Lately I have been teaching myself higher level physics and mathematics – reading books and watching Youtube videos on the subject. Here I am going to post some links to the resources I have been using for anyone else who may be interested. These resources are obviously not exhaustive of all the resources out there, but they’re the ones I’ve found to be very helpful. As I continue learning about these subjects, I will periodically update this post.
Youtube
Khan Academy: as if it needs any introduction. Khan Academy is likely the most popular source for free educational content on the internet. You can learn math between the most basic arithmetic all the way up to linear algebra and differential equations. Covers topics in science including physics, chemistry & organic chemistry, and biology. Also covers many other topics, like economics, finance, history, and computer science.
PBS Spacetime: a great resource for physics that stands between pop science and more rigorous (i.e. mathematical) treatments of the subject. They cover pop science subjects (black holes, quantum mechanics, cosmology, string theory, etc.) but go deeper into the concepts, often even brushing up against the complicated mathematics. They use a lot of great animations to help explain the subjects.
DrPhysicsA: a British guy who never shows his face (and hasn’t added a new video in several years) but goes through the mathematics of a wide range of physics at a level that’s easy to understand. A great place for the person who graduates from the PBS Spacetime level and wants to actually get a basic grasp of the mathematics involved. DrPhysicsA does a great job of meticulously going through every mathematical detail, not leaving anything for the viewer to get confused about between steps.
3blue1brown: a great resource for getting an intuitive understanding of math. He does a lot of videos on sort of “pop math” type stuff, but he also has playlists on the “essence of calculus” and the “essence of linear algebra” which are extremely helpful to people who want a visual and intuitive understanding of these topics. His “pop math” videos are great, too, and very well put together.
Andrew Dotson: a physics graduate student who makes videos about physics and math. He does a lot of vlogs, skits, meme reviews etc., but he also does videos about physics itself – especially check out his “derivation” playlist and his “new to tensors?” playlist.
TMP Chem: these videos are more chemistry related, but he touches on a lot of physics topics as well – things like statistical mechanics, physical chemistry, and so on. Most videos are fairly short (under 10 minutes) and he does a good job of explaining things.
XylyXylyX: a great resource for very high level math and physics (particularly his 70+ video playlist explaining general relativity). He does a great job of being extremely thorough, repeating important points often to ensure you know what to remember, and starting everything from very basic principles. He has playlists on topics that are difficult to find good resources for, including topology, Lie groups, tensors, and the aforementioned behemoth of a playlist on general relativity.
eigenchris: another fantastic resource for your tensor and general relativity needs. Does a great job of explaining the math in a step-by-step manner that doesn’t leave out steps and also giving excellent intuition behind what the math means. His playlist on general relativity is very easy to follow even for someone not as familiar with the material. His newest project (still in progress as of writing this) is about spinors, which are vital to understanding quantum field theory.
The Cynical Philosopher: of course I cannot go without mentioning my own Youtube channel. I have a playlist I am making about Quantum Mechanics and I have a playlist on the special functions encountered in differential equations (Hermite polynomials, Bessel functions, Legendre and associated Legendre polynomials, etc.). I also have playlists on group theory, advanced inorganic chemistry, the biochemistry of nutrition, and tensors (using general relativity as a pedagogical approach).
Books
Theoretical Minimum series by Leonard Susskind and Art Friedman.
What You Need to Know to Start Doing Physics
Quantum Mechanics
Special Relativity and Classical Field Theory
The following books by Jakob Schwichtenberg:
Physics from Finance
Physics from Symmetry
No-Nonsense Classical Mechanics
No-Nonsense Quantum Mechanics
No-Nonsense Electrodynamics
No-Nonsense Quantum Field Theory
The following books by Arieh Ben-Naim:
Information Theory – Part I: An Introduction To The Fundamental Concepts
Entropy Demystified
The Four Laws that Do Not Drive the Universe
The following books by Daniel A. Fleisch:
A Student’s Guide to Waves
A Student’s Guide to Maxwell’s Equations
A Student’s Guide to the Schrödinger Equation
A Student’s Guide to Vectors and Tensors
The following books by David J. Griffiths:
Introduction to Electrodynamics
Introduction to Quantum Mechanics
Introduction to Elementary Particles
Differential Equations with Applications and Historical Notes by George F. Simmons