Resources for Graduate Students
After the Master's degree and before the Ph.D.
This is 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 comprehensve exams) and before receiving their Ph.D. It provides
suggestions on such topics as choosing an advisor, beginning to conduct
research, writing up results, and submitting papers for publication.
A Brief Guide to Mathematical Writing
I have put together a Brief Guide to
Mathematical Writing. It provides a list of suggestions for
grad students who are beginning to do mathematical writing for the
first time in their careers.
The book How to Write
Mathematics by Paul Halmos is also an excellent guide to writing. In
addition, there is a
summary of Halmos' article
written by Peter Cameron.
Getting Started with LaTeX
Are you just starting to learn LaTeX? Here is an article template that
will help you begin writing. In addition to the template, I've made a
version with comments containing examples of some basic LaTeX commands.
By comparing the source and the typeset version you can learn a few tricks
that will help you write your own article.
LaTeX Template: [tex] [pdf]
LaTeX Template with Comments: [tex]
In addition to this template, you may find the following resources useful
as you begin to TeX.
- A Hypertext
List of LaTeX topics maintained by NASA.
- Doug Drinen has written a guided example of Beamer and LaTeX. If you
have this tex file and this image, you should be able to produce this pdf file.
- A Beamer
Quickstart by Rouben Rostamian.
- Detexify is
an online tool for helping you look up LaTeX symbols.
- A reference
sheet containing a list of symbols available in LaTeX.
- A second reference sheet. This one is
for Plain TeX, but most of the commands work in LaTeX and it contains
some symbols the previous sheet does not.
- The Not So Short Introduction to
LaTeX2e. This has the advantage of being free, but if you're going to
be doing some serious TeXing you should invest in a book. First Steps in
LaTeX by George Gratzer, and its big brother Math into LaTeX
by George Gratzer are both excellent books. Both are available on amazon.com.
- There are three main sources on the web for TeX information:
- The PracTeX
Journal is an online journal for practical TeX sponsored by the TeX
- Xy-pic is an
application that can help you draw figures.
How to Give a Good Talk
To have a career in mathematics you will have to give several talks on
your work. The following are several guides containing suggestions
for giving an effective mathematics talk.
The TA Handbook
If you have never been a Teaching Assistant (TA) for a class before, or
if 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
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
Resources for Young Mathematicians
Useful things to know when starting graduate school, as contributed
by experienced graduate students at UC Davis.
- Advice for the
Young Scientist by John Baez
- The Young Mathematicians'
Network is a loose organization of mathematicians in the junior part
of their careers. Their website contains a copy of their newsletter
"Concerns of Young Mathematicians".
- A one page letter that appeared in
the Notices of the American Mathematical Society in 1998. It
contains advice for young mathematicians as well as a brief list of
things one should be doing to prepare for a career in mathematics.
- "You and Your Research", a talk
given by Richard Hamming that centered on the question "Why do so few
scientists make significant contributions and so many are forgotten in the
long run?". Hamming discusses what he has learned in terms of the
properties of individual scientists, their abilities, traits, working
habits, attitudes, and philosophies.
- Birds and Frogs, an essay by
Freeman Dyson that was written for his planned Einstein Public Lecture. In
it he divides mathematicians into two types: birds, who "fly high in
the air and survey broad vistas" (i.e. seek abstraction, unification, and
generalization), and frogs, who "see only the flowers that grow nearby"
(i.e. study the details of specific examples).
- 10 Lessons for Mathematicians given
by Gian-Carlo Rota. This article is based on a talk delivered on the
occasion of Rotafest in April, 1996, and was reprinted in the Notices of
- The Princeton Companion to
Mathematics' section on advice to younger mathematicians, with
contributions by Sir Michael Atiyah, Béla Bollobás, Alain
Connes, Dusa McDuff, and Peter Sarnak.
- What is Good
Mathematics? by Terry Tao
- Terry Tao's Blog
contains a lot of great material for mathematicians and graduate students.
In particular, check out his sections on career advice and
- Mathematical Writing by Donald
E. Knuth, Tracy Larrabee, and Paul M. Roberts
- Should you cite Wikipedia in research papers? Wikipedia says "no".
Here is a Wikipedia
article discussing the issue.
- A guide
to creating and maintaining a CV from ProfHacker. Also, here is a CV and Resume Guide from the Rice Center
for Student Professional Development.
- Successful Researcher, a
blog containing academic career advice with links, tips, and more.
- It's All About Research
and Why am I so
confused?, articles from the AMS Graduate
- The Notices of the AMS has published a series of articles intended
for graduate students. These deal with different topics related to
starting a career in mathematics.
- The MAA has also publised various articles aimed a graduate students.
Some of the Best Writing About Mathematics and Mathematicians
Entertaining and Thought-Provoking Links
Legendary Math Writing
There are a number of urban legends about various written works in math
(shortest, longest, funny titles, etc.). Some of these are real, and
some are not. Here are some of the real ones.
Math Books Available Online
only real difference between grad school and
jail is that when you get out of jail there are agencies to assist you in
finding a job."
Here are some resources that you may find useful as you apply for jobs.
- Piled Higher
and Deeper -- a grad student comic strip
- xkcd -- a webcomic of romance,
sarcasm, math, and language
- Spiked Math Comics -- a math
comic to humor, educate and entertain the geek in you.
- Abstruse Goose -- a webcomic
about math, science and geek culture
- Saturday Morning Breakfast
Cereal -- a webcomic on topics such as love, relationships,
economics, politics, religion, science, and philosophy
- The Joy of
Tech -- a webcomic concentrating on technology-oriented themes
- Questionable Content
-- a webcomic about romance, indie rock, little robots, and the problems
- The Oatmeal -- a humorous site
on topics ranging from zombies, to horse care, to English grammar
- Some comic strips from newspapers: FoxTrot, Dilbert, and Calvin and
- Some homorous YouTube videos:
- How to write a thesis
- An advertisement for Math Grad School: The
- Things not to do at your thesis defense
- Why grad school isn't hell
- A funny