Since physics and math are closely tied, I felt this question would be appropriate for this message board. Although I have had no formal schooling in mathematics beyond basic calculus, I have a reasonable aptitude for and a profound interest in both mathematics and theoretical physics. I have recently begun studying General Relativity, and am trying to determine which areas of mathematics I will need to master in order to comprehend the technical aspects of Einstein's theory. The topics I believe to be most relevant are: single and multivariable calculus, ordinary and partial differential equations, linear algebra, vector analysis, tensor analysis, and differential geometry. If anyone out there has studied General Relativity and could let me know what topics need to be added to (or removed from) this list, any help you can provide would be greatly appreciated. Thank you.

That's a nice list you got. I would not remove anything and do not feel you have to add anything essential. But, perhaps, you can skim a popular book first and see for yourself what it takes. Perhaps you've done that already. (Just in case, there's a nicely written introduction by Einstein himself Relativity, Crown Publishers, 1961.) Tensor analysis and differential geometry rightly top your list. The rest are the rangs on the ladder that leads up there.

Thank you for the advise Alex. I read Einstein's Relativity last spring and found it most fascinating. Since the mathematics was kept to a minimum I was able to grasp the concepts fairly easily without getting hung up on the more technical aspects of the theory. More recently I found what looks to be a superb work titled Reflections of Relativity on the MathPages.com site. The mathematics therein appear to be quite involved, and no less intriguing. This is what prompted my initial question.

As a follow-up, I was wondering where the subject of topology would fit in with the topics listed above. Unless I'm mistaken, I believe differential topology and concepts relating to manifolds are also involved in General Relativity. Please let me know if this is an area you would also recommend I study. Thank you.

Dear NJZ,

truth be told, I find your intention staggering. The scope of your list is too comprehensive. Manifolds must be useful in your quest of course, but somehow I feel that by the time you up along your list, you'll be able to pass a better judgement whether or how much of the manifolds you need.

As the General Relativity was Einstein's attempt at a unified field theory, which since took up a radically different direction, your quest should eventually lead you to the string theory so that other branches of math would become relevant.

I am just incapable of seeing that far.

Thanks again Alex; I appreciate all of your helpful advice. I apologize for getting so far ahead of myself; I have to keep in mind that my interests are leading me along a mathematical marathon rather than a sprint. String Theory is another of my areas of interest, but I realize I am a long way from there at this point. If anyone else is interested, there is a great site at www.superstringtheory.com which has a lot of valuable information. In the meantime I'll look forward to more intriguing postings at CTK Exchange. Keep up the good work! :)

A related field that I think you would enjoy is quantum theory, which effectively takes Einstein's theory of relativity and crumples it up into a ball and throws it away.

email me for some good links

jman_red

I never finished the GR course (IIRC), but I found Schutz's "Geometrical Methods of Mathematical Physics" a good, clear explanation of the differential geometry required.

Andrew,

Thank you for the suggestion. From my understanding, differential geometry is a relatively advanced area of mathematics. What subjects would you suggest I study first as prerequisites to understanding Schultz' book?

NJZ