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Some algebraic geometry with the main purpose of understanding D-branes in the context of mirror symmetry is reviewed in Paul Aspinwall's 'D-branes on Calabi-Yau manifolds'.


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It is possible to test whether two mathematical formalisms are equivalent No, it is not possible. Mathematics allows you to talk about things about which you can't determine if they are equivalent. The word problem is a small example and most mathematical systems themselves suffer the same problem. So now consider the set of all possible ...


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I would recommend S.T. Yau's book on Mathematical Aspects of String Theory, following @Tomas Smith. There is also a two volume set based on lectures given at Princeton. The books can be found on Amazon at http://www.amazon.com/Quantum-Fields-Strings-Course-Mathematicians/dp/0821820125 and ...


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Some years ago, Gerard 't Hooft posted "How to Become a Good Theoretical Physicist", which is more inclusive than just string theory but which you'll probably still find a valuable list. Here's what he recommends for mathematics: "Primary Mathematics": Natural numbers: 1, 2, 3, … Integers: …, -3, -2, -1, 0, 1, 2, … Rational numbers (fractions): ...


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It really depends on what you want to research within string theory, but it's one of most mathematically intensive areas within physics. List a mathematical discipline, and chances are you can apply it within string theory. At a bare minimum, you'll need everything through quantum field theory and general relativity, which includes calculus of variations, ...


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Right now, I'm using a book entitled " An Introduction to Wavelets through Linear Algebra" by Micheal Frazier. Published in 1999, it's still a pretty good book, and contains a nifty refresher to linear algebra as well.


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You talk about being being prone to falsifiability, but science isn't prone to this being falsifiable is the point. You make predictions about situations where logically multiple things were possible. Then you ask if X can "give proofs in science" and again, it doesn't matter what X is, because we don't care about proofs in science because the point is to ...


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Pythagorean "Theorem" is in fact a theory, as was falsified in GR. General relativity did not falsify the Pythagorean theorem. The Pythagorean theorem is as true now as it was in Euclid's time. Euclid's geometry is a set of theorems that result from a set of axioms regarding the concepts of points, lines, and planes. The Pythagorean theorem follows ...


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Ultimately you will need some postulates (assumptions) about the way nature works before you can prove anything. The validity of your conclusion then rests in the validity of your assumptions. For example Einstein postulated that the speed of light is the same in all inertial reference frames when developing special relativity. An implicit assumption in ...



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