MHB Collaborative Mind Mapping for Abstract Algebra: Building a Visual Blueprint

[ModusPonens]

Hello

I've been doing a mind map of Abstract Algebra. A mind map is a visual representation of a subject, like algebra, organic chemistry, etc. , in a way that makes the subject structured in a more intuitive way, without losing the logical component. It's a map of the subject that make the important areas more evident. It also enables you to recognise your weak spots easily

As an attachment I show a mind map in construction. It is not the best example because it's not a final version, it's not complete and probably has some errors which are not typos. Besides, since I began doing mind maps recently, I'm not sure if this is the best organizational structure.View attachment 1984

If you want to know what a mind map is, more specificaly, and without the errors I'm making, you can watch the tutorial bellow.

Google has a fairly recent mind-mapping online software that allows collaborative projects. It's called Coggle and it's at coggle.it . It's very easy to work with and, of course, supports LaTeX.

So the question is: do any of you want to make a collaboration effort to build mind maps? We can try to experiment with the mind map I'm working on.



:)

 

[mathbalarka]

This is an interesting idea, definitely interesting for presenting a pedagogical way of visualizing AA. But then if you think about it, it has some disadvantages also, especially where the theorems and results are connected. How do one places the hierarchy of results then?

Nevertheless, I can give it a try if you want, although probably Deveno would write it out in 1/10 of the time I can with 100 times efficiency and error picking than me.

Have you thought about adding the conjectures in? Or probably I am misunderstanding the goal?

 

[ModusPonens]

This is an interesting idea, definitely interesting for presenting a pedagogical way of visualizing AA. But then if you think about it, it has some disadvantages also, especially where the theorems and results are connected. How do one places the hierarchy of results then?

Nevertheless, I can give it a try if you want, although probably Deveno would write it out in 1/10 of the time I can with 100 times efficiency and error picking than me.

Have you thought about adding the conjectures in? Or probably I am misunderstanding the goal?

Thank you. :)

1- That's something that can be done. I'm positive that it's possible to make bridges between branches to mark the dependence of a theorem on previous theorems. Nevertheless, I haven't done it yet. It takes a more in depth look at the subject.

2- As for the sequential order of the theorems, it can be resolved by interpreting theorem branches which are above as previous to the theorem branches bellow. This, however, has the following problem: I separated trivial results from propositions and from theorems in 3 branches. However, numbers can certainly be used to mark each result in sequential order.

3- It would be great to have Deveno on board. But I prefer having even just one collaborator than none.

4- Yes, you misunderstood the goal. But just the immediate goal. In the present time I just want to make a basic blueprint of abstarct algebra. That should include Groups; Rings; Modules; Fields and Galois Theory; Commutative Algebra . With priority to the first three, since I haven't studied the last two yet.
But that would be a very welcome and great development of this basic project.

I'm perfectly open to all suggestions on every aspect, be it structural, stylistic, conceptual, corrections, LaTeX tips, etc. After all, I just started doing this four/five days ago, so I know very little.