Source
r/math•
RareCollection1620

Order of study?

Removed - post in the Simple Questions thread

[removed]

Posted Jul 1, 2021, 9:09 PM UTC

14
[deleted]•

There are many many roads you can take in math. Maybe you could help us out a bit and tell us your main interests and your current knowledge. Then I'll write you a roadmap towards those.

2
RareCollection1620OP•

Thanks! I'm not really decided on main interests, but I guess I could say number theory and topology. But then again I’m reeaally not acquainted with the world that is maths well enough to name a main interest. Number theory and topology are things I’ve seen float around the internet and they seem to be fascinating.

1
[deleted]•

OK, here is my basic path towards these. Notice that this is the path I would personally take. Other people will no doubt feel I listed too many or too little prerequisites, but it would be what works for me.

  1. High school math: algebra -> geometry -> trig -> precalculus (Suggested source: Lang's basic mathematcs)
  2. Proofs (Suggested source: Velleman's how to prove it)
  3. Single-variable calculus (Suggested source: Lang's A first course in calculus). This can be done together with (1).

Branch 1: To topology
1.1) Single real analysis (Suggested Source: Bloch's Real numbers and real analysis).
1.2) Multi real analysis (Suggested source: Duistermaat and Kolk's Multidimensional real analysis)
1.3) Abstract real analysis (Suggested source: Carother's Real analysis). This can (and should) be done together with 1.2
1.4) Topology (Suggested source: Wilansky's Topology for analysis and/or Lee's Introduction to topological manifolds)

Branch 2: To number theory
2.1: Abstract Algebra (Suggested source: Pinter's a book on abstract algebra)
2.2: Number theory (Suggested source: Ireland, Rosed)
2.3 Algebraic Number theory (Suggested source: Jarvis)

After both branches, you might like:
3.1: Complex Analysis with some analytic number theory (Suggested Source: Freitag & Busam)

2
edderioferMODAlgebraic Topology•

Unfortunately, your submission has been removed for the following reason(s):

  • Your post appears to be asking for help learning/understanding something mathematical. As such, you should post in the Quick Questions thread (which you can find on the front page) or r/learnmath. This includes reference requests - also see our lists of recommended books and free online resources. Here is a more recent thread with book recommendations.

If you have any questions, please feel free to message the mods. Thank you!

1