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Applying to Graduate School in the Mathematical Sciences

Summary

This page contains information about graduate school in mathematics that I have gathered over the years. It is by no means complete, nor is it intended to be definitive. Everyone’s circumstances are different. This page contains information about

W&L math major alumni

In recent years W&L math majors have gone on to the following graduate schools (partial list):

Mathematics:

  • Wake Forest University, UC Berkeley, University of Southern California, University of South Carolina, University of Iowa, University of North Carolina, University of Virginia, The Ohio State University.

Statistics:

  • University of Iowa.

Other:

  • Cornell (Operations Research), Boston University (Mathematical Finance), Carnegie Mellon (Finance), Duke University (PhD in Physics), University of Virginia, (Medical School).

Preparing for graduate study in the mathematical sciences

Preparing for a Actuarial study:

  • Check out Be An Actuary, which is supported and maintained by the actuarial professional societies and some major employers.
  • Professor Dresden has an excellent website on preparing for an actuarial career at W&L.

Preparing for a math PhD: A solid foundation is required for graduate study in the mathematical sciences. W&L math majors (easily) satisfy requirements for most PhD programs.

  • Multivariable calculus and linear algebra.
  • Real analysis (311, 312), and abstract algebra (321, 322).
  • Recommended: complex analysis (303), geometry and topology (341, 342), and some kind of discrete math (122, or 361, 363).
  • Recommended for applied math: ordinary and partial differential equations (332, 333), statistics (309, 310).
  • Take more courses! Why not? It will give you a better feel for the different areas of mathematics.
  • If possible, try to take part in an undergraduate research experience. In addition to the Summer Research Scholars Program at W&L, consider applying to REU programs at other institutions. Click here for a list of such programs funded by the NSF.
  • If possible, try to present your research (talk or poster) at a conference. W&L students regularly present their research at the SUMS conference at JMU in October. It’s also worth trying to present your research at MathFest (held each year in August) or at the Joint Math Meetings (held each year in January). The W&L Provost’s office and Math Department will help fund these trips. There is also some national funding to help with travel expenses.

Additionally, you should plan to take both the General GRE and the Mathematics GRE in the fall of your senior year. During Fall semester, there is often a 1 credit Math 401 section GRE-prep course to help you prepare for the Mathematics GRE.

The courses that are most important in preparing for the Mathematics GRE are: Multivariable Calculus (221), Linear Algebra (222), Real Analysis (311), Abstract Algebra (321).

Preparing for a stats PhD: A solid foundation is required for graduate study in statistics:

  • Discrete math, calculus and linear algebra.
  • Statistics (309, 310), real analysis (311, 312).
  • A course with modeling in it (like ordinary differential equations (332)).
  • If possible, try to take part in a statistics undergraduate research experience.
  • If possible, try to present your research (talk or poster) at a conference. Local conferences provide great opportunities to talk, and there is also the Joint Statistical Meetings held each year in August. The W&L Provost’s office and Math Department has some funding for travel expenses.

Additionally, you should plan to take the General GRE in the fall of your senior year.

Other sources:

  • Nebraska IMMERSE has two interwoven components: one that strengthens the preparation of students who are about to enter their first year of graduate study in mathematics, and one that develops the teaching, research and mentoring skills of graduate students and early-career faculty.
  • Edge Program for women in mathematics is designed to help prepare women for PhDs in the mathematical sciences through a summer session, an annual conference, travel for research collaborations, travel to present research, and other open-ended mentoring activities.
  • Postbaccalaureate Program at Smith College is for women with bachelor’s degrees who did not major in mathematics, or whose mathematics major did not include some core preparatory courses.
  • Some students with a weaker background do a masters degree first, before moving on to a PhD program.

Anatomy of a math graduate degree

Math PhD degree:

  • Usually takes between 4 and 6 years depending on your background and research area.
  • Breadth requirement: You will take basic graduate courses during the first 1-2 years of the program. This gives you a solid mathematical foundation for undertaking high-level research. This is usually checked by exams (called the comprehensive or qualifying exams), or course requirements, or a combination of the two.
  • After the first year or two of a PhD program, some students realize graduate study is not for them. If the requirements have been met, they usually graduate with a masters degree (see below).
  • Years 1-2: find a thesis advisor.
  • Depth requirement: You will work with your thesis advisor on your research area. You will take courses in your area of specialization and also find a topic for thesis research. This is usually checked by a committee in an oral exam (called the preliminary or qualifying exam).
  • A dissertation committee is formed after the prelim/qual exam.
  • Foreign Language requirement: Not all universities have these, but many programs require that you be proficient in reading mathematics in one or two languages other than English. Your proficiency is usually evaluated by a math faculty member and will likely involve translating a mathematical passage (dictionaries are allowed). Language departments often offer courses that teach you to read in a foreign language.
  • Years 2-6: You will work closely with your thesis advisor on original research. The point of the doctoral degree is to show that you are a scholar who is able to conduct independent research. You may end up writing one or more research papers during this stage.
  • Thesis & thesis defense: All of your research is written up in a thesis (also called a dissertation). It is distributed to, and then read by your thesis committee. There is then an oral examination on the material.

Math MA or MS degree:

  • Usually takes about 2 years.
  • Often a certain number of courses at the graduate level are required.
  • Some programs require a thesis, others do not.
  • Some programs require courses or research projects which are of an interdisciplinary nature.
    Students with math Masters degrees find jobs in business (consulting and actuarial), education (both college and secondary education), industry (analysts and various computing activities), or government agencies. Still others have entered excellent professional programs in medicine, business and law, or graduate programs in statistics, biostatistics, or operations research. It appears that many employers prefer to hire candidates having strong mathematical training together with good programming skills.

Many masters degrees are not funded. There is a list of some that are below. Many, but not all, of these programs are in applied math and some have close ties to industry.

Finding graduate schools

Funding graduate study:
Unlike professional schools, graduate school in the mathematical sciences should not cost you money. Fellowships are available, though it is likely you will have to do some teaching (as a teaching assistant). You will not save much, but you will probably not go into debt during your PhD studies.

  • When you apply for admission to graduate school, you will also apply for funding.
  • Institutions with both masters and PhD programs usually give funding priority to students in the PhD program.
  • Click here for a blog post about some fellowships available to US citizens and permanent residents for graduate study in disciplines including mathematics.
  • NSF Graduate Research Fellowship Program for US citizens or green card holders (deadline late October or early November).
  • National Physical Science Consortium offers graduate fellowships in the physical sciences, with special emphasis toward the recruitment of underrepresented minority and female physical science and engineering students.

How many schools should I apply to?
This depends on each individual. Three is probably too few and thirty is probably too many. Most people apply to 8-16 schools. Your list should have a variety of different schools: your top choices, higher ranked schools which are a “reach”, and lower ranked schools which are “safe”.

It’s all about the right fit. 
Ability is important in succeeding in math graduate school, but it is often not the most important factor. Working hard, having self-confidence, and being in the right environment are all crucial.

When comparing different graduate programs, here are some things to consider:

  • Requirements with regards to coursework, research and teaching.
  • The size of the program (is it large or small)?
  • Consider the faculty – are they friendly and available for you to ask questions?
  • Is there just one potential PhD advisor in your area of interest or many?
  • Consider the graduate students – are they friendly? Do they collaborate?
  • What is the average time to complete a PhD? Does the funding cover that period?
  • Are you able to get funding? If it is year by year, what would disqualify you?
  • What is the cost of living?
  • What is it like to live in the surrounding town?

Other people and organizations have compiled more detailed lists of questions to think about when choosing a graduate school:

Search tools:
There are several websites which give searchable lists and detailed evaluations of graduate programs in mathematics (and other disciplines). You choose the criteria you want to include, and also what weight each criterion should have. The site then ranks graduate programs according to your criteria.

Other sources of advice:

What’s in an application?

Don’t forget that the application process begins well before you actually start filling out a form. As discussed above, you will need to work out how many and what kind of schools you want to apply to. Start researching schools now! Deadlines for applications are usually in December or January.

The application itself consists of:

  • Basic information: name, address, phone, email.
  • Education: degrees, dates of attendance and/or receipt of degree, honors, etc. List your major (and minor) and any graduate courses taken.
  • Work experience.
  • Publications: ex. a senior thesis, REU papers, published articles.
  • Talks: ex. Mathfest, department seminars, other undergraduate math conferences.
  • Teaching experience: ex. grading, tutoring, formal teaching training.
  • CV or resume. Remember to include the page number and your name on each page. (Much of the information listed here will be in this document.)
  • Statement of purpose. Note that every school has their own length requirements, but most essays have a length limit of 1-3 pages.
    • Allow several weeks (and many drafts!) to write your statement.
    • What is in a statement? Each person’s statement is different! To get started, ask yourself: Why do I want to pursue a math PhD, why am I interested in math? What do I want do with a math PhD? Why am I interested in studying at this school?
    • Show your statement to your friends and to a couple of math faculty that know you. We can give you useful feedback.
  • GPA – you can include both you overall and math GPA.
  • GRE scores. Plan to take the General GRE (and the Mathematics GRE, if applicable) no later than November. During Fall semester, there is often a 1 credit Math 400 section GRE-prep course to help you prepare for the Mathematics GRE.
  • Transcript(s).
  • Some applications may need a separate list showing all math courses taken.
  • Letters of recommendation (usually 3 letters).
    • Think carefully about who your letter writers are. They should be able to talk about your mathematical ability in detail.
    • Give your letter-writers at least four weeks before the first deadline.
    • Provide your letter writers with a CV or resume, personal statement, and transcripts so that they can use these materials as a reference.
    • Ask your letter-writers if they would like a reminder closer to the deadline.
  • Other relevant information like grants, summer support, conferences attended, committees, foreign languages, computer skills, etc.

What do I do now I have been accepted to graduate school?

The earliest you can expect to hear back from some schools is in early January. Most students will hear back in late February or early March, or even later.

Most graduate schools have a deadline of April 15 for you to accept or decline an offer. You should not be under any pressure to make an early decision.

Once you’ve been admitted to a graduate program:

  • Arrange to talk to faculty and students at the institution (the graduate director should give you names and email address when asked).
  • If possible arrange to visit the school. These trips may be funded by the graduate program.
  • When visiting, keep in mind the questions discussed above. You’ll want to talk to both faculty and students and really make sure you understand the details of the program requirements and the funding package.
  • If you have got into school A, but would prefer to go to school B, you can contact the graduate director of school B and ask about the status of your application. Often programs can give you an idea of where you are ranked, and if they think they may be able to give you an offer later on.
  • If you know you will definitely not attend a school, be sure to reply early. That way your spot can be offered to another student.

Talk to the math faculty at W&L about what is happening – they are happy to listen and give support during the decision process.

Life as a graduate student

Surviving your first year in graduate school:

Helpful hints to round out your degree:

Other sources of advice and some humor too: