I really didn’t know what I was doing when I applied for graduate school, and I am thankful for the assistance of the professors at my undergraduate university who helped me and the luck that got me into a few schools, including one that ended up being a good fit for me. But I could have used more help at all stages of the process.
If you’re in a similar position, Susannah Shoemaker’s posts on the subject for the AMS Graduate Student blog might be useful. In her first post, she suggests starting with some introspection about why you want to go to grad school. I particularly saw myself in that part of the post. She writes, “If I’m being completely honest, I applied to grad school in part because it was a well-defined, familiar path: more schooling (a known quantity), followed by a career in academia, which I imagined would be full of fulfilling teaching interactions and, importantly, blissfully free of business-wear and rigid 9 am start times.” In the second post, she focuses on crafting a good statement of purpose and advocating for yourself once the acceptances start coming in.
A few years later, you may be on the market for an academic job. Zsuzsanna Dancso, who writes the blog Math, Chocolate & Circus has some advice academic job applications and interviews. I appreciated the way she framed her advice. (Also, I kind of want a pizza now.)
I know you’ll probably be applying for a hundred jobs, but this is advice on how to get one of the few you actually want. I’m going to tell you to put in a lot of effort, and you should focus that effort where it counts. When I was applying widely, I had this rule of thumb: if I’d rather have delivered pizza in Toronto, I would not apply. Imagine living in your favourite location working in a boring unremarkable job; this is a thing you are allowed to do. As you’re writing a cover letter for a tenure track position that will make you strictly less happy, remind yourself that it’s ok not to.
It’s not just applicants who can use advice. Sexism in academic letters of recommendation has been a hot topic for several years, but I still hear about sexist letters making their way to the eyeballs of hiring committee members. Recommendation letter writers, you want to avoid embarrassing yourself and hurting applicants’ chances by accidentally writing a sexist letter. The Astrobetter blog has some letter writing advice for avoiding unconscious sexism. There’s also a handy poster (pdf) from the University of Arizona commission on the status of women. This online gender bias calculator will take the content of your letter and point out gendered words to you. It’s a blunt tool, but it should help you fend off some glaring problems. There is some more general advice about writing academic letters from the Science Professor blog and Inside Higher Ed. If you’ve got some recommendation letter writer’s block, Natalia Lukina has a list of words and phrases that might help you get the process flowing.
If you end up staying in academia (by no means the only successful career trajectory; see this post for information about non-academic math jobs), you may one day find yourself with the awesome responsibility of advising students yourself. At the Computational Complexity blog, Lance Fortnow has some advice about advising.