Resources for Graduate Students

This page contains a number of resources for Graduate Students in Mathematics at UH. Here is a list of the topics covered.

The Flammarion Engraving by an unknown artist
  1. Some Documents Containing Advice
  2. Advice and Thoughts on the Profession
  3. Professional Societies
  4. Online Resources for Research
  5. Attending and Giving Talks
  6. Mathematical Writing
  7. Teaching Experience
  8. Summer Programs for Graduate Students
  9. The Academic Job Search
  10. Harsh Realities

1. Some Documents Containing Advice

The following are a few (fairly detailed and lengthy) documents that contain advice about specific aspects of your graduate career.

After the Master's degree and before the Ph.D.

This is a Guide for Ph.D. Candidates in Mathematics that I wrote for graduate students shortly after earning my Ph.D. It contains advice for graduate students in mathematics during the period of time after they pass qualifying exams (or preliminary exams) and before receiving their Ph.D. In it you will find suggestions on such topics as choosing an advisor, beginning to conduct research, writing up results, and submitting papers for publication.

I've passed my quals, now what? A guide for Ph.D. candidates in Mathematics

Having a Grand Project

I gave a talk at the UH Math Department's Graduate Student Seminar advocating that every graduate student have a "Grand Project", something special that you choose to work on to make a personal connection with and contribution to mathematics. Here are the slides from my talk.

Having a Grand Project: Advice for Graduate Students

The TA Handbook

If you have never been a Teaching Assistant (TA) for a class before, or if you would like to be more effective in your teaching duties, take a look at the TA Handbook published by the MAA.

"A Handbook for Mathematics Teaching Assistants" by Tom Rishel

2. Advice and Thoughts on the Profession

Advice from the Greats

Paul Halmos Terence Tao
Freeman Dyson
John Baez
Richard Hamming
Sir Michael Atiyah
Steven G. Krantz
Uri Alon
Gian-Carlo Rota
Jean-Pierre Serre

Articles with Advice for Graduate Students

Thoughts on Doing Mathematics

3. Professional Societies

There are several professional societies for mathematicians. The two main professional societies are the AMS and MAA.
Sometimes the differences between the AMS and MAA are summarized as "The MAA is more concerned with mathematics education, while the AMS is aimed more at professional mathematicians". While there is some truth in this, it is a large oversimplification. The AMS and MAA are both interested in mathematics education at all levels as well as research mathematics, but their missions place different emphasis on various issues within education and research.

Since our math department is an AMS department member, all of our math graduate students receive free membership to the AMS. This means you should be receiving the AMS Notices and the AMS Bulletin in the mail. If you are not, check with the department's Director of Graduate Studies regarding your membership.

As a graduate student, you should consider joining other professional societies as well. (I highly recommend the MAA for anyone planning on a job in academia and SIAM for all applied students or for students planning a job in industry.) Membership information can be found on each society's website, and you should be aware that the student rates for membership are much cheaper than faculty rates. As a member of a professional society, you receive the monthly publications of the society, discounts on books and conference registrations through that society, mathematics and society news, information about mathematics opportunities, and access to certain online information. Your membership also supports the mathematics community and shows a level of professionalism that future employers like to see.

In addition to the AMS and MAA, some other popular mathematics societies with more specialized roles are the following:
Even if you are not a member of a particular society, their website can often be a source of very useful information for you. In particular, the AMS and MAA both have a list of resources for students on their websites, and these are accessible to everyone.

Student Chapters

Our department has an AMS Graduate Student Chapter (aimed at serving all graduate students), and a SIAM Graduate Student Chapter (aimed at serving graduate students in applied math). All graduate students should be involved in these two student chapters and regularly attend the events that they offer.

4. Online Resources for Research

Books and Papers

Answering Questions

Advice for Reading Papers

Here is some advice for students reading papers for the first time:
  1. Begin with the abstract to see if you're interested.
  2. Read the introduction and conclusions with extra focus on the main ideas and results.
  3. Skim the middle sections to get a feel for the flow, pay special attention to main theorems.
  4. Read select parts in more detail. Feel free to skip around depending on your level of interest and how much detailed info you need.
  5. When an especially deep understanding is required, it may be necessary to go back and read the entire article from start to finish.

5. Attending and Giving Talks

Attending Talks, Colloquia, and Seminars

The Graduate Student Seminar and the AMS and SIAM chapters have talks aimed at graduate students and should be accessible, relevant, and interesting to all graduate students. You should do your best to attend all of these.

Unfortunately, many colloquia and seminar talks are often bad; usually because they are too technical and difficult for non-experts to follow. Despite this, it is still beneficial for you and necessary for your professional development that you attend them. (Remind yourself that one useful talk is often worth attending ten bad talks.)

Try to get something out of every talk. Gain exposure to new ideas. Learn what topics are at the forefronts of research right now. Learn the concepts and words that come up in current research. Learn (perhaps by counterexample) what the elements of a good talk are. In addition, strive to understand at least some small part of every talk you attend. Here is some advice for doing so:

Giving Talks and Presenting Your Work

To have a career in mathematics you will need to give frequent talks on your work. The following are several guides containing suggestions for giving an effective mathematics talk.

6. Mathematical Writing

Here are some resources for Mathematical Writing.

7. Teaching Experience

If you are planning on having a career in academia (even one with a large research component), then teaching will be an important part of your future duties.

Teaching Experiences at UH

During your time in graduate school, you should make a conscious effort to get as much experience and training in teaching as you can. This will not only help you in your future career, but it will help you get a job as you enter the highly competitive academic job market.

If you intend to have a career in academia, you should seek out additional teaching opportunities beyond your TA duties. Here are a few options.

Summer Teaching Opportunities

If you want to use the summer to gain teaching experience, there are many K-12 mathematics summer programs that seek (and pay) graduate students and faculty to assist with teaching. Here are a few:

Teaching Resources

Some Advice as You Develop Your Teaching Skills

8. Summer Programs for Graduate Students

9. The Academic Job Search

Here is a page with advice for students applying for academic jobs.

Advice for the Academic Job Search

Students who are interested in non-academic jobs should refer to SIAM's list of Careers in Applied Mathematics.

10. Harsh Realities

"[O]f all the machines that humanity has created, few seem more precisely calibrated to the destruction of hope than the academic job market." ---Dr. Patrick Iber (At the time he wrote these words, Dr. Iber had a Ph.D. from the University of Chicago, a book contract with Harvard University Press, and a visiting lectureship at UC Berkeley.)

The drop-out rate in graduate programs throughout the U.S. has become increasingly high, and the job market for Ph.D.s is not particularly good, especially for academic jobs.

Furthermore, in academic jobs, the path to tenure has become longer and more difficult over the past few decades, with greater emphasis placed on obtaining grants and external funding. In addition, the hiring of more and more adjunct faculty and lecturers has led to a decrease in the number of faculty positions and more exploitation of academics with Ph.D.s.

On top of all this, the recent economic problems combined with the sequestration imposed by the U.S. government has made a bad situation worse, and created an environment of scarcity for both academic and non-academic jobs.

It is important to be aware of these issues and prepare for them The information here is meant to help you, not to discourage you. It is intended to help you make an accurate assessment of the current state of graduate programs and job markets for Ph.D.s, so that you can make informed decisions and plan for the future. It is important for all graduate students to start preparing for jobs and gaining skills to make themselves marketable in the early stages of their graduate career, long before earning their degree and applying for jobs.

Thoughts on Graduate School

The Adjunct Crisis

Data on the Profession

Interdisciplinary Work

Postdoctoral Positions and Tenure

To get a tenure-track job at a research university, you will need to do at least one postdoc. The following comic strips from Ph.D.Comics give you a sense of the impermanence of these positions, and the uncertainty of future employment, as you try to get your next position.

The Perils of Tenure

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