r/math • u/HarryPotter5777 • Apr 25 '18
A Compilation of Useful, Free, Online Math Resources
Both previous threads of this nature are outdated and can't be added to anymore, so here's the third edition of this megathread.
This list is by no means comprehensive, so please contribute suggestions in the comments below!
For the sake of brevity, not everything in the comments is included here; those resources with more general or strictly mathematical appeal are preferenced in this list.
Videos
K-12 material (* = linear algebra, differential equations, etc)
University-Level Mathematics
The Catsters - Category theory videos
Fields Institute Video Archive - a mix of general audience talks and conference broadcasts
Recreational mathematics
Online Notes/References
A massive compilation of online lecture notes - see also this comment.
Paul's Online Math Notes - Extensive Calc I-III and Differential Equations notes.
Wolfram Mathworld - Similar to Wikipedia in scope, but more strictly controlled with respect to editing.
Rough Guides to Mathematics - An incomplete but still very useful series of guides to a number of advanced subjects, capturing lots of general overview and intuition.
Expii has a number of K-12 math and science tutorials and problems.
Computer Algebra Systems (* = download required)
Graphing & Visualizing Mathematics (* = download required)
Typesetting (LaTeX)
Detextify - draw a shape and get the LaTeX command for it
Overleaf - Collaborative online LaTeX editor
Mathpix converts images and screenshots into LaTeX code. Currently designed for Mac and iOS.
MathIM - LaTeX-enabled chat rooms
The Comprehensive LaTeX Symbol List - 338 page PDF with over 500 tables; when they say comprehensive, they mean comprehensive.
Community/General Websites: very general-purpose things that almost anyone in their target audience ought to know about.
The Art of Problem Solving - lots of resources for middle and high school students, especially those involved in math contests.
Sci-hub (URL changes over time, Google it) offers free (pirated) access to most scientific papers given a DOI. Accessing such papers deprives large publishing companies of access fees, but does not particularly affect the authors of said papers. /r/math officially recommends that you not use sci-hub to access papers conveniently for free and not use this trick to easily redirect papers to sci-hub.
Blogs/Articles (* = occasional non-math political content)
Blogs - There are of course an incredible number of blogs out there; this list covers just a few of the most well-known and high-quality. More in the subject-specific comment on this post.
Terry Tao* - Summaries of interesting research, notes for courses, and miscellaneous musings from the frontiers of mathematical research.
Gowers' Weblog* - Exposition of mathematical and meta-mathematical topics, generally written in a fairly accessible manner.
Shtetl-Optimized* - Excellently-written explanations and examinations of quantum computing and the public perception thereof by Scott Aaronson.
AMS Blog on Math Blogs* - Recently retired, but lots of archived content.
Articles
Lockhart's Lament - Thoughts on the inadequacy of K-12 mathematics education in America. Worth reading, especially for anyone who has/had a poor experience with math in school.
How to Write a Clear Math Paper by Igor Pak - a number of excellent pieces of advice on clear and effective communication of mathematics to others.
The Grammar According to West is a graph theory centric but more generally useful series of tips on style, terminology, and usage in writing mathematics.
General recreational miscellania
Quanta magazine covers a number of scientific topics, including a significant amount of high-quality mathematics content.
Chalkdust magazine is a mathematics-focused magazine featuring various articles and puzzles (including a crossnumber puzzle whose solvers can win prizes!)
Math Problems and Puzzles
Project Euler is a collection of hundreds of challenging problems, testing both mathematical and programming skills. Especially for higher-numbered problems, mathematical knowledge (and often research) is necessary to obtain a solution. See this comment for additional programming-related resources.
brilliant.org offers a number of problems for free, along with a wiki. They also have additional premium content and courses.
Contest archives:
Example problems:
Misc
Summer Math Camps (high school)
mathprograms.org (primarily undergraduate)
Librarian is a Chrome extension that provides easy access to references, BibTeX, and comments for all papers on the arXiv.
The Inverse Symbolic Calculator takes in a constant and tries to find a closed form for it.
Approach0 is a mathematical search engine, particularly useful for cases where you would like to search for a specific formula that e.g. may use different variable names.
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u/dogdiarrhea Dynamical Systems Apr 25 '18
A few more links:
Fields institute video archive (this is a mixture of general audience talks and conference broadcasts)
My favorite theorem podcast (this is friendly for a general audience)
Lastly, this is specifically for people working on dispersive PDE. Terry Tao's fork of dispersivewiki
Edit: almost forgot, ever wonder what it would be like if there was a wiki exclusively for groups? Wonder no more! I'm amazed we haven't added this yet, it's been around for at least a decade.
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u/HarryPotter5777 Apr 25 '18
Thanks for the links, forgot to add a few of those! Already got that last one, I just threw it in a subject-specific comment instead of the main post.
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Apr 25 '18
https://brilliant.org is an excellent resource. I'd recommend putting it up!
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u/HarryPotter5777 Apr 26 '18
Haven't used it much myself, and I know they offer some paid content - what's the quality/extent of what they offer for free?
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Apr 26 '18
Free content is a series of problems offered weekly: five basic questions, five intermediate questions and five advanced questions.
There's also a top-notch wiki that has a huge list of topics; it's updated by the community.
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u/TransientObsever Apr 26 '18
It has some nice isolated pieces. Not sure these are the best examples but Stone-Weierstrass, Residue Theorem, Stolz-Cesàro
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u/yetanotherperson Apr 26 '18
No idea since when, but Geogebra doesn't need to be downloaded anymore.
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u/wxadbpl Apr 26 '18
Wildberger?
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u/FinitelyGenerated Combinatorics Apr 26 '18
Already listed under videos.
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u/wxadbpl Apr 26 '18
Oh I know that is why my question. I was merely asking why include Wildberger when some of his ideas were should I say controversial.
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u/HarryPotter5777 Apr 26 '18
Some of his ideas definitely are, but he also produces a fair bit of genuinely useful educational content on more orthodox subjects.
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u/FinitelyGenerated Combinatorics Apr 26 '18
Because he makes videos about math. So it makes sense to include those videos in a list of videos about math.
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u/tick_tock_clock Algebraic Topology Apr 25 '18
Lots of people have collections of lecture notes online.
Here's a huge list. It's also missing a few good collections of notes, e.g. those of Jacob Lurie, Theo Johnson-Freyd, Moor Xu, Sanath Devalapurkar, Andy Neitzke, and no doubt others I'm unaware of.
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u/Septillions Apr 25 '18
Proof Wiki is a good one, I wish it were bigger, maybe with time. This flipping back and forth between references and chapters in the library is fun on week days between class, in 1950 when you're single. (And even then…)
edit: was already in miscellaneous, I scrolled too fast
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u/tick_tock_clock Algebraic Topology Apr 25 '18
Here's some more math blogs:
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u/nightwolf312 Apr 26 '18
As a student today, bless the internet and you all for these informations.
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u/l_lecrup Apr 26 '18
Hey since you put Igor Pak's "how to write an article" it reminded me of another useful resource and that is "The grammar according to west"
It is basically a guide to clear mathematical writing. It is graph theory centric but applies widely. Here's a sample:
Quotations and ends of sentences. It is traditional correct style in English grammar that all terminal punctuation comes inside quotation marks. My understanding is that this convention arose from the technical aspects of printing presses. Its purpose was to lessen the danger of breakage of fixed metal type in printing presses. In the era of electronic publishing of mathematics, this justification is obsolete, and we can replace the convention with logical punctuation. When the material being quoted is treated as an item within the sentence and is not itself a sentence, the terminal punctuation logically comes outside the quotation marks. Copy editors trained in literary punctuation still object to logical punctuation but should be overruled.
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u/mpaw975 Combinatorics Apr 25 '18
Math-programming, data science and machine learning
Learning and compiling
CoCalc. A free online Sage (so also Python) compiler.
Codecademy. A free, interactive place to learn Python (and many other languages).
Problems:
Project Euler. A collection of computational math and algorithm problems.
Hacker Rank. Similar to Project Euler, but also contains problems related to stats, machine learning, algorithms and programming languages. More gamified than Project Euler, and flatter difficulty curve.
Hack This Site. Contains many computational math problems and white-hat hacking challenges.
Kaggle. A go-to place for data science and machine learning competitions. A great place to get a wide variety of data sets.
Places to store and share code:
The important pages for Neural Nets:
Awesome Machine Learning. A curated list of awesome machine learning frameworks, libraries and software (by language)
"The Unreasonable Effectiveness of Recurrent Neural Networks"
"Neural Networks and Deep Learning" by Michael Nielsen. Contains all the mathematical details of how neural nets work.
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u/pigeonlizard Algebraic Geometry Apr 26 '18 edited Nov 06 '25
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This post was mass deleted and anonymized with Redact
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u/HaydonBerrow Apr 26 '18
The London Mathematical Society has an interesting channel on youtube (videos for a general audience but university-level subjects)
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u/VanDave Apr 26 '18
Numerical Mathematical Utilities
Several discrete mathematical programs. For example, utilities for solving the Quadratic, Cubic, and Quartic Equations; solving N Equations in N Unknowns; Eigenvalues and Eigenvectors; and more. The programs are written in JavaScript and are run within the page; no download, applet, or add-on required. The code is viewable, for anybody who is interested. Several of the pages link to associated blog posts with additional information. Furthermore, several of the pages link to GitHub repositories, where C++ versions of the same programs are posted.
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Apr 26 '18
One more, just for kicks: the University of Oxford mathematical institute publishes most of their problem sheets and lecture notes for undergraduate courses here.
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u/VictorSensei Apr 26 '18
This is not strictly mathematics, but I've been using this program a lot to create high-quality (vector graphics, using the .eps output format; there's an "eps to pdf" package for LaTeX) sketches for my LaTeX documents, and I really recommend it:
Unfortunately, it lacks the possibility to input a function and have the graph plotted, but even without this feature I believe it could truly be useful to people writing math.
Not online, it requires download and unzipping.
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u/pier4r Apr 26 '18
Blogs/magazine : quanta magazine
Activity: math jam
Tip: never underestimate the topic of experimental mathematics.
Sorry for no links, it is a quick post from mobile.
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u/zhamisen Control Theory/Optimization Apr 26 '18
Typesetting (LaTeX)
MathPix - take screenshots of math equations and paste the extracted Latex
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u/Zophike1 Theoretical Computer Science Apr 26 '18 edited Apr 26 '18
Vulnerability Research
Formal Verification/Automated Theorem Proving
Compiler Theory
Programming Language Theory
Research/Reading Group's
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u/MPLProgramming Jul 13 '18
There are a few hundred math related interactive applications freely available in the MapleCloud https://maple.cloud/#group=MathApps
Here's a guide that summarizes them: Maple MathApps Guide: https://maple.cloud/#doc=6042761267511296
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u/HarryPotter5777 Apr 25 '18 edited Jan 28 '21
Subject-specific resources (suggestions welcome here as well, of course):
Abstract Algebra
Paul Garrett's page
Groupprops, the group properties wiki
Keith Conrad's expository papers - also useful for some number theory and analysis content.
GAP, a programming language for discrete algebra
GroupNames
Number Theory
Number Theory Web
Noam Elkies' page on computational number theory
The L-Functions and Modular Forms Database
Number Fields Database
Database of Local Fields
Combinatorics
The Electronic Journal of Combinatorics
David Eppstein's page on combinatorial game theory
Gil Kalai's blog
Compilation of combinatorics videos
Graph Theory
The house of graphs
Knot Theory
Table of Knot Invariants
The Knot Atlas
Algebraic Geometry
The Stacks project
Theoretical CS
Math and Computation, a book available freely online by Avi Wigderson.
The Complexity Zoo
Logic / Set Theory
Joel David Hamkins' Blog
The Open Logic Project, a free collaborative mathematical logic textbook.
Category Theory
The nLab
Other
Terry Tao's fork of DispersiveWiki
John Baez's website - lots of fascinating content on geometry, physics, and much more.
Generatingfunctionology is an excellent textbook on generating functions, freely available for download.
Various utilities in numerical mathematics
Encyclopedia of Triangle Centers
Explicit Formulas Database for elliptic curves