I 8445 |
Theory of Distributions 8302.1 |
PDE I 8445 |
PDE II 8446 |

ODE 8440 |
Probability 8480 |
ODE 8440 |
Probability 8480 |

Algebraic Number Theory 8521 |
Differential Geometry 8650 |
Analytic Number Theory 8520 |
Algebraic Topology 8618 |

Commutative Algebra I 8510 |
Commutative Algebra II 8511 |
Algebraic Geometry I 8615 |
Algebraic Geometry II 8616 |

Functional Analysis 8628 |
Mathematical Physics 8402.1 |

The graduate student must further complete a course of study approved by the doctoral program committee and pass a comprehensive examination. The active areas of research interest of the current members of the staff are: algebraic geometry, commutative algebra, number theory, representation theory, analysis (real, complex, functional and harmonic), analytic functions, applied mathematics, financial mathematics and mathematics of insurance, scattering theory, differential equations (ordinary and partial), differential geometry, dynamical systems, general relativity, mathematical physics, probabilistic analysis and topology.

*Note: Effective at the start of Winter Semester 2007, there is NO foreign language proficiency requirement for the Mathematics PhD. However, a student's Doctoral Committee still retains the discretion to impose a foreign language proficiency requirement. *