General Resources

Here are some useful and/or fun online resources and when studying higher mathematics:

Math Culture

Study Resources

The primary resource when really studying mathematics is text books. However there are some very useful general sites out there for gaining more insight and working exercises.

  • The Mathematics Stack Exchange – This is a great place to ask technical questions and get help with exercises. Just be sure to search beforehand to see if your question has been asked before. There is also similar site called MathOverflow, but this is meant for math researchers to discuss research-level math, so don’t post questions there.
  • Wolfram Alpha – A very nice, free online tool to solve computational math problems, including calculus, and to plot functions. It won’t help with proofs but many proofs have computational pieces to them where this could be useful.
  • 3Blue1Brown – This highly regarded YouTube channel features intuitive explanations of many concepts in math using stunning animations.

Recreational Mathematics

Recreational mathematics refers to math that requires little formal math education to understand, often in the form of problems or puzzles. Often times these puzzles, despite not requiring a lot of background knowledge to understand, require clever techniques, and often hint at a richer theory. They are a great way to practice your mathematical reasoning skills and are also just a lot of fun. It is also a great place to start if you’re looking to dip your toes into higher math in a fun way.

  • Matthew Scroggs’ Blog – This blog is all about having fun with math. Matt posts puzzles regularly and every Christmas has a math puzzle advent calendar, which I have a lot of fun with every year.
  • Cut the Knot – I have not explored too much here yet but it is a collection of math and math-related “miscellany and puzzles”.
  • Martin Gardner is pretty much the undisputed king of recreational math. He published math articles and puzzles in Scientific American for many years. Here some of his books:
  • Here some YouTube channels about interesting but understandable math topics and problems:
    • Numberphile – This is a very popular channel features many different ideas and math problems.
    • singingbanana – This is the personal channel of one of the mathematicians often featured in Numberphile videos. It also features interesting puzzles, problems, and games.
    • Mathloger – Another excellent channel with a little more of a technical flavor to it.

LaTeX

LaTeX is a free and open source typesetting system that excels at typesetting mathematics. Most academic journals accept papers written in LaTeX, and even full books are written using using it. It is the standard for written math communication. If you intend to communicate math online, it is well worth learning LaTeX, though it is quite different from word processors so there is a learning curve.

  • A nice article about LaTeX – This discusses its benefits as well as how it differs from word processors.
  • Overleaf – This is a nice platform that lets you get started writing LaTeX documents online without having to install a LaTeX system on your computer.
  • LaTeX-Tutorial.com – Looks to be a great site with tutorials on how to get started learning LaTeX. There are many other tutorials online, which are only a Google search away.
  • MathB.in – A nice pastebin that is LaTeX enabled. This is great place to tinker around with LaTeX without even having to setup a document, as well as sharing snippets of math with others.
  • hack.chat – This is a really nice, minimalist chat site that is LaTeX-enabled. You can join public rooms or easily set up private rooms.
  • Detexify – A cool little site where you can handwrite a symbol and it will give you possible LaTeX commands for that symbol. It’s pretty useful if you know a symbol you want to use but don’t know the command for it.