Quantcast XP Math - Forums - View Single Post - What mathematics should I know to study cosmology?
View Single Post
Old 07-28-2007   #4
Posts: n/a

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 ****ysis' 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.