Here are some resources I've found useful during my undergrad in math.
The internet is a deluge of information, and it's often hard to know where the best place to learn is. These are the sources I used most when needing to learn a subject.
- Real Not Complex: RNC aggregates great textbooks and lectures for almost all undergraduate and graduate level mathematics disciplines. It's a fantastic resource for anyone looking to learn a subject deeply.
- MIT OCW: It's still unbelievable to me that you can access lecture materials from top universities FOR FREE. It'd be silly not to make use of it
- PDF Drive: A great resource for finding textbooks and other papers that are otherwise expensive or hard to access.
- Math Overflow: This site has a very healthy population of mathematics professionals as regular visitors, and is of immense value to anyone needing some assistance with a problem
- Project Gutenberg: This site has over 60,000 free ebooks, which mostly are digital versions of old books that are otherwise hard to access.
- YouTube: Unsurprisingly, there's a ton of great content on YouTube for learning math. I'm not going to do justice to all of the great channels out there, but here are some of my favorite smaller channels:
It's all too easy to get lost in a Math-SciNet dump trying to find material related to your area of research. Here are some tools that might help with the search.
- Approach Zero: A search engine that is MathJax compliant? Sign me up!
- Pi Base: A database of topological counterexamples. Ever unsure about a topological claim? This is the database for you!
- Sci-Lag: A database consisting of nicely aggregated materials on open research problems.
- DOAJ: A database of free-to-access journals on all research topics.
- OEIS: The well-known integer sequence database. I can't tell you how many times OEIS has helped me find closed formulae for recursions
- Banff Mathematics Center: This center publishes all of their conference materials and research publications, which cover almost all active fields of research, for free!
- Zentralblatt Mathematics: A database of abstracts from peer-reviewed papers which is also completely open-access
- Project Euclid: An aggregate database of mostly open-access articles published in pure mathematics
- SIAM: A collective of math journals focused on applied research
- Journal of Expositions: This journal is unique as it publishes expositions on difficult topics, rather than novel work. It's very useful for getting acclimatized to a new field without needing to dig through jargon.
Need to use some computer assistance in your research? The internet is brimming with online tools that can help.
- Wolfram Alpha: The name synonymous with mathematical computing online. Surprisingly, I didn't use it all that much for my computing tasks.
- Sage Cell: An online computing platform for SageMath which is easily HTML embeddable. A fantastic alternative to WolframAlpha/Mathematica
- GAP-4: An open-source computing platform for computational algebra.
- TryAPL: An online platform for compiling APL, a language designed to ease provability and other model-theoretic computations
- Singular: A compiler for commutative algebra problems (i.e. computing Grobner bases)
- Math3d: A website that allows you to graph functions a la Desmos in higher dimensions, producing Blender quality animations
- TIO: An online compiler for 680+ languages. It's not great for programming projects, as there is no autocompletion, but for small shareable programs, it's quite useful
Writing up papers can be a pain. These tools may be useful.
- DeTexify: A website dedicated to helping you find the LaTeX/MathJax commands to generate your symbol of choice.
- Quiver: A website that let's you draw commutative diagrams with a lot of flexibility, and export as tikz or pdf.
- Overleaf: Formerly ShareLaTeX, this site gives you the benefits of google docs style cloud storage with TeX compilation.
- Functors: A blogging site with MathJax compatability. Need I say more?
- GeoGebra: A graphing tool similar to Desmos, but is far more versatile.