Graduate Studies
Program of Study

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This page is designed to assist the planning of courses for MA, MS and PhD degrees. These samples are offered only a starting point. Each student should work closely with his/her academic advisor to individually plan the program of study. This page has three sections:

The program of study should be recorded on a M1 form for master’s students and a D1 form for PhD students. Please be familiar with the following material:

Core and Advanced Graduate Courses: Definitions and Schedules

The table below constitutes 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. Plese refer to the full list of Mathematics courses 4000 and above.

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

Advanced graduate courses include three subclasses:

It is allowable to list a Topics or Seminar course mutliple 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

Additional Information:

List of Core Graduate Courses: subject to minor revision

Number Course Name Fall Semester Winter Semester
7500 Applied Analysis Yes Yes
7700 Advanced Calculus I Yes Yes
7720 Intro to Abstract Algebra I Yes ??
7900 Advanced Calculus II
Yes
7920 Intro to Abstract Algebra II
Yes
7940 Intro to Complex Variables Yes




8210 Basic Algebra Yes
8220 Basic Analysis Yes
8250 Basic Topology and Geometry
Yes
8410 Algebra I
Yes
8411 Algebra II Yes
8420 Real Variables I Yes
8421 Real Variables II
Yes
8425 Complex Analysis I
Yes
8426 Complex Analysis II Yes
8440 Advanced ODE I Yes
8441 Advanced ODE II
??
8445 PDE I
Yes
8446 PDE II Yes
8460 Mathematical Finance I
??
8461 Mathematical Finance II ??
8480
 Advanced Probability
??
8615 Algebraic Geometry I Yes
8616
  Algebraic Geometry II
??
8618 Intro to Algebraic Topology Yes
8628 Functional Analysis I
Yes
8630 Harmonic Analysis I Yes
8650 Diff. Manifolds ??
8680
 Stochastic Processes
 ??

Course Suggestions


Please note that both Graduate School and Mathematics Department policy requires that every graduate student be enrolled as a full-time student during Fall and Winter semesters. This requires (a minimum) of 9 credit hours (3 courses) for Master's students, and for PhD students who have not yet passed their Comprehensive Exams. PhD students who have passed Comprehensive exams are not subject to this requirement.

Any exemptions from the full-time requirement must be approved in advance by the student's advisor, the director of graduate studies, and the Graduate School. PhD students who have passed Qualifying Exams and are studying for Comprehensive Exams may request to enroll in 6 credit hours instead of 9. Failure to obtain prior approval for a reduced course load may result in the removal of the student's tuition waiver by the Graduate School. Pleae note that part-time status may affect the terms of some contracts outside the University, including student loans, insurance policies, and visas.

REVISED MS Course Suggestions
Fall Semester Winter Semester
Year 1
7700 Advanced Calculus I
7140 Matrix Theory
7940 Intro to Complex Variables
8440 Advanced ODE I		 7900 Advanced Calculus II
7500 Applied Analysis
7315 Intro to Mathematical Statistics
8250 Basic Topology and Geometry
Year 2
8420 Real Variables I
7300 Numerical Analysis
8470 Advanced Numerical Analysis
8440 Advanced ODE I
 8425 Complex Analysis I
8445 Partial Differential Eqns I
8250 Basic Topology and Geometry

8190/8090 Masters Project/Thesis



REVISED MA Course Suggestions
Fall Semester Winter Semester
Year 1
7500 Applied Analysis
7700 Advanced Calculus I
7720 Intro to Abstract Algebra I
7940 Intro to Complex Variables		 7900 Advanced Calculus II
7920 Intro to Abstract Algebra II
8250 Basic Topology and Geometry
8445 Partial Differential Eqns I


Year 2
8420 Real Variables I
7315 Intro to Mathematical Statistics
8220 Basic Analysis
8210 Basic Algebra
8440 Advanced ODE I
 8250 Basic Topology and Geometry
8410 Algebra I
8425 Complex Analysis I

8190/8090 Masters Project/Thesis



REVISED PhD Course Suggestions
Fall Semester Winter Semester
Year 0
7700 Advanced Calculus I
7940 Intro to Complex Variables
7720 Intro to Abstract Algebra I		 7500 Applied Analysis
7900 Advanced Calculus II
7920 Intro to Abstract Algebra II
Year 1
8220 Basic Analysis
8210 Basic Algebra
 8410 Algebra I
8425 Complex Analysis I
8250 Topology and Geometry
Year 2
Topics/Advanced course
Outside course		 8445 Partial Differential Eqns I
Outside course
Analysis specialization
8420 Real Variables I
8426 Complex Analysis II
 8421 Real Variables II
8628 Functional Analysis I
Algebra specialization
8411 Algebra II
8615 Algebraic Geometry I		 Topics/Advanced course
Other areas of specialization*
8420 Real Variables I
8440 Advanced ODE I
8650 Different Manifolds/Riemann Geometry		 8421 Real Variables II
8628 Functional Analysis I
8441 Advanced ODE II
Year 3
Analysis specialization
8480 (Stat 9810) Advanced Probability
8446 Partial Differential Eqns II
8629 Functional Analysis II
8630 Harmonic Analysis I		 Topics/Advanced course
8631 Harmonic Analysis II
Algebra specialization
8411 Algebra II
8615 Algebraic Geometry I		 Topics/Advanced course
8616 Algebraic Geometry II
Other areas of specialization*
8446 Partial Differential Eqns II
8440 Advanced ODE I
8460 Financial Mathematics I
8680 Stochastic Processes
8650 Different Manifolds/Rieman Geometry
8618 Algebraic Topology
 8465 Risk Theory
8441 Advanced ODE II
8461 Mathematical Finance II
8470 Advanced Numerical Analysis
8480 (Stat 9810) Advanced Probability

(*) Other areas of specialization include: Applied Mathematics, Financial Mathematics, Geometry, and Mathematical Physics


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