/sci/ - Science & Math

[Anonymous No.5004104]

Can any mathematicians give me an overview of the subjects in mathematics? I'm looking for a flow chart or a hierarchy of what one needs to understand before one can progress into a certain area. I'm looking at this from the perspective of a physics student, and I'm quite interested in how one progresses in mathematics after taking the normal course progression (Calc I, Calc II, Ordinary Differential Equations, Linear Algebra, Multivariate Calculus, Partial Differential Equations). I know that one can take "baby" (beginning Rudin level) real analysis after having a solid grounding in calculus, but how does one advance into the realms of topology, algebraic geometry, differential geometry, complex analysis, manifolds, complex manifolds, etc. What is the standard progression? Is there even one?

>tl;dr What is the progression of advanced math?

[Anonymous No.5004121]

Bump

[Anonymous No.5004142]

There is no standard progression. Chances are, if you finished 'algebraic geometry' in undergrad, you only know a glimpse of the subject. There are many areas in mathematics that you revisit once you know other things. So try to prove some stuff, see if you can get past it, then read other stuff and see if anything in the past clicks. Constantly revisit things.

[Anonymous No.5004150]

Here's a cool lookin graph. Usually for physics undergrads that is, you go calc 1, calc 2, calc 3, then diff eq. (at least for my school) You can choose to take classes like mathematical physics which helps because often times you'll learn a certain physics concept that requires a mathematical tool beyond the scope of your calc classes. Besides that, those higher level topics (topology, diff geometry, etc) are probably taken at the graduate level, and depend on what you focus on as a graduate student. Hope this helped

[Anonymous No.5004173]

>>5004150
This is pretty cool, thank you. Does anyone have any other infographics similar to this?

[Anonymous No.5004178]

>>5004150

This is not useful for real mathematics. It is for children.

[Anonymous No.5004184]

Here is my opinion:

1) abstract algebra
2) real analysis
3) complex analysis
4) topology
5) everything else that you listed

[Anonymous No.5004200]

>>5004178

>>5004173 here. By similar I meant similar in style but obviously more advanced in content.

[Anonymous No.5004213]

Here's this from the /sci/ sticky: http://hbpms.blogspot.com/

[Anonymous No.5004229]

http://en.wikipedia.org/wiki/Areas_of_mathematics

It's not easy to classify mathematics. You can look at it by its historical development, by its application, or organized by its structure. The above page should be helpful, but remember; math is a tool used by many disciplines, and the results from many areas of mathematics are used within these disciplines. The common progression from algebra, trig, calc, diffyq's, exists because of its use by the physical sciences but beyond that it diverges greatly by need.

[Anonymous No.5006230]

>>5004150
What should I learn if I know everything on here?

[Anonymous No.5006238]

>>5006230
On the picture I mean

[Anonymous No.5006242]

I'm interested in studying category theory. Any thoughts guys?

[Anonymous No.5006267]

>>5006242
go for it. it needs more recognition.

[Anonymous No.5006279]

Enjoy, OP.

[Anonymous No.5006284]

>>5006267
I plan to do it due to the fact that it might help in theoretical physics research via simpler modelling. what do you think?

[Anonymous No.5006298]

>>5006284
There are already some known relationships between category theory and physics, although its all way beyond my knowledge. Check out John Baez's blog.

I would say go with your gut, if you think category theory is interesting then study it.

[Anonymous No.5006297]

>>5006284
Baez wrote a lot about the relationship of category theory with physics. As a very basic introduction you should look at "Physics, Topology, Logic and Computation: a Rosetta Stone" by Stay and Baez. It's quite low level, but it gets you started, and the references provide you with a wealth of reading material on the subject. You can probably find it on arxiv.

[Anonymous No.5006305]

>>5004104
I guess this is obvious which is why no one thought of it, but if you look at descriptions of university courses online, you can track the prerequisites and that should be pretty accurate.

[Anonymous No.5006312]

>>5006297
I'm not a mathematician btw, just a math/physics undergrad.

[Anonymous No.5006317]

>>5006279
This lacks numerology. Where does that discipline fit in?

[Anonymous No.5006318]

>>5004150

I'm pretty sure this is based off A-Level mathematics (High school level for americans)

[Anonymous No.5006579]

>>5006242
Definitely do it. I'm planning on learning it myself via a quick intro from Dummit and Foote (there are a few pages on it in the back) and then "Categories for the Working Mathematician." Although I probably won't do anything with it directly, I met someone who has a good understanding, and it really helps one develop intuition and understanding in other fields. So even if it isn't directly useful, it will be useful in thinking about objects in more generality and seeing connections between areas of mathematics.

[Anonymous No.5006591]

>>5006317
>the two thousand and twelfth year of our lord
>numerology in math
>i shiggy diggy

pic related, mfw

[Doll of Wood No.5006786]

>>5006279
thanks

[Anonymous No.5006795]

>>5006279
Be warned: this doesn't describe order of study, just the relationships between different ideas of mathematics. The areas of study of the topics listed doesn't have to (or usually) correspond with the arrows presented. For example, group theory comes before the presentation of the idea of a semigroup (abstractly) pretty much always.

captcha: webirl gum-elastic