eCosmology

What mathematics should I know to study cosmology?

I listened to a CalTech presentation by Kip Thorne, and he referred to a ton of strange math such as tensor calculus. I want to know what kind of math is necessary to understand technical papers about relativity, galaxy formation, and the birth and death of the universe. Thanks! When I try to read academic paper regarding cosmology, I barely get past the abstract before being overwhelmed by strange greek symbols with no accompanying explanation. What kind of math is this? What branches of mathematics are necessary to understand these papers?

Public Comments

1. Get a very thorough grounding in Ordinary and Partial Differential Equations with some Linear Algebra. Then get a good book on Tensor Analysis or Differential Geometry. What you are seeing is probably tensor notation which is very difficult to figure out . . . it tends to have symbols with several superscripts and subscripts to denote contravariant and covariant character. But it is *essential* . . . you will find it in differential geometry books mostly these days . . . Schaum's and Dover have some really good books on it. I would recommend getting started with "Tensor Calculus" by Akivis and Goldberg and then getting the Schaum's Outline. Good luck.
2. A lot of the symbols and variables simply represent physical quantities that the writer of the paper assumes you already know about (why else would you be reading a technical cosmology paper ;) because you've read some introductory text on the subject. The best text on relativity and cosmology is Misner, Thorne, and Wheeler. It has a "mathematical track" for the technically minded, and a "nonmathematical track" for those who are merely proficient at nonhomogeneous nth order partial differential equations. Best textbook ever written on any subject, actually.
3. I personally am not going into this field (more of an observationalist...) but I do have friends who are. The big subjects I've heard are Diff. Eq. (ordinary and partial), Tensor calc (for which you need Calc 1, 2, and 3), Linear Algebra, and Statistics. Stats might be a good idea in any physical science, though.
4. You were probably inundated by the Christoffel symbols. They can look pretty intimidating the first time you encounter them. To start you'll need a strong foundation in calculus, differential equations and linear algebra. Normally those are the basics taught the first two years in any undergraduate science or engineering curriculum. Then, as has already been pointed out, you'll need a great deal of differential geometry (as usually taught in advanced calculus courses) plus lots of vector and tensor calculus. A solid grounding in mechanics (e.g. Goldstein's 'Classical Mechanics') and electrodynamics (e.g. Jackson's 'Classical Electrodynamics') is not only essential to understanding Special and General relativity but will also give you much needed practice applying Hamilton's principle, partial differential equations, differential geometry, integral theorems and vector identities. I would recommend taking graduate level classes in these two topics. By this point you would be ready to start learning tensors. My favorite source is Robert C. Wrede's 'Introduction to Vector and Tensor Analysis' published by Dover Publications. The last chapter gives a good introduction to General Relativity, too, but to follow it you will need to supplement Wrede's text with additional reading on that topic. Though most books on Relativity might do I'd recommend going directly to Einstein's original papers and books for that. However even Einstein made some mistakes now and then so you should supplement his writings with some more modern treatments on the topic. Wheeler's big, thick heavy text 'Gravitation' is one of the best sources. That should get you started. Good luck.
5. Caclulus, trig, geometry, algebra All are used.