By Ajay Kumar Raja
Mathematics is one of the most (if not the most) beautiful fields of study out there, but without visual examples it can be hard to see the difference between math and dry pedantism! Thankfully, these math resources make that joy a little more obvious to the as-yet uninitiated.
A graduate student at CUNY Graduate Center, Tai-Danae Bradley offers humorous, diagrammatical explorations into rich topics like Category Theory, Topology, and Galois Theory. While relatively accessible, some articles require more background than others; however, her Category Theory series is accessible to anybody with knowledge of what sets and functions are.
Suggested Level: at least some exposure to higher mathematics, group theory, topology, etc.
2. Math With Bad Drawings
Math With Bad Drawings, written by math teacher Ben Orlin, provides insight into exactly why we should care about mathematics, as well as compelling articles about the philosophy of education and funny asides about anagrams, fictional math courses, and fairy-tale graphs. A great math blog for the young or less mathematically inclined, but all (even full-blown mathematicians!) can enjoy and learn from it.
Suggested Level: anybody!
3. Wolfram MathWorld
Billed as “the web’s most extensive mathematics resource”, Wolfram MathWorld contains articles on nearly every conceivable math topic, from addition to Čech-Stone Compactification. A great reference point, often with useful diagrams when necessary.
Suggested Level: varies from article to article.
nLab has great advanced math resources — a quick description might be “MathWorld but more advanced” — and has a wealth of category theory references, but they’re also a great resource for anybody trying to study the higher levels of math. While unfortunately low on visuals, they’re a very useful resource nonethless.
Suggested Level: Algebra II, Set Theory. A lot of needed knowledge can be gleaned just by jumping from link to link.
5. Online Encyclopedia of Integer Sequences
Perfect for those who want to play around with numbers, the OEIS is an online repository of numerical sequences, like the Fibonacci Sequence (A000045) and the digits of pi (A000796), to more little-known sequences like the Kolakoski sequence (A000002). Furthermore, OEIS lets you hear what sequences sound like when transferred to a piano, gives graphs of their values, and even has puzzles! The perfect playground for a budding number theorist, or for anyone with a couple of spare hours.
Suggested Level: anybody!
Hopefully, you’ll have the chance to take a look at all of these math resources! And as always, these are just a sample of the many, many others out there.
Want more? Reach out to The Homeschoolist for ideas.
Ajay is a fully homeschooled math lover who is currently, a rising sophomore at a top research university, majoring in pure mathematics. Learn more about Ajay at astutelearning.weebly.com