Thank you for posting such clear and thorough lectures!

such clearity=========

This guy deserved a better cameraman. He didn't aim the camera on the professor during the whole intuitive explanation of what is a bundle.

Interesting points about the sociology of large physics projects, and about the military holding up gamma ray discoveries.

It's a shame this lecture cuts off at the end.

"He just looks, and you're dead!"

Can anybody kindly tell me what literature is being followed here.......the lecture is great but It helps having a literature reference that you can look at.

I'd like to keep my nose, thanks.

I love that he had to clarify the stone has no free will, in case anyone was confused.

This man crafts his lectures from diamonds. He even has board cleaners!

"What brings you closer to God? A Hamiltonian!" :-D (@1:15:10)

This is one of the best lectures ever !

I am a hobbyist who never graduated college 40 years ago but I never lost my interest in math and physics. Yes sir, Professor Schuller. You are a very good teacher. THis is very special to us, your students. Thank you.

Terrific instructor. Thank you sir.

Thanks for going out of your way to build physical intuition in the abstract concepts. Hallmark of a great teacher!

Fantastically Well-Planned!

Thank you so so much for such wonderful lectures. Your very great clarity about our imagination and the real world and the way you explained it was hugely motivating..

he is genius

This whole lecture series is amazing

For the first example how can he define the set P as linear combinaison of whatever element whithout define an add and mult law on x^n ?

Is there somewhere that the tutorial papers can be downloaded from? I'd love to print them off and work through them.

What is the prerequisite for this course?

Did anyone attend this and still have the questions from the tutorials?

Did anyone attend this and still have the questions from the tutorials?

I agree with the commentators below. He is an incredible educator. His presentations are super crisp and efficient. Thank you for posting these! Deeply appreciated.

For the circle to polar coordinates part, correct me if I'm wrong, but I think why people got confused is because arctan is defined only on the RIGHT hemisphere of the circle, with asymptotes on the output of arctan at -pi/2 and pi/2, so y(U) would only map between -pi/2 and pi/2 (180 degrees total) instead of from 0 to 2pi (360 degrees total). The line he removed in the domain should have been the VERTICAL axis (m=0), not the horizontal axis (n=0), to avoid dividing by zero in the ratio m/n. The other big problem with arctan is that it takes a single number, which is usually our ratio n/m. But if both n/m are negative, your result is positive. If either one of them is negative, than the result is negative. So there is information loss. Quadrant I and III look the same to arctan, as does II and IV. To go beyond this to map the entire circle to polar coordinates and use all of 0 to 2pi, you need more than just arctan... you need a sort of "enlightened" arctan that takes TWO parameters (so that the ratio m/n doesn't hide which of m or n is negative), or you need to do it piecewise with conditions that separate the four quadrants so you can treat quadrant I and quadrant III (both of which give m/n positive), and quadrant II and quadrant IV (both of which give m/n negative) distinctly. The two parameter version of arctan is better though as it also avoids the divide by zero issue (you pass in m and n separately, so no need to worry about n/m with m=0), which then allows you to avoid removing the m=0 line in the domain. In standard programming languages, this is called atan2(m, n). He should have used this instead of arctan to avoid all these issues. Or am I missing something?

The expression for 3-velocity written down at 1:24:56 is not the correct form. The right hand side should be divided by the gamma factor.

Very interesting and inspiring lecture.

I like how they made an effort in showing the students' questions in text. Very sweet.

Superb lecture

Muy fácil.

Thanks for uploading those lectures.

Very nice lectures

I'm definitely a huge fan of these lectures and the amazing strength of intuition utilized. My hunger to learn is awakened by these lectures. I have to say though, I'm not a huge fan of the "noses" analogy. I think it hinders the talk of dimensionality especially around 29:00 .

Can someone explain how he obtained the second derivative at 35:00?

Great dedicated professor.Very comprehensive lecture .Lucky me.

Fantastic lectures! This is the way it should be done . So clear, concise and even entertaining at time. German efficiency and thoroughness shows through. Thanks so much to the folks that posted it

This is a really beautiful and insightful interpretation of Newton's laws. Thank you so much Prof. Schuller!

Wow. This lecture blew my mind. Awesome, I gotta check out this line of research!

This professor is EASILY one of the best I've ever seen - every student should be so lucky to study from such an articulate, patient, and clear instructor at some point in their academic career!

I thought that the tangent spaces TpM for all point p in a manifold M were automatically disjoint, ie they dont share any elements.

A crystal clear series of lectures, thank you!

I'm loving these lectures. They are rigorous, well organized and entertainingly presented. Where else can I find a reverence to Machiavelli in advanced mathematics.

Does anybody have the exercise sheets?

Hi, I am struggling to prove that the map G is multilinear. Where does v,w and x fit into the vector space, are they each vectors or components? The map is defined using a1, b1,..., c2. What are these entries is terms of v, w, x? I understand what is to be proved I am just struggling to go through the necessary steps.

Thank you sir...your lectures were extraordinary

what did he do at 17:25? what's g(delta_x, gamma_dot)?

I love it when you give the axioms first before you start calculating shit, that removes ambiguity and confusion. thx m8.

dx2/dy1 has me a bit confused on problem 3. Should it be -3a^2? The way I'm interpreting the symbol is that the second component of x o y^-1 should be derived with respect to u. Is this not correct?

For anyone interested in the problem sheets: gravity-and-light.herokuapp.com/tutorials