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I'm a computer scientist with a huge interest in mathematics. I have also recently started to develop some interest about quantum mechanics and quantum field theory. Assuming some knowledge in the areas of topology, abstract algebra, linear algebra, real/complex analysis, and probability/statistics, what should I start to read to understand the math behind quantum mechanics and quantum field theory. If you could offer me books, and list them according to the order that I should read them, I would be glad.

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Sounds like you know more maths than me, and I'm supposed to be doing a PhD in quantum mechanics :) The maths of non-relativistic QM is trivial linear algebra, so you should just get stuck in. Since you're coming from a computer science background, I highly recommend you use Nielsen & Chuang's book on quantum computation as your reference. For relativistic stuff you also need some group theory and some geometry. – Mark Mitchison Feb 6 at 21:03
Honestly, linear algebra + complex analysis is all you need to dive right into quantum physics. Bonus points for knowing what an algebra is when you get to angular momentum operators. The difficulty in quantum stuff lies in abandoning classical intuition and in actually solving the horrendous equations, rather than in the abstractness of the math. – Chris White Feb 6 at 23:31

marked as duplicate by Chris White, Manishearth♦ Feb 7 at 13:29

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I would read Richard Feynman's lectures on the subject. Specifically the book QED. If you are striving to learn some general concepts, a knowledge of the math is not necessary but is helpful. The extremely basic Quantum Physics topics use differential equations and complex variables and equations. (The standard Schrodinger equation for instance)

Books by Stephen Hawking speak about Quantum Mechanics as well, and are great introductions to the concepts.

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