The math behind a couple of theories

[hover]

I was just wondering, what math is needed to fully understand the mathematics of general relativity, quantum mechanics, and string theory? Can you be specific in naming them? For example

General Relativity
Algebra
Calculus


I know there has to be more than that but that was an example. I am curious because I want to eventually learn the math behind these theories.

Thanks!

 

[Jame]

http://en.wikipedia.org/wiki/Mathematics_of_general_relativity

I'm not sure what you include in "Calculus", but the basic stuff doesn't really suffice since you need tensors and the more sophisticated differential geometry.

 

[sir-pinski]

Hi there! That's a great question. The math behind general relativity, quantum mechanics, and string theory is quite complex and requires a strong foundation in mathematics. Here are some specific areas of math that are used in each of these theories:

1. General Relativity: As you mentioned, algebra and calculus are important for understanding general relativity. In addition, differential geometry plays a crucial role in this theory. This branch of mathematics deals with the geometry of curved surfaces and is necessary for understanding the curvature of spacetime in general relativity.

2. Quantum Mechanics: Algebra, calculus, and differential equations are all important for understanding quantum mechanics. Linear algebra is also used extensively in this theory, as it deals with the behavior of vectors and matrices. Complex analysis, which deals with functions of complex numbers, is also used in quantum mechanics.

3. String Theory: Algebra, calculus, differential geometry, and complex analysis are all used in string theory. In addition, group theory, which deals with the properties of symmetry, is also important for understanding the symmetries of string theory.

Overall, a strong foundation in mathematics, particularly in algebra, calculus, and differential equations, is necessary for understanding these theories. It's also important to have a good understanding of linear algebra and differential geometry for a deeper understanding of general relativity and quantum mechanics, and knowledge of group theory for string theory. I hope this helps and good luck on your journey to learning the math behind these fascinating theories!