What are really helpful math resources out there on the web?
Please don't only post a link but a short description of what it does and why it is helpful.
Please only one resource per answer and let the votes decide which are the best!
Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
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I have learned a lot of mathematics while reading Wikipedia. Allowing a wide audience to contribute to articles seems to work out well in the case of mathematics. |
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For enumerative combinatorics, it's hard to beat Sloane's Online Encyclopedia of Integer Sequences. It is what it says on the tin. A huge list of integer sequences, with references, links, formulas, and comments. |
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The Tricki Quoting the site: "Welcome to a brand new Wiki-style site that is intended to develop into a large store of useful mathematical problem-solving techniques. Some of these techniques will be very general, while others will concern particular subareas of mathematics. All of them will be techniques that are used regularly by mathematical problem-solvers, at every level of experience." |
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I'm just adding Wolfram Alpha to the fray so it can be voted on like other suggestions. For people who haven't heard of it, it's an online computational engine. |
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5
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Hosts high-level maths discussions, forums have inline LaTeX rendering. |
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I use http://arxiv.org/ all the time. Researchers post their articles here, so it is a great way to see if anyone have already a proof or an idea on something. Some people regularly access it through
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Everything by John Baez. In particular This Week's Finds in Mathematical Physics, the n-Category Cafe, and the n-Lab. He has an amazing ability to make even the most esoteric topics seem obvious and inevitable. |
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http://wiki.henryfarrell.net/wiki/index.php/Mathematics/Statistics Large list of math blogs. Highly recommended in particular are Terence Tao's and Tim Gowers'. |
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41
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http://jmilne.org has lots of systematic, well-written courses. |
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If you haven't figured this out already, you can read large portions of textbooks before you buy them to decide if they're what you need. (If you actually want free books, there's a separate question that addresses that.) |
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Very good articles with lots of references! (never mind the .de, it's in English!) |
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Mathscinet, which contains summaries and reviews of published research papers. It's very useful when you want to get an idea of a paper without having to read it, and contains almost every paper ever published. |
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Free downloadable (and streaming) video lectures from the Institute for Advanced Study at Princeton: http://video.ias.edu/ Not exactly a resource, but a great way to listen to talks given by experts on the latest results in Computer Science and Math. |
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http://maths.dept.shef.ac.uk/magic/index.php Apparently UK has been building a depository/interactive system for graduate math courses. Click on "courses" to access archives. Many have lecture notes and other materials. I found this recently. Have not actually personally used it, but potentially very useful. |
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contains a lot of useful advice for people at various stages in their careers. In addition it contains a lot of discussions and explanations of the math that I find interesting. |
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Allows you to search for research articles. Gives you direct links to all online versions of the article it can find. Strenghts include that it can often give you direct links to files hidden on obscure (non-arXiv) preprint servers or personal webpages, and if you sit on a computer with access to ScienceDirect, Springerlink etc, you get direct links to these artices, via your university library. Weaknesses include lots of errors due to the reliance on their "intelligent" search engine rather than correct metadata from publishers, but this is likely to improve over time. To find what you really are looking for use the author tag, for example "infinite loop author:May" etc. |
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Don't forget http://gigapedia.com/ for tons of e-books. |
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David Ben-Zvi takes electronic notes on the talks he attends and posts them publicly. This can often be the best source of information for a subject which has not yet been written down. |
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Mostly for the student, including high school. But has more advanced forums, too. Latex easily used. |
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The nLab is an excellent resource, often containing more detail, explanation, and discussion than wikipedia, along with much more specialized and contemporary topics. (nLab was mentioned in the answer by Justin Hilburn, but it was listed there after other resources, and I think people scanning under the one-resource-per-answer dictum will miss it.) |
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Sloane's OEIS has already been mentioned. A similarly useful site is ISC, Simon Plouffe's Inverse Symbolic Calculator. Here you enter the decimal expansion of a number to as many places as you know, and the search engine makes suggestions of symbolic expressions that the expansion might be derived from. The answer might involve pi, e, Sometimes, it becomes difficult to calculate symbolically. Therefore, you can proceed numerically instead, and hope to recover the exact symbolic solution at the end, using ISC: sometimes proving that an answer is correct can be easier than calculating, or discovering, it in the first place. It can also be useful for discovering simplifications of nested radicals, for example. |
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I don't know if this reference is of sufficient generality: Finite Calculus: A Tutorial for Solving Nasty Sums It is only a paper, but it describes the methods of the so-called "umbral calculus": a really useful technique to know. |
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edit by jc: As of May 11, 2010, the work has been completed! This is a reference that is not yet complete, but it should be very useful when it finally does arrive: Digital Library of Mathematical Functions (DLMF) This will contain diagrams, tables, properties of, principal values of, and relationships between many important mathematical functions. For example, the trigonometric and other elementary functions are described, with very many formulae relating them. The Handbook is very good; the Digital Library will be even better. |
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Alexandre Stefanov keeps an extensive list of free math books / lecture notes. The list is divided according to subject and updated frequently. I have found some very nice books there. |
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CiteULike (by Springer), to organize in a library the titles and abstracts of one's preferred papers and books. (From the FAQ:) CiteULike is a free service to help you to store, organise and share the scholarly papers you are reading. When you see a paper on the web that interests you, you can click one button and have it added to your personal library. CiteULike automatically extracts the citation details, so there's no need to type them in yourself. It all works from within your web browser so there's no need to install any software. Because your library is stored on the server, you can access it from any computer with an Internet connection. |
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The optimization community seems to prefer this specific online repository instead of the more broad one arxiv. |
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It seems this link hasn't appeared above http://www.ams.org/mathweb/index.html The resources there are too rich to describe. |
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