This is an obviously incomplete list of some useful and amazing things from around the internet:
- [My Personal Website](http://www.JuanSLozano.com)
- [Math Stack Exchange](http://math.stackexchange.com/) is an amazing strictly Q&A site for any level of mathematics with a large mathematical community surrounding it.
- [Mathoverflow](http://mathoverflow.net/) is similar to the above, but restricted to the level of professional mathematicians.
- [Terrance Tao’s Blog](https://terrytao.wordpress.com/) is best described [here](http://math.stackexchange.com/a/96/87284) as “a very active math blog (both in posts and comments) and definitely covers some cutting edge math, even if it can be way over my head.”
- [On Evidence in Mathematics](https://www.simonsfoundation.org/mathematics-and-physical-science/shadows-of-evidence/) is an interesting look at what counts as evidence in mathematics and deals with some foundationanal issues along the way. Quote from page:
> “Petabytes allow us to say: ‘Correlation is enough.’ We can stop looking for models. We can analyze the data without hypotheses about what it might show. We can throw the numbers into the biggest computing clusters the world has ever seen and let statistical algorithms find patterns where science cannot.”
> But correlation alone will never replace the explanatory power of mathematics. Mathematics, the word, comes from the Greek µάθηµα, which means nothing less than “that which is learned,” a phrase that has an all-encompassing grandeur. No wonder, then, that to teach mathematics is so formidable a task; you are grappling with the pure essence of learning. To teach effectively, you had better use every species of true persuasion, of genuine evidence, that you can bring to the picture, with the rigor of proof as its frame.
- Poincare, on intuition is a wonderful essay from a great mathematician about the role of intuition in the creation of new mathematics. I would also say that Terrance Tao’s There is more to mathematics than rigor and proofs discusses the nature of intuition in a broader context
- Hamming on Striving for Greatness in All That You Do is not strictly math, but is very relevant to the working mathematician, I think.
- Qiaochu Yuan’s reading recommendations
- MSE’s reading recommendations for high-school me
Course Notes, books I want to read, et cetera
Harvey Mudd Lectures on Baby Rudin
Lewis Bowen Graduate Real Analysis
Arun Debray’s Lecture Notes
Peter Webb — A Course in the Representation Theory of Finite Groups
Rep Theory Notes — Teleman
Webb — An Introduction to the Cohomology of Groups
Ekin Ozeman — Group Cohomology and Number Theory
Lewis Bowen — Graduate Algebra