Is there any math that's actually useful for a scientist (specifically physics) beyond the typical:
Calculus 1
Calculus 2
Calculus 3
Differential Equations
Linear Algebra 1
Linear Algebra 2
Or is the rest a waste of time unless you're an actuary or mathematician?
Probability theory for statistical mechanics and QM?
Just because nobody else has found a way to use something doesn't mean it can't be used, and refusing to learn things that you don't "need" is the surest way to prevent innovation in any field.
Differential geometry for general relativity,
representation theory for the standard model,
and
Chern-Simons theory for Witten fans
all might be useful here and there
For engineering and physics:
Partial Differential Equations
Numerical Analysis
Complex Variables
Calculus of Variations
Differential Geometry
Probability and Statistics
Fourier and Functional Analysis
Abstract Algebra and Lie Theory
Coding and Information Theory
Dynamical Systems and Chaos Theory
Control Theory (Engineers)
Cryptography (ECEs)
> is there any math useful for physics outside of the typical engineering curriculum
Yes! Omg
oh lawdy.
Abastract algebra, functional analysis, Fourier analysis, partial differential equations, differential geometry, tensor algebra, and the list goes on as shit gets more niche.
>Itt: I have no idea how sex works so I might as well just cut my dick off
>I'm a 2nd year undergrad and I'm pretty sure I understand the entirety of modern physics
>let me make this thread to dickwave about this revelation
You're a fucking retard. Differential forms/geometry and tensor calculus are the essence of GR, Lie algebra and representation theory are the backbone of the standard model. Calculus of variations are the standard of any field theory.
And moreover, listing fucking undergrad nonrigorous math courses means nothing. You can't do modern QM with the baby shit they teach you in first year linear algebra. Even undergrad PDEs is a joke.
tl;dr Stop being a conceited bitch and look up for once in your life. You've covered a mere handful of square cm inside the enormous forest that is the current knowledge of science and mathematics.
EE/CE double here
We've done (in addition to the OP):
Numerical Analysis
Complex Calculus
Probability and Statistics + Stochastic Processes
Fourier Analysis
Coding and Information Theory
Control Theory
Discrete Mathematics
Thanks guys, I know there's so much out there to know and I'm excited to scratch the surface really. Sorry for the bait but I wanted some place to start looking.
You guys listed a TON of different fields of math, but which ones would be the most helpful for studying general relativity and quantum mechanics?
If you want to learn GR just read A First Course in General Relativity by Schutz. If you have linear algebra and calculus you'll be able to learn a lot. It develops a lot of basic differential geometry in a natural way. The first few chapters are surprisingly difficult. D'Inverno and Sean Carroll's notes on GR are useful supplements.
For undergrad quantum mechanics I really don't have a good recommendation. Some standard introductory books are Townsend, Griffiths, and Shankar.
Afterwards I recommend learning some math.
Hoffman and Kunze or Axler for linear algebra.
Artin, Vinberg, or Lang for abstract algebra.
Munkres, Mendelson, Gamelin and Greene, or Willard for topology, they're all good.
Spivak's Calculus on Manifolds or Do Carmo's Differential Forms and Applications for multivariable calculus. Sorry but they're both terse.
Marsden for basic complex analysis. Conway, Ahlfors, Stein and Shakarchi, Narasimhan for more advanced stuff.
Rosenlicht or Rudin's Principles of Mathematical Analysis for real analysis. Rudin's Real and Complex Analysis, Folland, or Royden are good picks for advanced real analysis.
O'Neill's Elementary Differential Geometry and Hick's Notes on Differential Geometry. There are many more but I like these two. After this you should tackle Wald's General Relativity.
Jordan's Linear Operators for Quantum Mechanics is very good for what it says it's for. Use this along with some graduate quantum mechanics books like Sakurai.
Once you start learning rigorous math you'll hit a stumbling block but try and work your way through it. If you need to read some books on proving things like Chartrand's Mathematical Proofs or Velleman's how to prove it. Remember that unlike most other subjects once you get a handle on math it'll usually stick with you and change your thought process, but only if you actually do problems yourself.
I came here just to say this. /thread.
wew lad :^)
These and also real analysis, complex analysis, and topology
Differential geometry, Topology, abstract algebra, algebraic geometry and algebraic topology all find their uses in parts of physics.
>Spivak's Calculus on Manifolds
Bad book for preparing for GR. Uses dumbed down definition of a manifold.
>no one said statistics yet
I think the first 2 or 3 chapters are excellent as a quick course just on multivariable analysis, which you would want before tackling anything serious on smooth manifolds.
Albert Einstein used very advanced mathematics when he discovered [Math] E = mc^2 [/Math]. Especially when he was figuring out the way to prove that thing. I don't think those finished and polished equations give right picture from math skills that is needed to form those equations. Granted that not all things are as mathematically challenging than what Einstein did, but what I try to say is that math can be useful if you know how to use it.
That's really interesting. What kinds of math did he have to use? Differential geometry?
This applies to everything btw not just math
Quite a bad example, assuming you're going to suggest Einstein knew about pseudometrics etc. This was done by Minkowski (mathematican) after the fact
>implying stats are math
It is like saying physics is math
only probability used in it can be called math