Math Branches to study

If you liked calc BC, you'll like differential equations and complex analysis.

Forgot to mention, I want to learn there on my own, in my free time.

>>8923980
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?

>>8923981
e^x

>>8923966
Read a book on proofs like Smith's
http://4chan-science.wikia.com/wiki/Mathematics#Proofs_and_Mathematical_Reasoning
Then read one of these:
http://4chan-science.wikia.com/wiki/Mathematics#Overview_of_Mathematics

>>8923987
[math]{partial} over {partial x} e^u = e^u {partial u} over {partial x} [/math]

>>8923993
Thanks anon, will check out.

>>8923966
>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 ?

>>8923985
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]

File: 31PkzsJ2LLL._SX328_BO1,204,203,200_.jpg (14KB, 330x499px) Image search: [Google]

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Geometric measure theory.

>>8923966
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.

>>8923996
Yeah, so it should be clear this is the Taylor expansion of e^x at 0.

>>8924229
ew.

File: maths.png (242KB, 1857x1396px) Image search: [Google]

242KB, 1857x1396px

Here's a flow chart for major areas of math and their prerequisites. Start from the bottom

>>8924480
Thanks anon! Thai si the kind of info I was looking for.

>>8924480
Pretty sure you need single var calc for probability

>>8924533
It goes Single Var. Calc --> Real Analysis --> Measure Theory --> Probability Theory

So knowledge of calculus is implied

>>8924480
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.

>>8924177
if you evaluate the laplace of sin(t)/t in 0 you can solve it easier

>>8925049
>laplace
confirmed engineer. >>>/lgbt/

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.

>>8924516
>>8924480
This is really incomplete.

>>8925058
It contains all of the basics, and I mentioned some things that are missing: >>8924558 . It's impossible to learn all of mathematics anyway.

>>8924177
""""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]

File: Yd7iBD7.jpg (278KB, 1920x1080px) Image search: [Google]

278KB, 1920x1080px

Algebraic topology? Algebraic topology!

>>8925646
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

>>8926401
[math]\leg[/math] *

>>8926401
>>8926406
[math]\leq[/math] **
sheesh

>>8923966
personally, i like the principal branch

>>8926401
cba desu, would have to get my complex notes out