What are some interesting math branches to learn on my own. I recently learned Calculus for my Calc BC AP, and actually enjoyed it quite a bit. What are some other math fields that are equally interesting and will teach me a lot. I have taken an interest (but have not started learning) in topology and analysis.
What are some others you faggots would recommend to a brainlet, who wishes to unbrainlet himself. Also post examples from each sub-branch of math, so that I can get a feel of it.
Math branches I know of, and have a slight interest about: - Topology - Analysis - Number theory Also, quick challenge, what function is the pic the Taylor expansion of?
If you liked calc BC, you'll like differential equations and complex analysis.
Nathan Bennett
Forgot to mention, I want to learn there on my own, in my free time.
Ryan Sanders
Differential equations was actually a part of the material to study. Probably not on a very high level.
Can you give an example of complex analysis?
Levi Roberts
e^x
Nicholas Gutierrez
Read a book on proofs like Smith's Veeky Forums-science.wikia.com/wiki/Mathematics#Proofs_and_Mathematical_Reasoning Then read one of these: Veeky Forums-science.wikia.com/wiki/Mathematics#Overview_of_Mathematics
Luke Jones
[math]{partial} over {partial x} e^u = e^u {partial u} over {partial x} [/math]
Thanks user, will check out.
Michael Walker
>Also, quick challenge, what function is the pic the Taylor expansion of? You want an actual quick challenge? What's the function represented by [math]\sum_{n=1}^{\infty}2^{n+1}n(x-1/2)^{n-1}[/math] for |x| < 1 ?
At your level something cool about complex analysis is evaluating infinite integrals such as [math]\int_{-\infty}^{\infty} \sin{x}/x dx[/math] which turns out to be [math]\pi[/math]
Sebastian Thompson
Geometric measure theory.
Jeremiah Rivera
First learn some linear algebra from Hoffman and Kunze or Axler. Axler is easier for beginners. Now you have to learn analysis and algebra. Rosenlicht and Herstein are good. Once you've done that you should probably take a look at Spivak's calc on manifolds.
Gavin Wilson
Yeah, so it should be clear this is the Taylor expansion of e^x at 0.
Colton Jackson
ew.
Ayden Sullivan
Here's a flow chart for major areas of math and their prerequisites. Start from the bottom
Brandon King
Thanks user! Thai si the kind of info I was looking for.
Benjamin Parker
Pretty sure you need single var calc for probability
Aiden Cruz
It goes Single Var. Calc --> Real Analysis --> Measure Theory --> Probability Theory
So knowledge of calculus is implied
Liam Cox
Some things should be added to this, like module theory, functional analysis, algebraic topology, algebraic geometry, category theory, homological algebra, lie theory, and maybe some others. But they're all very high-level math.
Colton Stewart
if you evaluate the laplace of sin(t)/t in 0 you can solve it easier
Dominic Myers
>laplace confirmed engineer.
Angel Rogers
Complex analysis is really cool as an intro to topology (since the proofs use open sets) algebra (since the complex numbers are a field) analysis (obviously) and category theory (since the complex numbers have their own specific morphisms, the analytic functions)
It is the best babby intro to mathematical structure, I was lucky to have stumbled upon it as a first non-calc course.
Owen Ross
This is really incomplete.
Jace Taylor
It contains all of the basics, and I mentioned some things that are missing: . It's impossible to learn all of mathematics anyway.
Matthew Peterson
""""challenge""""
Integrate because you can [use your favourite convergence test], get geometric series [eqn]\sum_{n=0}^\infty 2^n\left(x-\frac{1}{2}\right)^n[/eqn] which evaluates at [math]\frac{1}{2(1-x)}[/math] and its derivative is [eqn]-\frac{1}{2}\frac{1}{(1-x^2)}[/eqn]
Nolan Roberts
Algebraic topology? Algebraic topology!
Dominic Sullivan
Alright. what's the largest set in which this laurent series converges
[math]\sum_{n=-\infty}^{n=\infty}a_nz^n[/math] where [math]a_n = \frac{1}{n}[/math] for n > 0 and [math]a_n = 5^n[/math] for n [math]\leq[math] 0
