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I would like to get a list of mind maps of advanced mathematics topics. As an example, I have posted one below. I would be happy if you post such other maps. Making one and posting it here is also encouraged.

However, I am specifically not interested in those diagrams that pertain to either high school mathematics or an intricate web of highly specialized theorems. enter image description here

Many thanks!

Willie Wong
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Chulumba
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  • Sorry I forgot to tick the Community Wiki box. And now, the box does not show when I try to edit. – Chulumba Mar 26 '12 at 16:17
  • Not sure how you are using the words, "mind map," but Wikipedia says "... items linked to and arranged around a central key word or idea." Here, do you really want "formal systems" to be your "central key idea?" This seems like an unproductive use of a mind map – Thomas Andrews Mar 26 '12 at 16:17
  • @ThomasAndrews, how about "Visual aids" or "Visual maps"? – Chulumba Mar 26 '12 at 16:21
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    There is a table at the beginning of the book Abstract Algebra: an introduction by Thomas W. Hungerford resulting in a mental map of abstract basic Algebra as it is this that you want.I hope helped in your search. – Elias Costa Mar 26 '12 at 16:24
  • Do you know other sites with these mental maps math? – Elias Costa Mar 26 '12 at 16:25
  • @Elias, I just saw the map you referred to in Hungerford. It seems to me that the map there is not as structured, branching out at an increasing level of specialization as the one I posted above. I saw one other but I do not remember where. – Chulumba Mar 26 '12 at 16:38
  • The table that Elias mentions from Abstract Algebra: an introduction by Thomas W. Hungerford can be found on-line here: http://i.imgur.com/lCMlb.png

    (Taken from here: http://www.scribd.com/doc/47153639/Abstract-Algebra-An-Introduction-Thomas-W-Hungerford)

     – jcelios Mar 26 '12 at 17:22
  • The term "abelian fields" in that diagram is bizarre. Nobody uses it. The term "metric manifolds" also seems odd; semi-Riemannian manifolds is more common. – KCd Mar 26 '12 at 23:14
  • When seeing the term "mind map", is anyone else reminded of the idea of a "map of the cat" from Feynman's SYJMF? – KCd Mar 26 '12 at 23:15
  • @KCd, thank you for the comments. – Chulumba Mar 27 '12 at 08:14
  • Awesome map! I was mulling over this same idea a few days ago. I would like to contribute with Computer Science "side" of Mathematics. It will take a few days to get it together properly for me, but I hope to have something by then to share. – JakeClawson Mar 26 '12 at 18:16
  • @KCd: I wonder if the metric manifolds case is supposed to also include stuff like Finsler manifolds? – Willie Wong Mar 27 '12 at 09:13
  • @WillieWong, thanks for helping to make the post CW. But I do not know why I did not lose the points I earned for this post before it was made CW. – Chulumba Mar 27 '12 at 13:49
  • @Chulumba: short answer is: you don't. Points earned prior to CW-fication are always kept. Don't worry too much about it. :-) – Willie Wong Mar 28 '12 at 06:35
  • @WillieWong, thank you for the reply. I will be happy! – Chulumba Mar 28 '12 at 09:25
  • @WillieWong, my problem is exactly being discussed here:http://tea.mathoverflow.net/discussion/1336/chrome-crash/#Item_0 I am using Chrome on Windows and the tick box did not show when I clicked on 'edit' under my question. – Chulumba Mar 28 '12 at 14:09
  • @Chulumba: on the StackExchange2 network (of which Math.SE is a member, but not MathOverflow), users cannot mark their own questions CW. (Users can, however, mark their own answers CW.) – Willie Wong Mar 28 '12 at 18:14
  • @WillieWong, did not know. Thanks. – Chulumba Mar 28 '12 at 18:18
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    This is probably worth a link here: http://www.math.niu.edu/~rusin/known-math/ – yasmar Mar 31 '12 at 12:04
  • @yasmar, right you are. – Chulumba Mar 31 '12 at 17:19

7 Answers7

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Here is a mind map by Konrad Voelkel that I understand and which was quite helpful when I was going to revise for an exam in Complex Analysis.

enter image description here

And another that is beyond my head presently and probably way beyond this site too ;-) is the following which appeared here.(I keep this as a souvenir of how much abstraction there is in mathematics! I hope you would, too.)

enter image description here

Herband
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Although it is a bit messy, you may be interested in the following map:

enter image description here

If anyone knows who made it, please let me know!

Max Lonysa Muller
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Although I do not know whether you call it a mind map or not, the Periodic Table of Finite Simple Groups was a recent brainchild of Ivan Andrus, described in more detail in his blog post.

In picture, here it is:

clickable image

Community
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Herband
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5

I just found a fantastic map titled "A Map of the L-functions and Modular Forms Database" here.

The best way to view it including the alt text is by clicking through to get to the original website or observe the picture below

enter image description here

ItsNotObvious
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Mathing being
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  • The image can't be saved with the alternate text. How can I do that so that I can post it here in full detail? – Mathing being Jun 02 '12 at 12:13
  • I've added the picture for you; just took a screensnap of the web page and uploaded that. – ItsNotObvious Jun 02 '12 at 13:39
  • @ItsNotObvious, thanks but did you not miss the alt-text? Perhaps it is not possible to save it that way. – Mathing being Jun 02 '12 at 14:34
  • If you mean the text that shows up when you hover over each element, there is no straightforward way to do this other than to save the html of the page and copy/past the hints to the desired location; they can't be captured as part of the image because only one shows up at a time! – ItsNotObvious Jun 02 '12 at 15:29
  • @ItsNotObvious, okay. Thanks for the info. – Mathing being Jun 02 '12 at 19:40
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The Mathematical atlas : A gateway to modern mathematics

jimjim
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1

Here's a nice map of exceptional (aka interesting) symmetry objects.

enter image description here

zooby
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0

Map of all mathimatics

source https://www.youtube.com/watch?v=OmJ-4B-mS-Y

Hassen Dhia
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