Which book to read on quantum-related mathematics Recently I watched the "Big Bang Theory" and decided to google about quantum mechanics. It really intrigued me. But I also understood that I am too stupid to understand even the basic mathematics in there. So I decided first to improve my knowledge of mathematics. I actually had a lot of courses on calculus which were not very deep (the last topic was Fourier if i remember correctly and Z-transform) + a short course on statistics (Basic things like distributions). This is definitely not enough to understand all the basic proofs I encountered. The problem is I could not google anywhere which books for beginners I can read in order to understand the basics of all those mathematics. I know there are a lot of parts of maths, so could you help me out - what shall I start with - which part of maths is connected tightly to quantum mechanics? Would be very grateful for the links to the books which a dummy could understand (i mean difficult books would do if they are preceeded by links to books for dummies). This question might seem stupid, but I think this place is the best to ask it.
 A: See this: Mathematics for Quantum Mechanics
A: *

*I participated a course in coursera "Exploring Quantum Physics" earlier this year for fun. The course is well organized and pretty neat for undergrad students who have background in multivariate calculus, ode, and some elementary pde. It introduced some basic concepts, experimental motivation, and some classical examples like quantum harmonic oscillator, Dirac well, and spin which is unique in the quantum world. I thought it was easy to understand and the homework is very instructive (Maybe because I took graduate level QM course already, I saw some people having difficulties in homework in the discussion forum). The course is already over, but you can still access to the course archive. If you could see the homework, it is a nice exercise to watch the video lectures first then try to do the homework.

*There are some good answers in an MO thread: Where does a math person go to learn quantum mechanics?.

*My suggestion would be the same as the first answer in that MO thread: go take a classical mechanics course. At least you need to know some mechanism in attacking physics problem (they care units a lot, do expansion a lot, use heuristics a lot), notations (Physicists use drastically different notations), and some basic concepts (conservation of angular momentum for example).

*Lastly, the mathematics involved quantum mechanics is serious and not so "eye catching" as those thought experiments bearing quantum nature that appear in the pop culture, like $C^*$-algebra and the analysis in NLS.
A: Quantum mechanics lies heavily in abstract linear algebra, partial/ordinary differential equations, vector calculus, abstract algebra/group theory, complex analysis, and operator theory as some of the main ones I can think of right away
A: First read this:
Linear Algebra: Linear Algebra for Dummies
Differential Equations: Differential Equations for Dummies
Probability:Probability for Dummies
Group Theory: Schaum's Abstract Algebra (Chapter 9)
Afterwards see this PDF
