What would be a proper set of subjects, along with their order, for someone interested in string theory?

Question

If one wanted to study string theory, what subjects should they learn first and what order should the study them? I would imagine that there are opionions, but I suspect there is a natural order, or at least and heirarchy of subjects.

Answer 1

This is more of a comment than an answer, but I cannot leave comments, so here it is.

http://www.phys.uu.nl/~thooft/theorist.html

't Hooft's list. It is not specific for string theory but it may be useful.

Answer 2

Dear Humble, a great goal. One has to learn

1. Arithmetics (I omit reading of digits, letters, and the Greek alphabet)
2. Mechanics in terms of forces
3. Advanced and abstract mechanics, involving Lagrangians and Hamiltonians
4. Classical field theory - typically electromagnetism
5. Quantum mechanics, and its non-relativistic models
6. Special relativity and tensors (linear algebra is shared with the previous point)
7. General relativity and some cosmology
8. Basic quantum field theory (plus some basic background in experimental particle physics)
9. Some advanced quantum field theory, including renormalization, anomalies etc.
10. Some discrete group theory, but especially Lie groups, and their representations
11. Geometry and topology of manifolds, and perhaps some algebraic geometry etc.

Some of the entries may be exchanged but it would be a bit awkward to classify exactly which of the $11!$ orderings are OK and which of them are not. ;-) Most people have not been totally strict about any ordering and they could still get to the point 12 which is string theory. ;-) The subjects are not quite isolated from each other, after all, and one simply learns facts as she needs them.

I shouldn't have completely omitted thermodynamics and statistical physics, so please insert it between 5 and 6 and replace $11!$ by $12! = 479,001,600 $ in the previous paragraph. Well, because I have mentioned factorials, it may be good to say that some combinatorics is needed, too - although people usually get it in their leisure time via recreational mathematics. :-)

It is fortunately not true that one has to master all those subjects at 100%. Only a certain fraction of insights about each of them is really needed to jump on string theory. On the other hand, the fraction that is needed is not negligible and kind of covers the whole extents of those simpler subjects.

Good luck, Luboš