Mathematics of General Relativity: A Complete Course
There is no doubt general relativity is a difficult topic - at least, that's what most people seem to view it as.
I'm here to tell you that it doesn't have to be. All you need is a resource that teaches you the required math in a practical and beginner-friendly way, from the ground up.
Finally Understand The Math Behind General Relativity
General relativity is based on the mathematics of tensor calculus and differential geometry. Learning these is therefore absolutely crucial if you truly want to understand it.
The problem I often see, though, is that most books and courses do not teach these topics with the purpose of actually being able to apply them to general relativity.
Instead, what you find are resources filled with unnecessary abstraction, math jargon, incomprehensible notation and an infinite list of prerequisites.
While I would like to say understanding general relativity is a walk in the park, it's not.
But, I am here to tell you that most of the difficulties can be avoided if you build the necessary mathematical foundation first - and specifically with the intention of being able to directly apply it to general relativity.
That's what this course aims to give you - all the math you need for a deep and practical understanding of general relativity.
You'll learn everything you need to know - and a lot more - beginning from the ground up.
What You'll Learn
- Build the necessary mathematical foundation for general relativity as well as understand why we use tensors and differential geometry to describe it.
- Learn the math behind concepts like tensors, Christoffel symbols, covariant derivatives and curvature from the very ground up.
- Learn tools to efficiently manipulate and work with tensor equations and indices, as well as understand how they are used in general relativity through step-by-step examples.
- Understand how to connect all the math you learn directly to general relativity - something that's often missing in many other resources.
Here's What You Get:
Along with the main lesson content (see below), you also get practice problem sets and solution manuals with step-by-step solutions to all problems.
The course is structured into three high-level parts, each one consisting of a dozen lessons:
- Part I: Introductory Concepts - this part introduces you to the very basics of tensor index notation physics, a tool that is used everywhere in tensor calculus and general relativity. We also dive deep into co- and contravariant coordinate transformations, vectors and covectors (one-forms).
- Part II: Tensor Calculus - this part will build on top of the concepts you learned in Part I, first covering the metric tensor in-depth. After this, you'll learn about tensors more generally, all about working with them as well as many other tools like Christoffel symbols and covariant derivatives.
- Part III: Differential Geometry (Coming Soon) - here, we apply everything learned so far to differential geometry, the key area of math behind general relativity. You'll learn about curved space(time)s, the Riemann and Ricci tensors, geodesics and many other advanced concepts.
The key themes throughout this course are practicality - actually giving you tools you'll be able to apply anywhere - and applications to general relativity.
That's why each lesson includes tons of step-by-step, direct examples from general relativity and other areas of math and physics.
Who Is This For?
- Anyone wanting to develop the necessary mathematical foundation for general relativity starting from the very bottom.
- Anyone wanting a more intuitive and practical understanding of tensor calculus and differential geometry.
- College or university students interested in a deeper mathematical understanding, for example, alongside a general relativity course at school.
The sooner you get started, the faster you'll reach your physics goals - and this course will take you there.
In case you have any questions about the course, feel free to contact me at ville@profoundphysics.com.
Note that this is an early access version of the course available for a lower price, currently containing the first four lessons. More content will be coming in the near-future, which you'll get instant access to!