- #1
Aaronvan
- 44
- 2
I'm curious as to the highest level of mathematical skill required for adequate understanding of Einstein's theories. For example, how deep into PDE's do the field equations require?
The necessary mathematical skills for understanding general and special relativity include calculus, linear algebra, and tensor calculus. These mathematical concepts are used to describe the curvature of space and time, as well as the effects of gravity on objects in the universe.
Calculus is used to describe the curvature of space and time in general relativity. It is also used to calculate the effects of gravity on objects in special relativity, such as the time dilation and length contraction of moving objects.
Linear algebra is used to represent and manipulate the mathematical objects known as tensors, which are essential in describing the curvature of space and time in general relativity. It is also used in special relativity to calculate the transformation of coordinates between different reference frames.
Tensor calculus is a branch of mathematics that deals with the manipulation of tensors. Tensors are used to describe the curvature of space and time in general relativity. They are also used in special relativity to describe the transformation of coordinates between different reference frames.
While a strong background in mathematics is necessary for a deep understanding of general and special relativity, it is possible to grasp the basic concepts and principles without a strong mathematical background. However, a basic understanding of calculus, linear algebra, and tensor calculus is still required to fully comprehend these theories.