Video

New math vid when?

Why did you stop uploading lectures?

Why did you stop uploading lectures ?

I never understood why people start in the new univers they try to explain and expect those in the old univers to understand the lingo. If you start in the old univers people can develop the new univers themselves,

Best explanation I've seen

Didn't realize you were posting again somehow. I love your old mathematics videos, what have you been up to since then?

how is ur math life?

You're a seriously great lecturer!!!!!

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I'm sure you get a lot of comments about your math stuff already, but if it's not touchy or anything can I ask if theres a place where I can find the third talk in Wei Xi Fan's Galois talks? CZcams says it's unavailable... They've been really helpful for me and trying to piece together what was proven/how it was proven in the third talk doesn't work very well- Anyways, really nice video, great quality and stability!

I was following a channel on tensors, he kept going on and on, without really getting to a point ever, so i stopped it. Seems there is still a chance to understand tensors, at the moment I'm studying spinors, which are a bit less confusing. But you did clarify quite some things in this lecture already, of course i need zo watch it again. I like your passionate way of explaining, its very motivating.

i couldn't follow the audio....its like he was talking from the bottom of a barrel

I’m currently studying free structures. This video is really helpful! Thanks!

Great presentation.I'm confused. Maybe because I haven't done Abstract Algebra in a while. Please be patient. that for a bilinear map you use F(x1,x2,..,axi+xi',.,xn ), at around 18:01 . Wouldn't a bilinear map be defined on a pair of vector spaces, and thus be defined on pairs(x1,x2), rather than on n-ples (x1,x2,..,xn)? Maybe in 32:41, you can define the map on the basis elements, the pure tensors f(x)w ; f in V*, w in W that are a basis for V*(x)W and extend by linearity to V*(x)W, i.e., to the "non-pure" elements?

I need to compute a tensor product. Can I just say that given two tensors of size respectively 4x3x7x5 and 4x3x5x6 the output is a tensor of size 4x3x7x6 where we have basically 4x3 lined up products of matrices of size 7x5 and 5x6????? Is my understanding correct??

cool

Its a shame I did not see this earlier. CZcams does people dirty serving up far more sketchy descriptions of this content instead of this. This is quite clear. I like how he does not use abbreviations. Its worth it to a general audience to just write "isomorphism", imho. Great presentation, just shares knowledge, not trying to look smart. 👍

Very cool...

why did you stop posting math

Wish I'd seen this 35 years ago when the linear algebra portions of my physics degree were making my brain explode.

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Loathe based

You are very rich, rich people don't need mathematics 😂

What about mathematics?!😅

Amazing

Good presentation.

very good presentation and it is very clear. congrats

Would you ever consider re-publicing your old videos?

With a finite basis for V, then maybe V iso Hom(k, V) implies Char(k) > 0 ?

9:14 Intersecting the elliptic curve twice at P to get the tangent in a way that Q becomes P would be analogous to P + P rather than P + 0 though, right? I think the explanation makes sense if the intersection we talk about isn't the tangent but rather the reflection of P across the horizontal. As you drag the point Q to infinity, holding P fixed, the intersection approaches the reflection of P, so that when you reflect the intersection across the horizontal you get P back. Showing that P + Q, when Q is inf gives back P The fact that it bridges concepts so well while sounding so contrived makes me love it even more. What a hack 😆

Nice presentation.

that's pretty cool I guess

This is very useful! Would you care to make a written summary to be used as a reference?

That's true ₩% wow

part 3😢

why is part 3 private? Could you please make it public?

I have a question. (Here V(x)V is V tensor V, I don't know how to make the symbol) You defined tensors such that they linearize bilinear maps. So, in the case of a bilinear form B:VxV->K. we have B corresponds to a linear transform L:V(x)V->K. But after, you said B is identified with an element of V*(x)V*. Why did we do linearization in the first place if we won't be using linear transformations? And also, how does that linear transformation L corresponds to the element of V*(x)V*? Is [V(x)V]*=V*(x)V*?

This is incredible. Thank you.

Could you turn on youtube autogenerated captions for this? Even if it gets most of the math words wrong, it would help me follow the audio

7 years after his banger video on tensor product, the king uploaded once again hope you will someday make other videos on mathematics

Life of a burned-out magician.

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Hi there, where are you studying in canada? By any chance are you in UBC?

Great

wonderful!!!!

Demystified? Hmmm.

I’m a mechanical engineering undergrad that has taken intro to Lin alg and currently complex analysis. I must admit that some of these explanations are above the scope of my knowledge and bit confusing. I think it would’ve helped if I had learned Lin alg and geometric algebra in high school. I’ll definitely have to come back to this video in a while to fully understand everything. Thanks for the explanation!

thank you