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.