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Comment: Answer from a Grad Student (Score 5, Informative) 358

by zornslemma (#37236488) Attached to: Ask Slashdot: Math Curriculum To Understand General Relativity?
I work in cosmology and use general relativity extensively in my day to day work. I have also fielded similar questions from friends and undergraduates, so I can provide you with advice based on my experience.

What approach you use depends on how well you want to understand. I am going to assume that you want to understand the equations and how to manipulate them --- that when asked about the anomalous procession of Mars, you could sit down with a pencil and graphing calculator for an hour and tell them that GR accounts for ~40 arcseconds/century. To get there, you will need to cover a series of courses: Classical Mechanics, Linear Algebra, Special Relativity, Multivariable Calculus, and then General Relativity. If you also study Electromagnetism and Differential Equations, you will get a bit more out of it, but those subjects are not necessary.

Classical Mechanics (prereqs: none): You don't need anything beyond an AP physics level understanding of mechanics, but you do need that. MIT has all of the 8.01 (classical mechanics) lectures online.

Linear Algebra (prereqs: none): You need to understand what a vector is, what a matrix is, what a linear transformation is, and what traces and determinants are. You probably have this knowledge from stats. If not, trys Jacob or any similar text.

Multivariable Calculus (prereqs: Linear Algebra): A standard undergrad book is fine. You need to know how to transform variables and use multivariable differential operators. A standard course is online.

Special Relativity (prereqs: Classical Mechanics, Linear Algebra): Special Relativity is essential for understanding General Relativity. Of particular importance is the 4-vector notation and the Lorentz transformation. A. P. French is one of the classic textbooks.

General Relativity (prereqs: Special Relativity, Multivariable Calculus): The nice thing about introductory Physics texts is that they teach you all the differential geometry you need to understand. The unfortunate thing is they tend to be aimed at Physics graduate students. There are a few undergrad textbooks, but they are not as rigorous and not as worthwhile to read. The classic General Relativity textbook is Misner, Wheeler, Thorne, but MWT is better as a reference text than as a first course. Better textbooks would be Wald, General Relativity, and Carroll, Spacetime and Geometry . Of the two, I would recommend the latter.

You should keep in mind that the texts will be hard and the learning curve will be steep. The best way to understand the material is to do most of the problems in the undergraduate books or all the problems in the graduate texts, and ideally, have someone read over your problem sets. It will, however, be rewarding.

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