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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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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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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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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I occasionally find mathoverflow.net rather helpful. In particular, there's a good list of answers to your specific question here. |
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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://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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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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Detexify is a quick and easy way to find the name of a LaTeX symbol. |
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MathOnlineRecently launched by Andrea Ferretti Here one can collect lecture notes, survey articles, books and so on. All the material can be organized and searched by author, topic, language, level and so on. Registered users can add new books, add tags, write reviews, vote, keep a list of the favorite books and see other people's profiles. |
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Very good articles with lots of references! (never mind the .de, it's in English!) |
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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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Mostly for the student, including high school. But has more advanced forums, too. Latex easily used. |
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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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The open source software package SAGE at sagemath.org can calculate, well, almost anything you want. The mission of the SAGE group is: Creating a viable free open source alternative to Magma, Maple, Mathematica and Matlab. The most useful resource online is www.sagenb.org, where one can log in and use SAGE online, without having to install any software. |
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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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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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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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I am surprised nobody yet have put pointers to books and papers. For older stuff you can find a lot at Gottingen Digital Library, Numdam and JSTOR. |
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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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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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Hosts high-level maths discussions, forums have inline LaTeX rendering. |
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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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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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