Employment in Academic Institutions
For academic jobs that begin in the Fall, the first application deadlines will generally be around October 1 during the preceding year, and new jobs will be posted throughout the academic year. A few places might have deadlines in late September, but this is not typical.
Most tenure-track and postdoctoral positions will have application deadlines between October and December, but there are always exceptions to this rule. Usually, a second round of job ads are posted starting in late fall for lecturer and visiting positions. A third round of job ads will start to appear in the spring, usually for 1-2-year visiting positions. Thus, it is impotant to keep watching the job ads and to plan to apply for jobs throughout the academic year.
You can find academic job advertisements at the following websites.
American Mathematical Society Employment Services: this is a page with a large number of resources
SIAM, The Society for Industrial and Applied Mathematics Job Listings
The Chronicle of Higher Education Job Listings
Inside Higher Education Job Listings
If you are interested, information about the NSF postdoc application process is available at https://www.nsf.gov/funding/pgm_summ.jsp?pims_id=5301 and the deadline is typically in mid-October. Fun fact: the NSF abbreviation for the Mathematical Sciences Postdoctoral Research Fellowship is MSPRF. While everyone outside NSF calls this the "NSF Postdoc", inside the NSF it is referred to as "mouseproof".
For most applications, you will need to prepare a cover letter, CV, teaching statement, research statement, and a statement on diversity and inclusion. You will also need to get letters of recommendation from 4-5 faculty, including at least one letter focused on teaching. The Graduate Student Council has collected sample job application materials from alumni and faculty, which you can view here: http://www.ms.uky.edu/~gsc/resources.php Your letter-writers will often ask to see your materials 2-3 weeks prior to the first application deadline, so it is a good idea to start working on these materials early.
If you do not yet have a CV, here is a LaTeX CV template: https://math.as.uky.edu/sites/default/files/UK_CV_template.rtf Note that you will need to change the file name extension to .tex instead of .rtf to compile this in LaTeX.
Historically, UKY graduate students apply to between 40 and 150 jobs over the course of a year, depending on what types of constraints they have on geographic location, type of institution, etc. It is strongly recommended to maintain a spreadsheet to organize your job search process over the course of the year.
Finally, a collection of helpful articles from the AMS Notices Early Career section regarding academic job searches is here: http://www.angelagibney.org/the-ec-on-the-academic-job-market/
Employment in Business, Industry, and Government ("BIG jobs")
A wealth of information regarding jobs in business, industry, and government can be found at the BIG Math Network: https://bigmathnetwork.org/
A collection of helpful articles from the AMS Notices Early Career section regarding BIG job searches is here: http://www.angelagibney.org/the-ec-on-jobs-in-big-math/
For jobs in business, industry, and government, a resource for finding job advertisements that is most-often recommended by our alumni is https://www.linkedin.com/.
The job search process for BIG jobs is significantly different from academic jobs. Many UK Math PhD alumni work in business, industry, and government, and they are great resources for learning about searching for BIG jobs. If you would like to connect with one of our alumni to talk about searching for jobs in these areas, please contact the Director of Graduate Studies.