Hey, what kind of mathematics are needed to understand the bulk of QM and GR?
Ordinary calculus probably works, for both subjects. If you only want to understand it and make a few calculations. If you want to do research you need alot more mathematics.
Well, I'm a high school student and I'm very interested in Quantum Mechanics and General Relativity. I even took a class on classical physics here at school, but just the basic stuff.. I have pre-calculus down and just wanted to know what was needed to contribute thanks alot :D btw.. that was a really quick response
Not to go deep into details and the formalism and just gather a superficial knowledge of QM:linear algebra,calculus,complex analysis+special functions and ODE+PDE-s.
For GR,well,calculus and linear algebra is more that enough to understand the nongeometrical exposure by Dirac .
 P.A.M.Dirac "General Relativity",1975.
The short answer is that QM requires linear algebra, calculus, and operators. GR in full splendor requires all that plus differential geometry and tensor calculus.
If you start with the Schrödinger equation you will see what you all need. i think if one can solve this equation he has understood the mathematical concept.
John Baez has a nice link about "how to learn math and physics". As far as QM is concerned, you will need at least:
Ordinary differential equations
Partial differential equations
Complex analysis is not necessary to use/understand QM.
And the evaluating of integrals using special functions and the theorem of residues should one pick from a cookbook...?Think about scattering and its integrals (usually Laplace and Fourier's transforms).
Hmm... I would still say that complex analysis is not necessary to understand QM, although I will now say that it is necessary to use QM.
The trouble with this is that the Schrodinger equation and the deductions that follow from it do not exhaust the whole of QM. For instance, how can you derive spin from Schrodinger? You can't.
Is it possible to understand GR from the quantum mechanical perspective?
Quantum mechanics doesn't put much emphasis on differential geometry (Spivak style) but instead makes heavy use of algebra.
You could formulate each theory in the other's favorite framework.The way the way these 2 are still taught is called "traditional".But that still doesn't mean that geometrical quantization,for example,is useless.
Do you actually mean Linear Differential Equations when you wrote "ODE"? ODE refers to ordinary differential equations to distinguish it from partial differential equations. ODE refers to non-linear diff eq.s. This was actually a class I took and I too was initially confused by the difference until I saw the text and spoke to the prof.
You have a long way to go, and a lot of classical physics to learn before you can start to appreciate or even understand QM or GR. Thinking about QM without the fundamentals (of classical mechanics -lagrangian and hamiltonian formulations, statistical mechanics and electrodynamics) laid down, is not the best way to go.
Let's not exagerate now. There are many good books with zero math in them which doa good job at describing QM to the layman.
But the OP was suggesting that he wanted to learn QM the mathematical way.
There's only one way to learn the formalism of QM and that is:realizing this is theoretical physics and mathematics should be central.
Start with topology,the key ingredient of functional analysis.
What topology book do you recommend?
I don't reccomend a specific book on topology.You'll have to figure out by yourself what kind of mathematics you need to brush on,if you read the first 4 chapters of Bogolubov,Logunov & Todorov "Introduction to Axiomatic Quantum Field Theory",Benjamin/Cummings,1975.
Separate names with a comma.