Your research would be interesting if you could investigate the geometric interpretation of superposition hypothesis proposed but Anthropic, how features form geometrically during training, this would be break through to explain the rest of the “dark matter” features in AI models. What are your take on this, i am curious?

e^-π+1=e^π+1🤔

I am a almost 17 at year10 now,but I already knows that I would be a mathematician,but my other subject is sucks,what advice would you give,bc I cant get into other sub,and I want to get in a good university

Great video, great explanation and great advice! Only problem is that the music is too loud.

Frankly, this was horrible.

zero=(0,0,0) which one is equal elure number

wowwwww

No... effing.... way!! Wedge products make things so easy I'm so pissed that it's not taught earlier. I'm done with my master's and I can't believe how much of physics could be simplified by geometric algebra. It's a war crime that it's not used!

FYI, i asked ChatGPT to suggest a youtube video for learning this Geometry of Linear Systems.. it gave me this link...!

good material, great use of Manim, worse than useless audio. so thumbs down and not subscribing

👍 I have not had the opportunity to teach mathematics as much lately, given the amount of focus I have given to my research. I enjoy the process of teaching and interacting with students and so have decided to return to some online tutoring. If you're interested in personal help, I've posted my tutoring services on Fiverr: www.fiverr.com/s/dDYkBlz

👍 I have not had the opportunity to teach mathematics as much lately, given the amount of focus I have given to my research. I enjoy the process of teaching and interacting with students and so have decided to return to some online tutoring. If you're interested in personal help, I've posted my tutoring services on Fiverr: www.fiverr.com/s/dDYkBlz

👍 I have not had the opportunity to teach mathematics as much lately, given the amount of focus I have given to my research. I enjoy the process of teaching and interacting with students and so have decided to return to some online tutoring. If you're interested in personal help, I've posted my tutoring services on Fiverr: www.fiverr.com/s/dDYkBlz

Thank you so much for this video it was super helpful!

goosebumps from the beauty of how well this proof is explained

How to get to shade up or down the boundary line

did not get this. needed a definition as i never saw this notation Looked up in wiki Glossary of mathematical symbols: ∂ 1. Boundary of a topological subspace: If S is a subspace of a topological space, then its boundary, denoted ∂ S {\displaystyle \partial S}, is the set difference between the closure and the interior of S. so, [a,b] - (a,b) if those are intervals.

Thank you very much for sharing your insights. This video has been a great help, bringing me closer to understanding Green's theorem, particularly the concept of the wedge product.

I came away from this video feeling like I learned nothing

This was ace! I've struggled with this concept for years and never seen it like this and related to area before! 😮 When the formula for the determinant just falls out like that... glorious.

This proof assumed that e^z was defined, other wise how do you make sense of e^{ix}...

Handsome . 😊 💜

VERY VERY NICE VIDEO I LIKE THIS THANKYOU SO MUCH SIR

Not sure about the notation f(z/R1) -- shouldn't it be f(R1*z)?

wait, "Kindergarten"? seriously?

Hi Kyle thank you for the video, it was really helpful... Please assist, where can I find the memo for the practice problems?

3:40 Integral of dfdx doesnt make any sense. Its just integral of df, or df/dx * dx

I can't believe I'm currently taking Differential Equations yet I'm here having an epistemic crisis because I've realized that most things I've learned in math I've taken for granted instead of establishing them to be true. Nonetheless thank you for the simple proof.

Bro really awesome

This video is GREAT!!! Perfectly explained. The proof for i^j=-j^i was GENIUS

😊 thanks I understand wedge of vectors is so similar to cross vector..

shouldn't there be an x in the solutions at the 3rd example? e^[(3+2i)x] and e^[(3-2i)x] respectively?

Why did we learn the wedge product in linear algebra 2 and analysis 3 without any geometric intuition? I finally understand the point of this, thank you!

0:21

Your explanation was simply bad.

Yep, still don't get it at all

Why does this seem so much easier than vector calculus if it's more powerful too lol

Are you familiar with Bressoud, David M. Second Year Calculus: From Celestial Mechanics to Special Relativity. Springer-Verlag, 1991. Thank you for posting these. I just realized that I need to up my LaTex game with Hodge star and the musical isomorphisms.

Why is the area given by i^j and not j^i? Or would that depend on the sign of the product, and we would just switch order to get the possitive product?

I don;t think the title is any good.

3:03 but if wouldnt we call f'(x) d(f(x))/dx rather than d(f(x))? This would make the integral Integral of df(x)) from a to b Integrating would give us f(b)-f(a)

Research in any subject of science doesn't mean that we are creating i believe its all about contributing specifically mathematics.

Thanka for your work

Also, by proving that |g(z)| <= 1, it shows that |f'(0)| <= 1. More over, if equality holds on any of these |f'(0)| = 1 or |f(z)| = |z|, then we can show there is a constant c with |c| = 1 such that f(z) = cz, that is, f is a rotation in the complex plane. Here's why: Equality holds precisely when |g(z)| = 1, but since g is a holomorphic function defined from the unit disk (minus the origin) onto the unit disk, it means it achieves a maximum value at some point, so by the Maximum Principle, g(z) = c, and that |c| = 1. Now g(z) = f(z)/z, from which it follows f(z) = cz. (As it is done on Conway's Functions of One Complex Variable I).

Ngl. Even as an undergrad, this is nostalgic and relaxing to an odd degree (pun intended).

Love for India best explanation ever 😭👍🏻

Provide lectures on sieve theory

There's a typo in the initial statement of the product rule, just if anyone's confused. It's not u'v+vu' but u'v + uv'

I might argue that integration and derivatives are indeed opposites functionally, but that their is a geometric perspectives of being opposites that is simultaneous/equivalent to their relation, and that has to do with the relationship between a volume and it's boundary, as expressed by density function (and understanding that density function is a dual game between the Radon-Nikodyn derivative vs Reisz Representation). Moreover, I might argue that their is even a 3rd different perspective on what is "opposite to what" in this deep theorem, and that touches on homology vs cohomology.

amazing little video. what a treasure/pleasure