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Online Resources

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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.

Collaboration/productivity resources:

  • 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.

Literature Search/References/Databases

  • 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.

Highly specialized/branch-specific databases/projects: