Most of these statements are meant as suggestions or opinions, and not requirements.
- Start early! You may want your letter writers to see your application materials before you start applying, and you need to give your letter writers time to write! Also, the order in which applications appear to the university is the same order in which they were submitted. So if you submit your applications on the last day, expect your application to be near the bottom. Even though most departments will do a very good job of taking every application seriously, you will stand a better chance if you are near the top, suggesting that you do not put things off until the last minute.
- For each job, you should look at the department webpage: see if there are professors whose research interests overlap with yours. Typically, every postdoc/visiting assistant professor is associated with a mentor. So it is important to see if there is someone you can work with. Moreover, you or your advisor can consider contacting your desired mentor, to judge their interest level. You should also consider mentioning people in your cover letter / research statement that you want to work with. If there is no one in the department who you would work with, then there is a high chance you will be rejected (although sometimes someone will want to mentor you because they realize your work can be applied to their area).
- Be aware that there are no interviews for most postdoctoral positions. In particular, you should only expect interviews at the Joint Mathematics Meetings if you applied for positions at smaller teaching colleges, or for tenure-track jobs at smaller universities. Also, you usually will not hear back from any postdoctoral position until near the end of January. It is a tradition that the NSF postdocs are decided first, and most universities do not send out offers until after the NSF. So you should not worry about the possibility of becoming unemployed until late March (I have personally managed to get job offers as late as May).
- Unfortunately, most jobs will never inform you that you were not hired.
- Spend a lot of time working on your research statement, and expect to go through many drafts. Make sure to have your advisor read it, and try to get people who are not in your subject area to read it as well, to see if it is well-written enough that a `typical’ mathematician can understand what you are doing, and why it is `important’. You should look up advice on how to write a research statement. For a postdoc, your research statement and your letters of reference are the most important parts of the application.
- This point is a suggestion, if you want to do something risky to get your application to stand out. If you can, get a letter of reference from someone who is not associated with your current institution. Your advisor’s letter is the most important letter, but any letter from outside your department will be considered very highly as well – because such a person can write as an `objective’ observer.If you have research with someone from a different institution, then that person is an ideal choice.
- If you took the time to meet people at conferences, and gave presentations on your research, and discussed your research with someone who showed great interest in your work, then you could consider asking that person. As usual, refer such suggestions to your advisor, and remember point 0 above. If you are not comfortable getting a letter from `outside’ your institution, do not worry: this is a suggestion, not a requirement.
- If it is late March, and you do not have a job yet, you need to consider what your second option is. Industry jobs tend to hire year round. You could also consider staying in graduate school another year, focusing on publishing your results, and then try again next year. I know of people who ended up doing the latter approach, and the second time they were on the market they got hired.
Finally, feel free to leave comments asking about further questions.