Included below are just some websites, apps, and programs I have used while I was in graduate school. If you have any questions or suggestions on questions you’d suggest be addressed here, please feel free to contact me. Note: some things are restricted to Apple devices.

Writing by hand: I do all of my handwriting on my iPad Pro (10.5-inch). If you also have a (new enough) macbook and iPad, you can use the iPad as a second monitor. Moreover, the “airdopping” of pdf from one device to another is convenient. I use Notability for taking notes, writing lecture notes (e.g., see lecture notes posted in Math 2410Q Spring 2020), working out calculations, and screen sharing for virtual collaboration.

Typing math: I do all of my typing on a macbook. Everyone writes in LaTeX. Sublime is a common text editor I’d recommend. There are others that people use (including WYSIWYG editors). I use macvim with vim-latex. I use skim for pdf viewing.

Paper Organization: I use LiquidText on my iPad to organize pdf files for papers and textbook by subject and research project. I have a (somewhat) mirrored filesystem on my macbook, though one can use bibdesk as a pdf database (this is what I do).

Reference Organization: I use BibDesk for organizing references (i.e., papers/texts I may cite in my research). I copy the bibtex code from mathscinet, which adds the bib entry to a master .bib file. You may tag and annotate references, and use it as a database for recalling references. It also generates a unique cite key for each entry to input to \cite{…}.

Finding Papers: I use mathscinet all the time. Many universities give you access to this service. E.g., if you’re at UConn, you may use this. For newly posted papers (which may be unpublished), is used. For daily viewing, I use Lib arXiv. It is advised to try to view arxiv once a day just to see what is “hot” (i.e., actively researched), but I try to do it at least once a week. Protip: when googling a paper, try appending your search with filetype:pdf. This restricts the search results to pdf files only. Lastly, note that your university might not have access to all papers–in this case, you could try searching arxiv or the author’s own website.

Keeping a Schedule: I use the forest app to help make sure I work enough hours a day (at least 8 hours) and to make sure I stay focused during work time (if you fail, your tree dies). I also sometimes use SleepTown to maintain a proper sleeping schedule (if you fail, your building dies).

Presentations: The most commonly used LaTeX package for making slides is beamer.

Prelim Prep: There are many resources online for prelims in math. (Note: some universities call these exams “quals” or “qualifying exams”.) The Berkeley Problems in Mathematics is useful. I used this book as a source for practice problems. It also has solutions–if you have limited time, it could be useful to simply view as many solutions as possible. UConn also has a page with previous prelims. Many other people have their solutions posted online.

Conferences and Summer Schools: Here I will just include some conferences and summer schools I can currently recall. You can find many conferences that are held by the AMS here. Many universities hold “summer schools” in which you spend one or two weeks at a university and attend lectures or workshops. This can be found out by word of mouth or googling.