Tensors are usually taught as part of differential geometry. As prerquisite you need calculus and vector analysis. Before that you need a thorough high school math education.darkSun said:I'm just wondering, what mathematics would be required to learn GR? If I'm not mistaken, SR only requires algebra, but GR looks much more complicated! (and interesting)
I know it needs differential equations, and tensor theory, but what mathematics would you need to learn tensors?
The purpose of learning mathematics for general relativity is to develop a deep understanding of the mathematical concepts and techniques necessary to fully comprehend and apply the theory of general relativity. It allows scientists to make accurate calculations and predictions about the behavior of objects in the presence of large masses and high velocities, which is crucial in fields such as astrophysics and cosmology.
Some key mathematical concepts needed for general relativity include differential geometry, tensor calculus, and the mathematics of curved spacetime. Differential geometry is used to describe the curvature of space and time, while tensor calculus is used to describe the relationships between different quantities in curved spacetime. The mathematics of curved spacetime is essential for understanding the fundamental principles of general relativity.
Mathematics helps us understand the concept of spacetime curvature in general relativity by providing a precise and rigorous way to describe and calculate the effects of massive objects on the fabric of spacetime. This is done through the use of mathematical equations, such as Einstein's field equations, which relate the curvature of spacetime to the distribution of matter and energy within it.
While a strong background in mathematics is not absolutely necessary to understand general relativity, it is highly recommended. General relativity is a highly mathematical theory, and a solid understanding of mathematical concepts and techniques is crucial for fully comprehending and applying the theory. Without a strong mathematical foundation, it can be challenging to fully grasp the intricacies and complexities of general relativity.
Yes, there are many online resources available for learning the required mathematics for general relativity. These include online courses, textbooks, lecture notes, and tutorials. Some reputable sources include MIT OpenCourseWare, Khan Academy, and Coursera. It is also recommended to consult with a mathematics professor or tutor for personalized guidance and support.