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How to give good mathematics talks:
How to write good mathematics papers:
Computer algebra resources:
- SAGE — Free and open source extension to Python for advanced mathematical work/computation, can be run in-browser.
- Pari/GP — Free, and somewhat better for abstract algebra than SAGE, but there's a somewhat steeper learning curve for the syntax. Can be run in-browser.
- Magma — Difficult syntax, but probably the most complete (non-graphical) computer algebra system. Stanford University has a license paid for by the Simons Foundation.
- Mathematica — A more graphically-driven computer algebra system. It is particularly useful for discrete math/combinatorics, calculus/analysis, and making pretty pictures.
- Wolfram Alpha — Useful if you want to check your work or solve a system of equations quickly.
- Github — A highly functional collaborative environment for working on documents in a group with solid version control.
- Overleaf — For collaboration and cloud storage of LaTeX documents.
- Google Drive — Cloud storage. You all have accounts through Stanford, and through Gmail if you use it.
- Dropbox — Yet another cloud storage service.
- Slack — A chatroom-type environment for collaborative work or just socializing. Has LaTeX compatibility.
- Wikipedia — Has reasonably good coverage of mathematics.
- Mathworld — An online math encyclopedia specialized towards certain interests by the same company as Mathematica so it tells you how to do things in Mathematica.
- MathSciNet — The AMS' literature search engine.
- Arxiv — A free online repository of scientific articles. Probably 60-70% of math articles make it to the Arxiv before publication.
- Math Stack Exchange — A forum for more elementary questions.
- Math Overflow — A forum for more advanced questions.
- OEIS — The Online Encyclopedia of Integer Sequences! Possibly the most useful website ever.