Johnson Ronald Williams Donald Williams Brian

Allen William Garcia Kevin Taylor Jeffrey

Johnson Cynthia Smith Kenneth Young Elizabeth

Johnson John Hall Jennifer Martin Joseph

Gonzalez Matthew Lopez Deborah Moore Patricia

Wilson Thomas Walker Nancy Davis Sandra

Taylor Donna Brown Jessica Brown Amy

Martinez Kenneth White Michelle Jackson George

Wilson Jessica Taylor Thomas Garcia Frank

Jones Kevin Brown Margaret Jackson Deborah

Great lecture! Everything is very well-explained. Thank you so much for teaching us such a fascinating course, Prof. Schuller!

Finally I’m back, hopefully I can finish the rest of lectures.

A beautiful moment at -31:21 where he asks "hang on, what am I trying to show" The guy's a genius!

I love the fact that you can see him actually working out the implications of what he's trying to teach while he's presenting it. Which so convincingly shows that he's thinking about the proof rather than merely reciting it!

In the first 15 minutes His definition of T1 is wrong, he should have written Q is not an element of U. But, he'll probably correct it later on in the video, because somebody will probably point it out to him.

so much chalk go off

47:00 Translations commute, why is this called a free action?

I find his side comments about "gender and diversity" troubling. In no way does this attract from his quite obvious of the subject. I simply subtract those comments and move on.

1:11:22 Why is A^b_a written as a component of the (1,1) tensor? Could we to the same by taking a (0,2) tensor that acts on a pair of vectors directly rather than including covectors in the picture?

UH representation!

Although I'm quite certain that he could do it, it would've been nice if he had defined multiplication in the integers. Because he skates right over that when defining the rationals.

It would've been nice if in the section about choosing the proper representatives and the proper maps when dealing with equivalents classes, that he had provided the counter example.

It would've been nice if in the section about choosing the proper representatives and the proper maps when dealing with equivalents classes, that he had provided the counter example.

The comment about 'gender theory in a nutshell' seems .... odd.

Is he saying 'naive'?

where can we get the problem sheet?

Can somebody point to the assignments ? Moreover can somebody suggest a book to go along with the course?

At 1:23:50, when he writes the first transformation, I believe he flipped the jacobian, since the index mu is covariant and thus the jacobian is “old over new”, ie del x/ del y. Thus the “correction” he then goes on to make is actually incorrect, in my opinion.

this is elite level teaching ...

The dim(G)=dim(V) in the definition of the soldering form should of course be dim(M)=dim(V).

Near the end when he covers deRahm cohomology he refers to the domain of the exterior derivative maps as vector spaces. But since the domain are differential forms of the previous order (that is, (r,0) tensor fields on the manifold), are these domains usually vector spaces or rather are they usually modules? In other words, do we in physics prefer for some reason to equip a generic grade of (r,0) tensors with the ring of C^infty (M) (0-form), over the field F that underlies the fiber bundle structure of TM?

Which book do you use in your lectures?

22:51 ¿🇪🇦?

Great stuff, thanks :)

I'm a bit confused. He says that phi(K) is not a topological manifold, but it's an immersion of the Klein bottle into R3, which means that phi is a smooth map, does that not require that the target space be a manifold?

Lmao did he say whore X1 whore X2? 8:25

59:10 THEY DID SURGERY ON A SPHERE

I am watching this for meditative purposes. I don’t understand a word (even if I have an engineering degree and had some courses in math and physics)…😂

This is such an incredible series

The way he writes t & f makes him always correct.

1:04:57 Why did he call {0} the empty set? Was it an error? 1:43:10 Did he mean "and all curves homotopic to it"?

I have to disagree with the esteemed professor on his remark concerning the the connection 1-form ω having sort Γ(TP) → Tₑ G =: 𝔤 at around 8:20 and before Indeed, TP ≃ VP ⊕ ᵢₙₜ HP by the connection induced from ω, and this connection is equivalently described as a fiber-wise projection operation Π : TP → VP which is technically a retract of the short exact sequence of vector bundles over P VP ↪ TP dπ:-> TB (The final map is of course the pushforward, what the professor has brrn calling π_*) Indeed, the map ι : 𝔤 ≅ VP ↪ TP that the professor discussed in the previous lecture has the property that ω ∘ ι = Id_𝔤 and that ker ω = HP Hence, any global vector field X ∈ Γ(TP) directly decomposes into ver(X) + hor(X), and we see ω(X) = ι⁻¹ ∘ Π (X) = ι⁻¹(ver(X)) ∈ Γ(VP) ≅ Γ(𝔤 × P), the final isomorphism is precomposition with ι⁻¹ (pointwise) Now certainly 𝔤 has the same dimension as G while Γ(VP) is an infinite dimensional vector space, so immediately we see there is an issue and the professor's sort cannot be correct What the professor would want to write on the left hand side is that ω restricted to the space of fundamental vector fields on P, those vector fields Xᴬ for A ∈ 𝔤 which are exactly the G-translation invariant vector fields on P, takes values in exactly 𝔤 The discrepancy is that a vector field can everywhere take values only in VP yet not bet invariant under translation by G, in just the same way that only very few vector fields on G are translation invariant under the regular left and right actions of G on itself. Indeed, *defining* the Lie algebra 𝔤 of G to be this very space of fundamental vector fields on G is a very common approach to the fundamentals of Lie theory, as this makes the adjoint actions (whence the all important Lie bracket) much more transparenrlty defined Thus, summarily, the sort of ω as considered herein is nothing more or less than Γ(TP) → Γ(𝔤 × P) ≅ Γ(VP)

47:46 Aren't there just 4 possibilities? How are i and ii not included in iii-vi?

@06:11 You can quickly see that squiggly G is an equivalence relation. Naturally, only an idiot wouldn't see that quickly! If you don't see it quickly, you can thus consider quotienting yourself out. Obviously... In other words, if you are not clear about it remember the words of Wittgenstein "What we cannot speak about we must pass over in silence." (reference in here: kzbin.info/www/bejne/jGWcmpKCgp11Zqcsi=JusKHTVPOMFEK8Pb&t=0:49).

Can you Upload more lectures ?

1:21:07 Why define consistency in terms of there existing a q which cannot be proven? Wouldn't it be simpler to define it directly in terms of there not existing any 2 axioms which are the negations of each other?

1:17:00 Can someone clarify? There's something quite fishy about the claim that, the "axiomatic system for propositional logic is the empty sequence". Although I'm no big expert on logic, this sounds almost certainly incorrect. Propositional logic has its own set of axioms, and rather, many, alternative ones-each producing the same propositional calculus. E.g. en.wikipedia.org/wiki/List_of_Hilbert_systems lists some of these axioms for propositional logic. Am I missing some nuance that differentiates what Prof. Schuller is saying, and what I'm juxtaposing it with?

yo its a bit sus to say the word n forms outloud bro

2:40 was intense man I didn't know what's gonna happen

38:20 R (in the usual topology) is not homeomorphic to Z x [0, 1). This is easy to check, as Z x [0, 1) is not connected whereas R is.