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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.

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What is your background? – Raskolnikov Jan 18 '11 at 10:12
@Raskolnikov: if there is a natural order of requirements (and I am pretty sure there is) how does that depend on ones background? – Marek Jan 18 '11 at 10:36
Well, first you have to learn arithmetic, then you have to learn Euclidean geometry, then algebra and trigonometry, then calculus, then... see what I mean? – Raskolnikov Jan 18 '11 at 10:40
@Raskolnikov: yes, I see what you mean and I say that you are being absurd :) – Marek Jan 18 '11 at 11:34
up vote 3 down vote accepted

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

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

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I forgot about t'hoofts list, granted, not specific to string theory, but it includes it in the hierarchy. – Humble Jan 18 '11 at 23:16

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

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Arithmetics? :-) – Sklivvz Jan 18 '11 at 17:36
I have a pet peeve, and thats when people don't learn at least a little semiclassical gravity before jumping into string theory. Also, conformal field theory is very necessary. Of course in practise a graduate student simply does not have enough time to learn all this material before having to delve into the subject. – Columbia Jan 18 '11 at 17:50
don't forget: flipping burgers and making fries! – Jeremy Jan 18 '11 at 20:24
@Lumo: I think your answer is great and is original and is clearly superior in its inclusion of factorials. I hope it doesn't offend that I spread some points to other users. I did give you a vote for compensation though! – Humble Jan 18 '11 at 23:26
@Jeremy: I saw a Sid Harris cartoon once that depicted a dishevel looking individual sitting by the side of the road with a cardboard sign reading "Will calculate Feynmann diagrams for food". – dmckee Feb 5 '11 at 1:07

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