Most helpful math resources on the web

Question

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!

I edited your question a bit, my main goal was to remove the reference to WolframAlpha; and make the text easier to read. But feel free to revert if you like! (You can see the edit history and revert by clicking on "edited ... ago") — Ilya Nikokoshev, Nov 04 '09 at 21:23
The answers below are great. Here's an idea I don't see that may be interesting to think about starting: An online example repository. This would be a place where one could upload and search various "first nontrivial example" notes. I think such a thing would really move mathematics along. — Jon Bannon, Apr 20 '12 at 13:38

score 168 · Accepted Answer · edited Apr 13 '17 at 12:58

168

I occasionally find mathoverflow.net rather helpful.

In particular, there's a good list of answers to your specific question here.

edited Apr 13 '17 at 12:58

Community

1

answered Mar 08 '10 at 14:37

Cam McLeman

8,417

26

interesting occurrence of the Droste effect, http://en.wikipedia.org/wiki/Droste_effect – Sean Tilson Apr 18 '10 at 02:58
21

@Cam, you've taken MO off the list of helpful math resources that don't list themselves, thereby averting Russelian calamity. Good on ya. – Gerry Myerson Nov 16 '10 at 03:13
14

mathoverflow.net? Never heard of it. – NPC Nov 16 '11 at 08:40
23

I don't like this website. It advertises itself in one of its threads. – Niemi Aug 28 '12 at 08:36

score 126 · Answer 2 · edited Sep 21 '21 at 01:24

126

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 a SPIRES search engine at https://inspirehep.net/

edited Sep 21 '21 at 01:24

David Roberts

33,851

answered Oct 23 '09 at 19:38

Per Alexandersson

15,598

11

and they have rss feeds! – Andreas Holmstrom Oct 25 '09 at 04:56
2

There is also https://hal.archives-ouvertes.fr/ (archives ouvertes is open archives in french) – Héhéhé Sep 23 '21 at 00:49

score 113 · Answer 3 · edited Oct 23 '09 at 20:34

113

http://www.wikipedia.org

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.

edited Oct 23 '09 at 20:34

Ilya Nikokoshev

14,934

answered Oct 23 '09 at 20:03

Kim Greene

3,583
10
42
41

3

See especially the mathematics portal http://en.wikipedia.org/wiki/Portal:Mathematics on which page there are links to more-specific mathematical portals, and to mathematics categories. – Rhubbarb Nov 11 '09 at 09:16
1

Other wiki sites: Scholarpedia, Knot Atlas, Manifold Atlas. – Junyan Xu Dec 20 '11 at 03:03

score 109 · Answer 4 · edited Jan 19 '22 at 11:43

109

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.

edited Jan 19 '22 at 11:43

Zsbán Ambrus

1,924

answered Oct 23 '09 at 19:19

Robert Parviainen

151

3

Of course there's much more than enumerative combinatorics -- it's very strong in number theory, for example. – Charles Oct 07 '10 at 01:06
+1 for being the least obvious among the top five answers. – Amritanshu Prasad Aug 28 '12 at 08:23
1

Neil Sloane's home page http://neilsloane.com/ has links to some of his other useful databases cataloging, for example, lattices, spherical codes, Lennard Jones cluster, Hadamard matrices, and so on. – Yoav Kallus Apr 12 '13 at 22:20

score 74 · Answer 5 · answered Oct 24 '09 at 02:21

74

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.

answered Oct 24 '09 at 02:21

Thanos D. Papaïoannou

2,220

4

I agree. But it's unfortunate that often the "summary and review" often consists of nothing more than the abstract of the article and the bibliography. – GMRA Oct 27 '09 at 17:23
6

Of course every mathematician should be familiar with this. Be glad you are doing it today. Back in the day I would have to walk to the library, search through multiple index volumes of Math Reviews, and maybe find what I wanted. But I still did it once a week or so... – Gerald Edgar Oct 28 '09 at 13:51
4

Beyond the reviews at MathSciNet one of the most beautiful features of the website is that it allows you to page back and forward through the history of the topic at hand. You're reading the review and you can click on the link that offers you the papers that cite this paper. So if you happen across an old paper that's concerned with a topic you're interested in, and want to know if anyone has done anything more recently on that topic, you're just a click away. I don't know when that feature was added but when I was a young mathematician I would have killed for that feature. – Ryan Budney Nov 05 '09 at 04:15
19

I'm not in academia any more and so can't access Mathscinet (and JStor). It's very frustrating. – Anonymous Mar 08 '10 at 16:39
1

Finding forward and back references is indeed one of the most amazing and useful things about MathSciNet, but be aware that not everything will show up. Articles collected in books and older articles don't have their references in the database. The cutoff seems to be around 2000, but it may be different for different journals. – Tom Braden Jun 18 '10 at 12:43
2

For people without institutional access, Zentralblatt might be a very good alternative. The functionality is on a similar level, but Zentralblatt is open access. – Lennart Meier Sep 21 '21 at 13:21

score 66 · Answer 6 · answered Oct 23 '09 at 20:00

66

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.

answered Oct 23 '09 at 20:00

Justin Hilburn

1,544

11

I'm partial to both John Baez and the nLab, but the two don't have much intersection any more. The nLab is sometimes short on making really esoteric topics seem obvious. – Todd Trimble Aug 28 '12 at 11:06

score 62 · Answer 7 · answered Mar 08 '10 at 13:36

62

Detexify is a quick and easy way to find the name of a LaTeX symbol.

answered Mar 08 '10 at 13:36

Amy Glen

659

It's definitely fun, though it doesn't look particularly reliable. I tried two times to draw a path integral sign, and it didn't give me the right command even once. – darij grinberg Mar 08 '10 at 14:03
1

@darij: it is trained on user responses, so the more you use it the better it will get. I got a version of the path integral sign with an arrow in the circle two out of three times. – Qiaochu Yuan Aug 24 '10 at 03:13
3

and I can recommend to use it. It has been written by a friend of mine and he always wants larger datasets to train it.The more people use it, the better it will be. – HenrikRüping Oct 27 '10 at 09:59

score 60 · Answer 8 · answered Oct 24 '09 at 12:08

60

Terence Tao blog

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.

answered Oct 24 '09 at 12:08

mkolar

151

score 57 · Answer 9 · answered Oct 25 '09 at 04:56

http://scholar.google.com/

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.

score 51 · Answer 10 · answered Oct 23 '09 at 20:33

51

http://jmilne.org has lots of systematic, well-written courses.

answered Oct 23 '09 at 20:33

Ilya Nikokoshev

14,934

And version 2.00 of "Algebraic groups" has just been released! For those of us who grew up on Borel and Springer, and are now trying to dip our toes in the waters of non-smooth schemes without going into the full machinery, this seems like a gift from the heavens. – LSpice Jun 08 '16 at 13:46

score 41 · Answer 11 · edited Jun 08 '16 at 09:47

41

Unfortunately Library Genesis is down and has been down for some time now, so I'm taking the liberty of editing this answer. A working site that is similarly useful is libgen.info and someone has collated a blog of links here.

Original answer follows:

At the Library Gensis or the translated version here, you can browse and download as many high-quality and modern Mathematics books, surveys, etc as you wish. This i-resource must be on every mathematician's i-shelf.

Here is some list:

599 books on Number Theory;

303 books on Complex Analysis;

325 books on Algebraic Geometry;

588 books on Partial Differential Equations;

97 books on Abstract Algebra;

107 books on Commutative Algebra;

181 books on Harmonic Analysis;

133 books on Fourier Analysis;

349 books on Functional Analysis;

356 books on Differential Geometry;

88 books on Riemannian Geometry;

783 books on Topology;

286 books on Combinatorics;

323 books on Graph Theory.

This is enough for illustration. You will find more, enough to get you in a downloading craze!

edited Jun 08 '16 at 09:47

Martin Sleziak

4,608

answered Apr 10 '11 at 12:49

Unknown

2,815

1

The list continues$\ldots$434 books on Group Theory. – Unknown Apr 10 '11 at 12:52
The list is not particularly useful, as most books on Group Theory don't have "Group Theory" in their name, and conversely, many books appear doubled, tripled or n-tupled in the archive (not that this was bad!). – darij grinberg Apr 10 '11 at 15:22
2

The link, however, is one of the most useful locations of the internet. – darij grinberg Apr 10 '11 at 15:22
@darij, I can can't debate on that as I found most classic and modern texts, monographs,etc in the Group Theory list. Did you proceed to the succeeding pages? If not, you have not yet seen the treasure! I agree with you that the site is one of the most useful though. – Unknown Apr 10 '11 at 16:57
6

Aside from the copyright issues, I find this site and similar (extracoder, eknigu, lib.by etc.) one of the most useful math resources from the web. – Marcin Kotowski Apr 10 '11 at 18:31
Impressive indeed, including classic and modern texts, but... I looked at "complex analysis" and there are materials there whose title just contains words "complex" and "analysis". e.g., "3D analysis of functionally graded material plates with complex shapes and various holes", so the count is an overestimate. – Margaret Friedland Nov 16 '11 at 15:06
13

Rather than 'aside from the copyright issues', I would say 'because of the copyright issues'. If we had a working system of copyright, we would not have to resort to questionably legal means of getting information that naturally belongs to all of humanity. – A. Pascal May 29 '12 at 07:53
3

Fortunately LibGen is back! – LSpice Jun 08 '16 at 13:48

score 39 · Answer 12 · answered Oct 23 '09 at 20:40

39

http://books.google.com/

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.)

answered Oct 23 '09 at 20:40

Qiaochu Yuan

114,941

16

One extremely useful way to use Google Books is as an "instant index." For example, I have the book ZZZ open in front of me. There is a term yyy I don't know the definition of. I look up yyy in the index of ZZZ. Ooops, no index! So I search for yyy at the Google Books page for ZZZ and order by pages. Done. – Sam Nead Mar 08 '10 at 14:24
8

An annoying feature of this site is that a lot of the book portions do not include the preface or introduction which is usually the first thing I want to read about a book. – Anonymous Mar 08 '10 at 16:41
2

The preface/introduction parts can be often found in the book preview on http://www.amazon.com. For the books published by the AMS these are often availble right on the AMS bookstore website (http://www.ams.org/bookstore). – mathphysicist Jun 04 '10 at 17:43
1

Google books also provides bibtex entries. Which is pretty useful to me. – Pablo Lessa Nov 15 '14 at 19:14

score 38 · Answer 13 · answered Mar 07 '10 at 23:29

38

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.

answered Mar 07 '10 at 23:29

Álvaro Lozano-Robledo

1,674

1

For anyone looking here more recently than the original answer: sagenb.org has been/is being replaced by the SAGE cloud: https://cloud.sagemath.com/ – Aeryk Nov 15 '14 at 19:41
1

Another update, sagenb, then cloud.sagemath, is now https://cocalc.com/ – Álvaro Lozano-Robledo Sep 02 '18 at 02:37
2

Now https://sagecell.sagemath.org/ – Peter Taylor Sep 21 '21 at 11:51

score 37 · Answer 14 · answered Oct 25 '09 at 10:06

37

Don't forget http://gigapedia.com/ for tons of e-books.

answered Oct 25 '09 at 10:06

Wanderer

5,123

24

Several people have flagged this answer as requiring moderator attention. Please use your own judgement as to the legality of any site on the internet, and remember linking is always okay. – Scott Morrison Mar 08 '10 at 02:24
@drvitek: That link doesn't work (and a quick google search turned up a geocities version which is also dead...) – Simon Apr 24 '11 at 10:37
Sadly it has become invite-only. – Junyan Xu Dec 20 '11 at 02:10
As explained in the Wikipedia article, Gigapedia/Library.nu no longer exists. – Martin Sleziak Jun 06 '16 at 04:40

score 33 · Answer 15 · answered Nov 05 '09 at 03:19

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.)

score 27 · Answer 16 · answered Oct 23 '09 at 19:46

27

http://mathworld.wolfram.com/

answered Oct 23 '09 at 19:46

John D. Cook

5,147

3

The book for this website is the "Concise Encyclopedia of Mathematics" by Eric W. Weisstein, CRC Press. The website is "Eric Weissteins's MathWorld", from which there are links to areas of mathematics and to other on-line mathematical tools. Both book and website take the form of a mathematics dictionary. This site is excellent, but beware that as it is associated with Wolfram Research, there is a bias towards the commercial mathematics package "Mathematica". – Rhubbarb Nov 11 '09 at 09:26

score 26 · Answer 17 · answered Mar 08 '10 at 01:03

26

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.

answered Mar 08 '10 at 01:03

Felipe Voloch

30,227

2

Hi Felipe ! Let me add a link to DML http://www.mathematik.uni-bielefeld.de/~rehmann/DML/dml_links.html
This site contains links to Gottingen, Numdam, Jstor and some others.
– fcukier Dec 20 '11 at 03:57

score 26 · Answer 18 · answered Oct 24 '09 at 02:13

26

MIT OpenCourseWare

answered Oct 24 '09 at 02:13

person

13

2

Seconded. The combination of lecture notes and lots of problems is hard to beat. – Qiaochu Yuan Oct 24 '09 at 03:30

score 26 · Answer 19 · answered Oct 27 '09 at 17:05

26

Videos from MSRI.

answered Oct 27 '09 at 17:05

Noah Snyder

27,820

This is a treasury full of great talks! The quality of the videos is also excellent. – Jan Weidner May 25 '10 at 12:22

Jeffrey Giansiracusa · Answer 20 · 2010-04-26T12:29:53.330

24

Zentralblatt-MATH

MathSciNet has been listed above, but I didn't see Zentralblatt-Math. It does much the same thing as MathSciNet, although it has in fact been doing it far longer. Most papers get reviewed on both databases, and this redundancy if often very useful (although people frquently argue about whether or not we really need both nowadays - there have been many long discussions about this in various places).

Unfortunately, many students these days seem not to be aware of Zentralblatt. It is definitely a useful resource and if your institution pays for a subscription then it is certainly worth knowing about it and using it.

edited Apr 26 '10 at 12:29

answered Apr 26 '10 at 06:39

Jeffrey Giansiracusa

6,169

1

Just to add one point. One can even use Zentralblatt in a fairly meaningful way without subscription. The only limitation one has is I believe that only 3 results are shown for each search but one gets full access to the items. Thus if one knows fairly precisely what one wants or is willing to 'restrict and repeat' the searches a bit (restricting the years of publication for example) it is not even necessary to have a subscription. – Dec 20 '11 at 21:13
2

Zentralblatt is now free and open access to everybody, I believe. – Roland Bacher Sep 21 '21 at 12:34
Now that it is free, Zentralblatt is infinitely more valuable than Mathscinet for people outside academia or developed countries. – pinaki Jan 19 '22 at 21:02

score 21 · Answer 21 · edited Sep 21 '21 at 11:52

21

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, sin, cosh, sqrt, ln, and so on.

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.

edited Sep 21 '21 at 11:52

Peter Taylor

6,571

answered Nov 05 '09 at 23:28

Rhubbarb

524

http://pi.lacim.uqam.ca/ is the new version of the site, run by Simon Plouffe. – Sam Nead Apr 10 '11 at 16:23
2

The new URL is http://isc.carma.newcastle.edu.au/ – Yoav Kallus Nov 15 '14 at 20:39

score 20 · Answer 22 · edited Nov 02 '18 at 16:52

20

MathOnline

Recently 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.

edited Nov 02 '18 at 16:52

Community

1

answered Apr 25 '10 at 23:01

Anton Geraschenko

23,718

This is probably the single most valuable resource online for students of all levels.btw,Anton-I recently posted a link to your collection of TeX-ed lecture notes with you as the author.Hope you don't mind,but wanted to get the word out on your great work. : ) – The Mathemagician Jul 12 '10 at 02:08
1

Does anyone know whether MathOnline is still out there? I cannot access it now. – Yiftach Barnea Jun 17 '12 at 10:19

score 19 · Answer 23 · answered Oct 23 '09 at 19:25

19

http://www.wolframalpha.com/

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.

answered Oct 23 '09 at 19:25

Kim Greene

3,583
10
42
41

1

There are a bunch of rep 1 users who really want to discuss this, but can't post comments, so they're posting answers. I'm going to just move all those comments here and hope the problem goes away. – Anton Geraschenko Nov 06 '09 at 18:21
11

Paul Stuart says: I think Wolfram Alpha is just a waste of computational effort. Whatever comes from the Wolfram corner I'd be wary. It ranges from acclaimed proofs to acclaimed "correct computation". Note they are infamous for making claims or assertions that aren't true. So, think twice. – Anton Geraschenko Nov 06 '09 at 18:21
4

Qiaochu Yuan says: In all honesty, I use Wolfram Alpha whenever I can't be bothered to remember what the real syntax for a command in Mathematica is. – Anton Geraschenko Nov 06 '09 at 18:22
Reid Barton says: You can easily get it to give you nonsense--try entering "klein bottle" – Anton Geraschenko Nov 06 '09 at 18:23
3

dimitry (user 1087) says: @Qiaochu: That's just simply sad news altogether. There is a good point raised by Paul Stuart and that is the point raised about reliability. Wolfram Alpha, is a black box. God knows how reliable its answers are. If I aint completely sure, Wolfram had been (not unfairly) accused of being sloppy in many of his claims in his previous work on ANKS. If this is based on work in ANKS I'd be wary too. – Anton Geraschenko Nov 06 '09 at 18:25
interesting (user 1504) says: i find it interesting that someone posted one paper that refuted 44 claims posed by wolfram and that this was deleted. as a matter of fact this paper can be considered circumstantial evidence for what dimitry was pointing out. Obviously this forum seems to be run by wolfram enthusiasts. – Anton Geraschenko Nov 06 '09 at 18:27
1

Qiaochu Yuan says: Math Overflow is not a forum. It has no collective opinion on Wolfram, and this is not the place to discuss your opinion of his work. – Anton Geraschenko Nov 06 '09 at 18:28

score 18 · Answer 24 · answered Oct 23 '09 at 21:16

18

http://eom.springer.de

Very good articles with lots of references! (never mind the .de, it's in English!)

answered Oct 23 '09 at 21:16

Lars

4,400

I think Google must re-index them after recent change of their system ... – Junyan Xu Dec 20 '11 at 02:24
1

The link to eom.springer.de is dead. The website of the Encyclopedia of Mathematics has now moved to encyclopediaofmath.org. – The Amplitwist Jun 19 '22 at 12:59

score 17 · Answer 25 · answered Oct 23 '09 at 19:23

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."

http://www.tricki.org/

score 15 · Answer 26 · answered Oct 28 '09 at 13:55

15

The Art of Problem Solving

Mostly for the student, including high school. But has more advanced forums, too. Latex easily used.

answered Oct 28 '09 at 13:55

Gerald Edgar

40,238

3

I learned more in high school from reading posts on Art of Problem Solving than from any other source. Of course, this is before I discovered the blogosphere. – Qiaochu Yuan Nov 05 '09 at 03:39

score 14 · Answer 27 · answered Oct 24 '09 at 04:21

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.

Zoran Skoda · Answer 28 · 2010-10-07T00:28:24.877

Proceedings of all past ICM-s can be found here: http://www.mathunion.org/ICM

The following nlab pages list some of the main resources

http://www.ncatlab.org/nlab/show/Online+Resources -- a long list of math blogs and forums
http://www.ncatlab.org/nlab/show/math+institutions -- main institutions
http://www.ncatlab.org/nlab/show/math+archives -- preprint/journal/book/review archives

http://numdam.org is a collection of old issues of many mainly French math journals. http://www.mathnet.ru site has links to free old issues of most of the Russian math journals (and even some video lectures) in Russian and links to some non-free English versions. There is also an English mode of the site: http://www.mathnet.ru/index.phtml?&option_lang=eng. A smaller free depository of old issues of Polish math journals is http://matwbn.icm.edu.pl (click on the flag for English).

Max Planck maintains links to a very long list of journals, most of which are proprietary and usable only from their site, but the list is still useful because a sizeable fractions of links are also to free journals or some volumes of journals which are free, and those are mainly usable from all locations. The current URL is http://rzblx1.uni-regensburg.de/ezeit/fl.phtml?bibid=MPIMA&colors=3&lang=en&notation=SA-SP

Many resources can be found at the sites of main world math institutes like ihes, mpim-bonn, Oberwolfach, msri, kitp, ictp, rims, ias, Steklov, Clay, crm Barcelona, Mittag-Leffler, Banff, Fields, Newton, ihp Paris

AMS keeps a long list of math societies throughout the world with links to their sites, which are often useful. One should also recommend more general AMS directory of links Math on the Web http://www.ams.org/mathweb/index.html.

DML: Digital Mathematics Library http://www.mathematik.uni-bielefeld.de/~rehmann/DML/dml_links.html
contains some (but not all) of these resources organized in a unified way. — fcukier, Dec 20 '11 at 05:17

score 12 · Answer 29 · answered Oct 23 '09 at 20:27

12

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'.

answered Oct 23 '09 at 20:27

Qiaochu Yuan

114,941

3

The link is broken and now we have http://www.mathblogging.org/. – Junyan Xu Dec 20 '11 at 02:28

score 12 · Answer 30 · edited Jun 08 '16 at 12:37

12

http://maths-magic.ac.uk/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.

edited Jun 08 '16 at 12:37

Neil Strickland

55,003

answered Oct 24 '09 at 05:59

Max M

804

2

A similar "access grid" network comprises the Universities of Bath, Bristol, Oxford, Warwick and Imperial College London. The main site (which includes links to archived course material) can be found at http://tcc.maths.ox.ac.uk/. – Nicholas Jackson Oct 24 '09 at 11:04
And there's a similar one for Scotland: http://www.smstc.ac.uk – Tom Leinster Oct 27 '09 at 17:12
Australia has one also: http://www.amsi.org.au/index.php/ice-em/access-grid
Unfortunately there is not nearly as much archive material as one would hope for.
– Terry Tao Oct 27 '09 at 20:46
1

Now when all of these have unified search capabilities, that would be a great day! – Max M Oct 31 '09 at 22:20

score 12 · Answer 31 · answered Oct 27 '09 at 15:00

12

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.

answered Oct 27 '09 at 15:00

David E Speyer

150,821

Anurag · Answer 32 · 2016-06-08T18:27:08.737

10

Sci-Hub is pretty helpful in accessing articles, even for those researchers who already have access to several journals. The interface is great, the site is pretty fast, and the database is huge. See this article and other linked articles there for a nice overview of who all are downloading pirated papers.

Edit: as pointed out in the comments, it should be noted that there is an ongoing lawsuit against the website.

edited Jun 08 '16 at 18:27

answered Jun 08 '16 at 11:10

Anurag

1,157

3

You should probably mention it is the subject of a legal case, even if the jurisdictional issues complicate matters. – David Roberts Jun 08 '16 at 16:11

score 10 · Answer 33 · edited May 20 '10 at 00:50

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)
(book and associated website;
will replace Abramowitz & Stegun's Handbook of Mathematical Functions)
NIST / Cambridge University Press
expected 2009/2010
http://dlmf.nist.gov/

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.

The website, hardback and paperback of DLMF are now all available. — Rhubbarb, Aug 17 '10 at 00:19

score 7 · Answer 34 · answered Sep 21 '21 at 11:39

7

Overleaf.com is an excellent online LaTeX platform that allows you to collaborate with others, track changes, etc.

It also has many helpful pages on how to use Latex.

answered Sep 21 '21 at 11:39

Gabe K

5,374

score 7 · Answer 35 · answered Apr 10 '11 at 13:28

http://www.projecteuler.net

From website: Project Euler is a series of challenging mathematical/computer programming problems that will require more than just mathematical insights to solve. Although mathematics will help you arrive at elegant and efficient methods, the use of a computer and programming skills will be required to solve most problems.

From me: I have personally found it beneficial to go through these to help work at how I think about math problems.

Papiro · Answer 36 · 2013-01-03T14:07:05.820

6

I recommend archive.org. Books from Fourier, Lagrange, Euler... old stuff.

edited Jan 03 '13 at 14:07

answered Aug 28 '12 at 07:59

Papiro

1,568

score 6 · Answer 37 · edited Mar 29 '23 at 19:27

6

A community database of rings examples, searchable by properties: http://ringtheory.herokuapp.com/

It is very similar to pi-base, which is a more famous database but for topological spaces examples.

edited Mar 29 '23 at 19:27

Steven Clontz

963

answered Jun 06 '16 at 00:02

Tadashi

1,580

score 6 · Answer 38 · answered Nov 16 '11 at 20:52

6

While not as comprehensive as wikipedia, if you find an article on the scholarpedia on a topic, it should be the first place to look:

http://www.scholarpedia.org/article/Main_Page

answered Nov 16 '11 at 20:52

pang

1

score 6 · Answer 39 · answered Dec 20 '11 at 02:47

6

http://citeseer.ist.psu.edu/ caches a lot of papers that has been posted online. It often comes up within the first few search results in Google. (But you cannot view the cached documents online, since they are directly downloaded.)

answered Dec 20 '11 at 02:47

Junyan Xu

478

Théophile Cantelobre · Answer 40 · 2013-01-26T06:38:11.047

All math.[institution].edu/~[professor]/ sites are great with, in of themselves, many links to the favorites of the page's professor.
It is like walking up to the professor at coffee and asking him about the tools he uses (resources) and how it applies to his research . A big cafeteria with the world's professors ressembled and willing to answer any questions... or at least those who keep their site up to date.
An example: http://www.math.ucla.edu/~tao/
Professor Tao's page is mostly blue (links).

score 5 · Answer 41 · answered Mar 07 '10 at 19:34

5

It seems this link hasn't appeared above http://www.ams.org/mathweb/index.html The resources there are too rich to describe.

answered Mar 07 '10 at 19:34

Sunni

1,858

score 5 · Answer 42 · answered Oct 23 '09 at 19:31

5

http://www.physicsforums.com/

Hosts high-level maths discussions, forums have inline LaTeX rendering.

answered Oct 23 '09 at 19:31

J M

136

score 5 · Answer 43 · edited Aug 12 '15 at 07:40

5

The manifold atlas is pretty cool. I haven't spent enough time on it though... It seems like a different type of mathematical venture. Hopefully, it will inspire other similar projects. http://www.map.mpim-bonn.mpg.de/index.php/Main_Page

edited Aug 12 '15 at 07:40

Dario

643
1
7
20

answered Jul 12 '10 at 00:32

Sean Tilson

3,676

score 5 · Answer 44 · answered Nov 06 '09 at 09:31

5

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.

answered Nov 06 '09 at 09:31

Henning Arnór Úlfarsson

1,125

Henning - I'm going to steal this and add it as a comment to the gigapedia answer. (It seems it might be more visible there, and thus help serve to discourage people from (mostly) illegal downloads.) – dvitek Oct 27 '10 at 05:10

score 5 · Answer 45 · edited Jun 08 '16 at 09:45

5

Topology Atlas at York University is a great site with an awesome Q&A board (it of course, was not just restricted to Topology) and has been around for years.

edited Jun 08 '16 at 09:45

Martin Sleziak

4,608

answered Oct 26 '10 at 22:24

Tien Anh

1

score 4 · Answer 46 · edited Jun 08 '16 at 09:45

4

http://www.proofwiki.org

It is a Wikipedia, for proofs.

edited Jun 08 '16 at 09:45

Martin Sleziak

4,608

answered Apr 12 '13 at 15:40

Piyush Grover

2,261

score 4 · Answer 47 · answered Apr 06 '15 at 05:45

4

answered Apr 06 '15 at 05:45

Alexey Ustinov

11,875

score 4 · Answer 48 · answered Nov 16 '11 at 12:24

4

Resource for books is book.fi - select English from upper right.

Resource for (mostly free) papers is projecteuclid.org

answered Nov 16 '11 at 12:24

joro

24,174

score 3 · Answer 49 · answered Aug 19 '12 at 10:59

Two sites created by my former wonderful A level Mathematics teacher: www.whitegroupmaths.com www.a-levelmaths.com

He has generously written tons of topic summaries, worked revision problem sets and other learning material made mostly free to us students. Felt he deserves a mention for all his efforts :) Thanx n hope u will benefit from them!

Estella

score 3 · Answer 50 · answered Mar 08 '10 at 02:19

Since someone mentioned The Digital Library of Mathematical Functions, we better also include The Wolfram function site: http://functions.wolfram.com/

It's really useful for special function identities - especially since they are also available in Mathematica input form that you can copy straight into your code.

score 3 · Answer 51 · answered Mar 09 '10 at 03:32

3

Many free Mathematics e-books are available to view and/or download here.

answered Mar 09 '10 at 03:32

Amy Glen

659

score 3 · Answer 52 · answered May 12 '16 at 01:48

3

LMFDB has been officially launched yesterday (10th May of 2016).

It is an integrated knowledge database of L-functions and modular forms with a nice web interface that helps visualize the connections between these mathematical objects.

answered May 12 '16 at 01:48

Tadashi

1,580

score 3 · Answer 53 · answered Sep 21 '21 at 09:30

3

I use

https://groupprops.subwiki.org/wiki/Main_Page

e.g. for looking up less well-known definitions in group theory.

answered Sep 21 '21 at 09:30

Martin Seysen

558

Rhubbarb · Answer 54 · 2021-09-22T23:00:00.520

3

I don't know if this reference is of sufficient generality:

Finite Calculus: A Tutorial for Solving Nasty Sums
by David Gleich
https://www.cs.purdue.edu/homes/dgleich/publications/Gleich%202005%20-%20finite%20calculus.pdf
(The original link at http://www.stanford.edu/ no longer exists.)

It is only a paper, but it describes the methods of the so-called "umbral calculus": a really useful technique to know.

edited Sep 22 '21 at 23:00

answered Nov 05 '09 at 23:41

Rhubbarb

524

1

It's nice, but I don't think it ever comes to actual umbral calculus. Just working with finite difference operators and falling factorials is not umbral calculus yet. – darij grinberg Mar 07 '10 at 23:20
I think Gosper's algorithm is worth mentioning here. – teil Apr 25 '10 at 23:44
The link seems to be broken. – Roland Bacher Sep 21 '21 at 12:43
@RolandBacher thanks for letting me know; broken link replaced; try the new one. That paper is now hosted at Purdue not Stanford. Perhaps Gleich has moved Uni. – Rhubbarb Sep 22 '21 at 23:04

score 3 · Answer 55 · answered Nov 06 '09 at 21:26

3

www.optimization-online.org

The optimization community seems to prefer this specific online repository instead of the more broad one arxiv.

answered Nov 06 '09 at 21:26

Shake Baby

1,638

score 3 · Answer 56 · answered Apr 11 '11 at 12:16

3

Quite impressive is this site:

"PlanetMath is a virtual community which aims to help make mathematical knowledge more accessible" - or how they put it: "Math for the people, by the people":

Planetmath

answered Apr 11 '11 at 12:16

vonjd

5,875

score 2 · Answer 57 · answered Jan 03 '13 at 17:51

Jahrbuch Database

http://www.emis.de/MATH/JFM/

A sort of Mathscinet and Zentralblatt for the period 1868-1942. Most of the reviews are in German. It is interesting to read the reviews written by mathematicians like Frobenius, Hilbert, Minkowski, Hasse, E. Noether, Artin, Mittag-Leffler, Landau, Van der Waerden, ...

score 2 · Answer 58 · answered Mar 08 '10 at 13:58

2

There are some great things here at the small but fine Clay Institute Online Library

answered Mar 08 '10 at 13:58

Peter Arndt

12,033

According to a little box on the right hand side of the front page http://www.claymath.org/index.php "CMI publications are available in PDF form at most six months after they appear in print" but that seems not to be the case for the most recent publications... – j.c. May 20 '10 at 01:08
True, it's written there. But for example the outstanding book "Harmonic Analysis, Trace formulas and Shimura Varieties" from 2003 is still there. For me the CMI can stay inconsistent with respect to that :-) – Peter Arndt May 21 '10 at 14:03

score 2 · Answer 59 · answered Nov 15 '14 at 14:17

2

OntoMathPro, a crowdsourced ontology of professional math knowledge.

answered Nov 15 '14 at 14:17

Nikita Zhiltsov

101

janmarqz · Answer 60 · 2010-04-26T17:22:54.430

2

People: consider http://www.digizeitschriften.de/ tons of classical papers in english...

I think it is worth to check the 39 journals collection on world class referee-ed mathwork.

One paper on Mathematische Annalen (which is the very amusing): "On the holymorphic flow with an isolated singularity", is the famous GSV, gives you an index formula...

edited Apr 26 '10 at 17:22

answered Apr 26 '10 at 05:04

janmarqz

345

score 2 · Answer 61 · answered Nov 06 '09 at 12:28

CiteULike (by Springer), to organize in a library the titles and abstracts of one's preferred papers and books.

http://www.citeulike.org/

(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.

score 2 · Answer 62 · answered Apr 11 '11 at 12:20

2

A good online LaTeX equation editor: Here

answered Apr 11 '11 at 12:20

vonjd

5,875

score 2 · Answer 63 · edited Jun 08 '16 at 09:44

2

For people who are interested in prime factorization : http://www.mersenneforum.org

edited Jun 08 '16 at 09:44

Martin Sleziak

4,608

answered Nov 16 '11 at 19:39

jjcale

2,768
14
16

score 1 · Answer 64 · answered Mar 08 '10 at 17:13

1

Very nice Notes and Videos from the Southwest Center for Arithmetic Geometry are available here!

answered Mar 08 '10 at 17:13

Peter Arndt

12,033

score 1 · Answer 65 · answered Apr 26 '10 at 03:39

1

For students (or even teachers!),the Abdus Salam International Centre for Theoretical Physics has lots of lectures in Advanced Math.Every year the lectures are different.Enjoy! http://www.ictp.tv/diploma/index08-09.php?activityid=MTH

answered Apr 26 '10 at 03:39

pi2000

91

wlad · Answer 66 · 2021-09-28T17:21:50.403

https://www.sympy.org/en/index.html

SymPy is a Python library for symbolic mathematics. It aims to become a full-featured computer algebra system (CAS) while keeping the code as simple as possible in order to be comprehensible and easily extensible. SymPy is written entirely in Python.

If you ensure that the following code runs every time you start an iPython session:

from sympy.abc import *
from sympy import *
import sympy
init_printing(unicode=True)

Then you will have a CAS experience comparable to what you get with Sage. Now while on paper Sage might have more features, I keep finding myself moving back to Sympy in my own work. Also, the UI and function names are fairly similar to what you get in Sage, so you can easily move between them. I recommend giving this a try.

Also, avoid using the utility isympy as a substitute to running the above five lines of Python code.

score 1 · Answer 67 · answered Nov 16 '11 at 07:37

Mathematics Dictionary & Glossary for students at http://www.tuition.com.hk/mathematics/

This is a very comprehensive source of mathematical definitions.

With over 2000 terms defined, this dictionary is ideal for supporting students who are studying mathematics or related subjects. All terms in our dictionary are cross-referenced and linked for ease of use, making finding information quick and easy.

score 0 · Answer 68 · answered Apr 12 '13 at 14:11

0

NPTEL provides E-learning through online Web and Video courses in Mathematics organized by Indian Institute of Technology. http://nptel.iitm.ac.in/

answered Apr 12 '13 at 14:11

GA316

1,219

score 0 · Answer 69 · answered Mar 12 '10 at 10:55

0

I just found a very interesting site which has lots of free math videos even up to some more advanced topics:
http://www.hippocampus.org/

answered Mar 12 '10 at 10:55

vonjd

5,875

score 0 · Answer 70 · answered Nov 15 '14 at 16:52

0

For knot theorists, there are two really cool databases:

knotinfo and its cousin linkinfo, both maintained by Cha and Livingston.
knotatlas, maintained by Bar-Natan.

answered Nov 15 '14 at 16:52

Marco Golla

10,402

score 0 · Answer 71 · answered Apr 26 '10 at 08:09

0

http://www.math.fsu.edu/Virtual/

This site contains plenty of useful math resources.

answered Apr 26 '10 at 08:09

Jim B

111

score 0 · Answer 72 · answered Jun 18 '10 at 06:39

0

If you want to find a relationship between data in the form of closed form formulas this tool is - to the best of my knowledge - the best one:

http://ccsl.mae.cornell.edu/eureqa

answered Jun 18 '10 at 06:39

vonjd

5,875

score 0 · Answer 73 · answered Oct 17 '10 at 22:19

0

An excellent catalogue of mathematical information available on the web is Keith Mathhews'

http://www.numbertheory.org/ntw/gateways.html

and if you are interested in Number Theory, see

http://www.numbertheory.org/ntw/

answered Oct 17 '10 at 22:19

anon

1

score 0 · Answer 74 · answered Oct 27 '10 at 01:35

0

http://functions.wolfram.com/

answered Oct 27 '10 at 01:35

I. J. Kennedy

1,813

2

We have that already - see above – vonjd Oct 27 '10 at 06:27

Most helpful math resources on the web

74 Answers74

MathOnline