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This explanation is very elegant. Thank you for making this!!

Need the Godelian approach..

<3

Thank you, very lucid and clear explanation

This is brilliant stuff❤

40:00 I'm here, listening to what you have to say

My question is that why would the area evolve along with vector field. Is the area proportional to the length of the vector field at that point. This is not very clear in the video

After having seen this absurdity, I do not conceive that this is a serious test for access to any mathematics faculty, they are biased questions, which do not evaluate the student's mathematical training, nor their overall aptitudes. A ridiculous process, not typical of a prestigious University.

what is lagrangian? is it the determinant? i know matrices, i have no problem with them

bro the vsauce thing killed me😂

Sehr gut

near 30:06, the assumption that you can replace f(z) with f(a) as you shrink the loop further and further, seems to not hold if the denominator is instead (z-a)^2, why is that? If f(z) = z, then the residue of z/(z-a)^2 at a is nonzero because there is a 1/(z-a) term, but logically, I feel like you should be able to apply the same argument, shrinking the loop further until f(z) = z is approximately f(a) = a, but this suggests the integral should be 0, but its not. Why is this?

Now do about logarithms.

Thanks, love the connection to the Polya field, work and flux, helps to understand why integration over the poles of holomorphic and meromorphic functions gives the results they do, other than just using Cauchy's theorem or the residue theorem outright every time.

0:25 The ratio of 1/0 is very well defined. However this notion that 1/0 is undefined is what leads to the insanity of the Newtonian limit and all the hand waving and subterfuge when it comes to "approach" and the epsilon-delta proof. The correct answer, 1/0=1, is a slope, which equals a derivative, which is a slope that is sine/cosine. When the cosine=0 then its conjugate, the versine, becomes 1. Thus to form the limit, the quantity x=cosine must not only approach zero it must actually obtain a value of zero whereupon it is immediately replaced with its conjugate, a versine of 1, thus yielding sine/versine=1. That is the true limit which in QEC we call the Eulerian limit. Also in QEC it can be quite easily proven that pm1=pm 0=pm i=pm\sqrt{-1}=pm 1/2=mp 2.

THANK YOU THIS WAS VERY HELPFUL FOR MY UNDERSTANDING 🔥🔥🔥

archemedes was the first western mathematician to discover calculus pretty much I mean what you are describing is the reiman integral

das crzy bro

Thanks! I was looking for an intuitive explanation on this topic. It helps a lot.

ghh

Hello. 1. Do we need to pay money to geogebra for using the geogebra generated images,etc.. in youtube videos?. 2. Do we need to pay money to latex editors for including mathematical equations in youtube videos?

Representation theory (Cartan subalgebra, Dynkin diagrams, classification of classical Lie algebras) would be a great future topic not covered in a visual, intuitive way by anyone else.

This series is simply amazing! I especially appreciate the time spent on the background and motivation of the topics, including the historical overview in the first video. Your style does a fantastic job of building a very natural framework for the subsequent ideas to 'stick to.' I am studying physics and I feel this has given me a whole new perspective on the framework of classical and quantum mechanics.

I'm not a native speaker and I wanted to thank you for your incredibly clear pronunciation. 💚👍 Fascinating topic. I'll definitely be watching more of your videos.

im so glad a hongkonger makes great math videos

Very good give information

Honestly I am alredy glad I understood the first 10 minutes. Will have to study more until one day i finnaly understand all of this.

⚠If someone is confused by the explanation (or lack thereof) at 8:00 , it is misleading, since that argument only works separately for point 1 or point 2. What actually happens is that you have not 2 but 4 points: (0,0), (1,0), (0,1), (1,1). And now you look how the parallelogram (which was initially just a square) is changing under effect of the matrix A = {{a,b},{c,d}} : A*0 is just a 0 matrix, so the first point is stationary, (1,0) -> (a,c), (0,1) -> (b,d) and (1,1) -> (a+b,c+d). So now if you add some Δc to c, then both (a,c+Δc) and (a+b,c+Δc+d) has moved up by the same amount, so the right side of the parallelogram hasn't changed in length AND is still at the same distance from it's counterpart, so the area didn't change. But if after that you do any change to the point (0,1)-Δb and/or Δd-then it would squash or stretch the parallelogram, as (0,1) -> (b+Δb,d+Δd) and (1,1) -> (a+b+Δb,c+Δc+d+Δd) while (0,0) is still in place! The correct answer looms at 9:50, but it still glossed over and has to be explained that what we got is the area 1+e*(a+d)+e^2*(a*d-b*c), now we have to subtract the starting area of 1 and divide by _e_ and the area, as we are looking for the proportion of the derivative of the area to the area itself. Thus we get a+d+e*(a*d-b*c), and since _e_ is infinitesimally small, we are left with a+d.

I wish we had these videos during our physics undergrad 4 years ago

Riemann sphere fan

That was intuitive?😂

Watched the whole thing, great explanation!

Why did we take probability = lamda/n ??

23:15 THIS. I have needed this so bad. Like... I have known for a long time what sine and cosine mean and how trig functions work, obviously I needed to for my calc classes. But they nonetheless have always felt like a bit of an... arbitrary construction? Seeing this and realizing there is really a more fundamental mathematical basis behind them is just... so so so enlightening to me. I really can't get enough of complex analysis. This is so so satisfying and you are incredible at teaching it!

19:00 when we multiply f(g(u)) with g'(u) shouldn't it represent mass instead of Density? (At the bottom) Something like this Mass : f(g(u))g'(u) Instead of Density: f(g(u))g'(u)

algebraists are the best lego solvers 😂

Worst video , so easy concept with too much complex and just anything. 😅

Really nice video. I've never seen the Inclusion-Exclusion principle being taught that way.

Thank you so much for making this series

thanks

One question: how does this relate to the observable effect of the particle having a magnetic moment (which looks like the particle is spinning)?

think the interval (1000!-999, 1000!) would work for the first part of the second question, what do you think?

I'll come back to understand this with a phd..

from Morocco thousands thanks...despite i was lost at the middle....of the video

or is it?🤣🤣