michigan university math phd

Advice and Resources for Mathematics Graduate Students

Qualifying Review

Students often stress a lot about the QR Exams. Here we gather some advice from students who have made it through this process. For details on the Qualifying Review Process , please see the official math department webpage. It is important to note that the Qualifying Review is not just a sequence of exams: each student is carefully discussed by the Doctoral Committee to determine readiness to pass the Qualifying Review, including their academic record at Michigan (courses, grades, comments of professors) as well as plans with a tentative advisor. The process is not just an all-or-nothing exam score above a certain number. 

That being said, we acknowledge that students do stress about the QR exams, and every math PhD student must pass exams in three subjects (although it is acceptable also to  “course out” of one of the subjects). The Math Department QR Exam page .   has  outlines of each exam’s syllabus,  past QR exams and some solutions. (Beware though, some solutions might have some errors! Write to us if you think you found one!)

Qualifying Review examinations (QRs) are offered in the following four areas – Algebra, Topology, Analysis, and Applied Analysis. Exams are offered before fall term (late August/Early September), before Winter Term (early January) and after winter term (early May). There is no penalty for trying and failing: students are encouraged to try an exam as soon as they think they might be ready.

Students must pass one of these exams by January of their second year. We advise and expect students to try one in May of their first year, after spending that year preparing for the QR exam in that subject by taking the corresponding “Alpha Courses;” if needed, student can make a plan to prepare through the summer and/or fall. Of course, students who have studied the material at the graduate level already are encouraged to take the exams even earlier: your score on the QR is a good data point for choosing classes. It is usually a big mistake to skip the alpha courses without having passed the QR exam in the corresponding subjects.

All three exams should be passed by January of the third year.  You can also `course out’ of one of the QR exams: instead of taking a qual, you can take two courses  specific courses in that area and earn at least B’s. Please read the more detailed rules on the math department website.  

The applied analysis qual is often cancelled, due to no one registering for it.   

Take the alpha courses.

The alpha classes (Math 593, 594, 591, 592, 596, 597) are designed to prepare you for the quals. You might think that are not related to your field of interest, but the content of these courses is something every mathematician should be proficient in.  For those with more applied interests, you can substitute Math 556, 572 for 592 and 594.

Start taking the QRs early, and try again and again.

Start early and don’t be afraid of taking a QR exam even if you are not fully prepared. Sometimes the quals are easy and you might get lucky, and there are no penalties for failing a given qual. 

Don’t be afraid of coursing out.

If you only have one QR remaining and have not been able to clear it despite multiple attempts, consider coursing out. 

Focus on one Exam at a time

Try to get at least one QR done at a time. You can study for multiple quals at a time, but study more for one particular area, that you feel the most confident about. 

Form study groups

If you plan to study on your own, you might often not feel motivated enough to do it. In such cases, it is good to have form a study group to keep you focused. In addition, your study partners might know how to solve some problems that you don’t. You can easily find people studying for a particular exam by either asking around or sending an email to the math graduate student list. Additionally, the AWM sometimes has  QR study sessions before the exams.

Take timed practice exams

Many people perform very differently under time pressure. Try to solve a past QR exam in three hours. This will simulate the time pressure that you will face during an exam and will make you better prepared for it. 

• The alpha courses are designed to prepare students for the QR exams, in addition to being a great overview of the particular areas by masters in the field (and potential dissertation advisors).  It is not a good idea to skip these courses unless you first pass the QR exam. 
• Before taking the exam in a particular subject,  you can sit in the appropriate alpha courses without registering to review, and/or as seek out course notes and problem sets from previous alpha classes. You can make a habit to work with the first year students on their problem sets, even if you are not in the course.
• Past QR Exams are probably the best resources to study for QRs for those who have already taken the courses.
• Mel Hochster made extensive study materials for the Algebra QR exam, including practice problems and solutions, over a period of time in the early 2000’s:
• Review Materials from Fall 2002
• Review Materials from Fall 2003
• Also, scroll down Mel’s website :  toward the bottom are Old Algebra QR Exams with solutions from January 2004, May 2004, September 2004, and January 2005.
• Harry Richman has written out solutions to some Analysis QRs –   http://www-personal.umich.edu/~hrichman/quals.html
• Eamon Quinlan’ s notes for the Analysis QR-  http://www-personal.umich.edu/~equinlan/Analysis%20Notes.pdf  

Sanal Shivaprasad

I took all the quals as soon as I came in. In retrospect, this was probably a bad idea. I was just settling in to a new place, and the quals were right after a tiring week of the teaching orientation. I remember that period as being one of the most stressful times at the university. 

I would recommend you try to take as many of the quals as you can when you come in (maybe 1 or 2), while not stressing too much about it. And, don’t expect to get any studying done in the week right the quals before, due to the teaching orientation.

Rachel Webb

For me, the best way to study for a test is to take old versions of the test. I start doing old tests from the beginning of my study, beginning with the oldest one available. At first it may take me several weeks to get through a test, as I need to go reread relevant parts of the textbook and maybe work several easier homework problems before I can solve the test problems. But solving the tests slowly gets faster, and by the end of my study I can solve a test in one or two days.

I would definitely recommend studying for the quals through past exams. I personally went through around 4-5 past exams in Analysis and Algebra, and made sure that I understood each problem (some older Analysis exams do not have solutions, so I asked them on Stack Exchange). Taking notes on some common tricks is also useful — for instance, the density argument in Real Analysis. 

Another minor aspect is that for some Analysis/PDE students, the “Applied Analysis” exam might be worth considering. My experience is that, having learnt numerical differential equations, the Applied Analysis exam was a lot easier to me than the Algebraic Topology exam. The skills tested turned out more useful as well. 

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Mathematics

Department of Mathematics Western Michigan University Kalamazoo MI 49008-5248 USA (269) 387-4510

Doctor of Philosophy

You may apply for the Doctor of Philosophy in mathematics with a master’s degree or directly upon completion of a bachelor’s program. In addition to satisfying the general admission requirements of the Western Michigan University Graduate College, you must have acquired a sufficient level of mathematical background as determined by the mathematics faculty of the Department of Mathematics.

The  six-year schedule of courses  will help plan your education to graduate in a timely manner.

WMU catalog description

Mathematics education

The Doctor of Philosophy in mathematics education focuses on K-12 mathematics curricula, teaching and learning mathematics and research and evaluation in mathematics education. Programs may focus on:

• Preparation for mathematics education faculty positions in colleges and universities.
• Supervision and curriculum development positions in school systems.
• Evaluation positions in education-related institutions.

Application instructions

WMU has a new online graduate application system that allows all students (domestic and international) to submit required information into one system. General application information for the University, as well as specific requirements for individual programs, are captured into this system.

Thank you for your interest in applying for this graduate program.

Contact us for more information.

Each summer, course offerings are sensitive to sufficient enrollment and availability of qualified faculty to teach them. Thus, courses listed in the six-year plan may not be offered according to the indicated schedule. Students are advised to check schedules and meet with an advisor frequently for any changes in offerings that might affect their program plans.

Comprehensive exams

Dissertation Defenses

January 2023.

Candidate: Caryn Mays For the degree of: Doctor of Philosophy Department: Mathematics Title: Irregular Domination in Graphs Committee: Dr. Ping Zhang, Chair, Dr. Gary Chartrand, Dr. Clifton Ealy, Dr. Dinesh Sarvate Time/Place: Wednesday, January 11, 2023, 9 to 11 a.m.,  Virtual meeting

Candidate: Andrew Bowling For the degree of: Doctor of Philosophy Department: Mathematics Title: Zonality in Graphs Committee: Dr. Ping Zhang, Chair, Dr. Gary Chartrand, Dr. John Martino, Dr. Ebrahim Salehi Time/Place: Wednesday, January 18, 2023, 9 to 11 a.m., Virtual meeting

Seek out others with your same interests. Find mathematics faculty according to their research, scholarship and teaching expertise.

Summer work and programs

Check out possible summer opportunities .

Accessibility Tools

Highlight links, change contrast, increase text size, increase letter spacing, readability bar, dyslexia friendly font, increase cursor size, graduate program.

All accepted PhD students will be offered a teaching assistantship for a maximum of six years of study. The stipend in the first year will be $23,740.

All accepted PhD students will receive this fellowship. The fellowship reduces teaching in the first year to tutoring only.

The application fee for US citizens with GRE math subject scores in the upper 50 percentile will be waived.

The University awards these fellowships to outstanding PhD applicants. The fellowships cover tuition and health insurance and award a stipend of $28,500 for the first and fifth years with no teaching responsibilities. In other years the student is supported by the department teaching assistantships.

The College of Natural Science awards these fellowships to outstanding PhD applicants. The fellowships cover tuition and health insurance and award a stipend of $28,500 for the first year of study with no teaching responsibilities. In other years the student is supported by the department teaching assistantships.

The Department of Mathematics awards these fellowships to outstanding PhD applicants. The fellowship consists of a departmental teaching assistantship and an addition stipend of $8,000 in the first year of study.

Doctoral Degrees in Mathematics

• Ph.D. Degree in Mathematics
• Ph.D. Degree in Applied Mathematics
• Dual Ph.D. Degree

The Master's Degree in Mathematics

• Master of Science Degree in Industrial Mathematics
• Master of Science Degree in Mathematics*
• Master of Science Degree with Concentration in Applied Mathematics*

* These degrees are open only to students currently enrolled in a PhD program at MSU

Student Documents

• Absence Policy for GTAs
• Annual Student Progress and Performance Review
• Committee Report
• Graduate Student Academic Grievance Hearing Procedures
• Graduate Student Handbook ( docx )
• Record of Comprehensive Examination
• Record of Dissertation
• Responsible Conduct of Research and Scholarship
• Travel Funding Form
• Travel Procedures
• Travel Request Letter

Accessibility Tools

Highlight links, change contrast, increase text size, increase letter spacing, readability bar, dyslexia friendly font, increase cursor size, about the doctoral program.

This program is designed for those who show promise of becoming leaders in local, state, national and international mathematics education communities. The program prepares researchers and leaders to address critical issues in mathematics education by developing analytical perspectives for research, engaging in reflective teaching, and deepening mathematical knowledge.

In addition to required coursework in mathematics, students in this program take courses and gain research experience in mathematics education. During their time at MSU, doctoral students in the Mathematics Education Graduate Program usually teach (undergraduate mathematics and teacher education courses, including mathematics for elementary school teachers) and work on mathematics education research and development projects. For those who intend to seek academic jobs as mathematics educators in collegiate mathematics departments, do research about undergraduate mathematics teaching and learning, and/or teach mathematics content courses to undergraduate students, this Ph.D. program might be the most appropriate placement.

Students who may be Interested in the Program

• Graduates of undergraduate mathematics or mathematics education programs with interests in research and academic careers;
• K-12 teachers intending to return to the classroom or to leadership in schools and districts who desire strong, research-oriented knowledge and experience in mathematics education; and
• Graduates of undergraduate mathematics or mathematics education programs with interests in careers in curriculum development, policy, assessment, etc., not necessarily with a focus on research.

Experience Gained at MSU

Students in the Ph.D. program in Mathematics Education will have opportunities to acquire an understanding of and experience in various aspects of the mathematics education field, including:

• investigation of mathematical learning and teaching;
• the development of instructional materials;
• participation in policy formation;
• development and use of assessment; and
• the integration of technology into mathematics learning and teaching.

Students will address issues of research ethics in the Mathematics Education Proseminar courses, MTHE 926 and 927.

Mathematics Focus

A career at any level in mathematics education requires substantive knowledge of the core discipline of mathematics.  Therefore, the degree is designed so that a student can pursue the equivalent of a master’s degree or more in mathematics suitable to his or her area of focus.  With his or her guidance committee, each student will plan a set of courses in mathematics that, together with the student’s prior coursework and teaching experiences, is appropriate for the student’s career plans.

Jointly Administered

The Mathematics Education Doctoral Program is administered jointly by the College of Natural Science and the College of Education , with the College of Natural Science as the lead college. Graduate students are awarded many opportunities and fellowships through both colleges. Please contact Lisa Keller , Assistant Director in the Program in Mathematics Education, with any questions regarding the Mathematics Education Doctoral Program.

Mathematics Education Graduate Program

Beth Herbel-Eisenmann, Director of PRIME and Math Ed Doctoral Program [email protected]

Lisa Keller, Assistant Director of PRIME [email protected]

Name, Academic Program Coordinator/Grad Secretary

619 Red Cedar Road C110 Wells Hall Michigan State University  East Lansing, MI 48824  (517) 432-1490