Could someone please give me a complete list of all the mathematics that i need to know in order to...

[seriously disabled]

Could someone please give me a complete list of all the mathematics that I need to know in order to be able to understand quantum field theory and string theor/superstring theory/M-theory.

 

 

Edited March 21, 2014 by seriously disabled

[imatfaal]

No - probably not. Here are a few approximations

 

HOW to BECOME a GOOD THEORETICAL PHYSICIST - Gerald 't Hooft

http://www.staff.science.uu.nl/~hooft101/theorist.html

 

The Theoretical Minimum - Leonard Susskind

http://scienceblogs.com/builtonfacts/2013/02/12/the-theoretical-minimum-by-susskind-hrabovsky/

There are the levctures at Stanford (google them for youtube/apple versions) and the books. This is the classical mechanics edition - qm will be out by christmas, but this one has a lot to going on with.

 

It is a terrible thing to say - but I don't think that everyone can understand, at a good mathematical level, things like string theory etc. Ed Witten got a fields medal for the maths he had to invent to push the physics along - this is not simple stuff

[ajb]

It will depend on your tastes and interests, but a non-inclusive list of more advanced mathematics you would be expected to know include (in no particular order);

• Algebra; vector spaces, rings, fields, abstract algebras, Lie algebras.
• Category theory; the language and basic notions such as functors and natural transformations.
• Differential geometry; manifolds, metrics, fibre bundles, vector bundles, tensors, differential forms, Cartan calculus, connections, symplectic and Poisson structure etc.
• Lie theory; Lie groups and Lie algebras, a little representation theory.
• Functional analysis; Hilbert spaces, Fock spaces, linear operators and some basic results from measure theory, Index theorems.
• Calculus of variations; Euler-Lagrange equation, deriving equations of motion, Hamilton's principal, the notion of an action etc.
• Algebraic topology; homotopy groups, differential complexes, various homology and cohomology groups.
• Algebraic geometry; sheaves.

From there you will develop your tastes and interests...maybe this list also reflects mine so others may well suggest other things.