Advice and resources for new researchers
Here are some helpful thoughts and resources for undergraduate or graduate students just getting started in mathematical research.- Resources for mathematical literature
- LaTeX - Writing papers and presentations
- Job search advice (PhD students)
- Undergraduate math research
Resources for mathematical literature
- MathSciNet is the premier location for published articles in mathematics. MathSciNet has many useful functionalities, including the following.
- Find articles that are referenced in a paper you are reading. If available online, there is usually a link to the published paper.
- Read a short summary of the content of the paper (usually different from the abstract and written by a reviewer, not the author).
- Find later articles that cite a given paper. Click on the 'From References' link in the citations box on the upper right of the review page for the article.
- Compute your Erdös number (mine is 3).
- arXiv.org is a place where preprints (and sometimes also fully formated published versions) of mathematics and science articles can be freely posted and accessed by all.
LaTeX - Writing papers and presentations
- Getting started with LaTeX
- How to install a LaTeX distribution and editor on a Windows, a Mac, or Linux (Ubuntu) computer.
- A template for a new .tex document. This is a good place to start for writing your first LaTeX document.
- Some useful LaTeX resources
- LaTeX cheat sheet. A handy reference list of commonly used formatting commands and symbols.
- LaTeX Wikibook. A very good online reference.
- Short and not so short introductions to LaTeX.
- tex.stackexchange. An online forum for asking and answering questions on TeX and LaTeX.
- Detexify. A fun little application to find the LaTeX command by hand drawing the desired symbol.
- Time saver: Search for information on how to set up forward search and inverse search for the LaTeX editor and viewer that you are using.
- Using BibTeX to create a bibliography in LaTeX
- A short guide to getting started with BibTeX.
- Examples of different BibTeX styles.
- Often the easiest way to create your .bib file is to obtain the BibTeX entry for papers from online resources.
- MathSciNet: Click on 'select alternative format' at the top of the page and select 'BibTeX'.
- Google Scholar: Click on 'Cite' under the entry in search results and then select 'BibTeX'.
- Making presentation slides with the Beamer package
- A Beamer tutorial with lots of examples.
- Gallery of the standard Beamer themes.
- Files for the Purdue Beamer theme that I use. An example presentation using this theme.
- If giving a poster presentation of your research, download a free LaTeX poster template.
- Advice on preparing a math talk.
- How to give a 20 min talk (Rick Durrett).
- General tips on giving talks (Jordan Ellenberg).
Job search advice (PhD students)
- Plan ahead: As much as possible, begin thinking about what type of job you would like (research university, teaching university, or industry) as early as possible in your graduate studies. Consiously do things during graduate school to make yourself an attractive candidate for this type of job when you graduate.
No matter what type of job you think you want, talk to graduate students who are a few years ahead of you to find out how the job search process works.
Here are a few specific things to consider doing to prepare yourself for the different types of jobs.
- Research
- Become a member of the American Mathematical Society (AMS). Graduate student membership is free if your university has a institutional membership.
- For graduate students in probability or statistics, become a member of the Institute of Mathematical Statistics (IMS). Student memberships are FREE!
- Be aware of the current research in your general area. Read journals, attend department seminars, and go to conferences (often there is funding for graduate students).
- Give talks. This is a great way to let people know who you are before you start looking for jobs. Start by giving talks in graduate student seminars if possible (start a graduate student seminar if there isn't one). Once you start obtaining results for your thesis, volunteer to give talks in department seminars and look for opportunities to submit a contributed talk at a conference. Ask your advisor for suggestions/help with finding appropriate opportunities for you to give talks.
- Apply for funding to attend summer schools in your research area. Your advisor can help you to find appropriate summer schools to attend.
- Get to know people in your field from other universities. Let them know about the results of your thesis. Not only will they potentially be postdoctoral advisors for you, but they can write letters of recommendation for you. Many graduating students only have letters from the university where they are graduating from, so it can help to set you apart by having letters from outside your university (but make sure they know your research well enough to write a good letter).
- Teaching
- Consider becoming a member of the Mathematical Association of America (MAA), the national math society that is more focused on undergraduate math education. Student memberships are not very expensive, and you will learn very valuable information from the publications.
- If possible, look for opportunities to be a lecturer for a course rather than a TA for a discussion section. This will give you extra experience that puts you ahead of other fresh PhD students looking for tenure track teaching jobs.
- Learn about methods of teaching other than the regular lecture format and look for opportunities to try using these methods. Doing this will prepare you to write a much stronger "Teaching Statement" in your job application.
- Colleges and Universities focused mainly on teaching strongly value faculty who can direct undergraduate research. Look for opportunities as a graduate student to help out a professor who is directing undergraduate research projects. Think seriously about what sort of undergraduate research projects might fit well with your research area.
- Attend MAA section meetings. Attend these conferences to make connections with people in your local area who are professors at smaller colleges/universities and/or who are interested in undergraduate math education.
- Attend national MAA conferences such as Mathfest and the Joint Math Meetings. Both conferences have a number of sessions where you can listen to people discuss new ideas/innovations in undergraduate math education. Many smaller colleges do their first round of interviews at the Joint Math Meetings, so if possible plan on attending this during the final year of graduate school. Also, if you attend the Joint Math Meetings, sumbit a contributed talk (plan ahead since abstract submissions are due in September).
- Industry
I don't have much advice in this area since I've never applied for math jobs in industry. If your PhD advisor also doesn't know much about industry jobs, make sure you take the time to talk to recent grad students who have taken jobs in industry.- Become a member of the Society for Industrial and Applied Mathematics (SIAM). Memberships are free for students at member institutions.
- Take graduate classes to prepare you for jobs in industry (math finance, computer programming, etc.).
- Look for opportunities to do internships in the summers.
- Research
Undergraduate math research
If you are interested in participating in a summer REU, you can find listings of potential programs at- https://sites.google.com/site/mathreuprograms/ - general list maintained by Steve Butler from Iowa State University.
- http://www.nsf.gov/crssprgm/reu/list_result.jsp?unitid=5044 - NSF funded REUs.
- http://www.ams.org/programs/students/emp-reu - list maintained by AMS.
If you have done some undergraduate research, it's very important to find some venue for you to present your research. Consider the following options.
- Make a poster summary of your results. Download a free LaTeX poster template. Present your poster at a local MAA section meeting.
- Give a presentation of your research at a conference. A good list of conferences to consider is here.
- Write up your research, and submit it as an article. A list of undergraduate math journals is here.