Hi Prof. Borcherds! If you are looking for ideas for future series, I for one would love an accessible introduction to elliptical curves, particularly for cryptography and in the context of non-linear diophantine equations.
This video is great, your series in complex analysis is just the best, it’s helped me greatly to understand these basic theorems on a deeper level, thanks!
Thank you very much for making these videos public sir! Was devastated by the complex analysis course I took in my undergrad and am very interested in properly learning the subject. Will be following along this series!
19:35 I’m sure that Prof. Borcherds was joking but I’ll explain if someone wants to know. Because we choose i to be in the upper half-plane we get the complex numbers rotated 90 degrees counter-clockwise when multiplying by i. If you plot exp(ix) series you will get the counter-clockwise spiral because of this. Seems good enough reason to me
Good that REB spent some time on the differing (but equivalent) ways of defining the complex integral. In my opinion, the older writers do it best -- principally Titchmarsh in "Theory of Functions" and Copson in "Theory of Functions of a Complex Variable." Stewart and Tall also spend some effort on it, defining it in terms of the Riemann-Stieltjes integral.
I will never understand why mathematicians are so keen on saying that things are obvious. Even if one thinks that something should be obvious, it doesn't do much for a struggling student to tell them that something is obvious. In fact, I think it can be quite frustrating. I sometimes wonder if it's so that mathematicians can inflate their own ego. If not, I can't really see why
Integration is dual to differentiation. Infimum is dual to supremum. Points are dual to lines -- the principle of duality in geometry. Convergence (integration, syntropy) is dual to divergence (differentiation, entropy). Reductionism is dual to holism. Limits, boundaries, barriers = duality. "Always two there are" -- Yoda.
You're helping a lot of people with this!
Thank you so much for these lectures. They are an absolute godsend!
Hi Prof. Borcherds! If you are looking for ideas for future series, I for one would love an accessible introduction to elliptical curves, particularly for cryptography and in the context of non-linear diophantine equations.
This video is great, your series in complex analysis is just the best, it’s helped me greatly to understand these basic theorems on a deeper level, thanks!
Thank you very much for making these videos public sir! Was devastated by the complex analysis course I took in my undergrad and am very interested in properly learning the subject. Will be following along this series!
19:35 I’m sure that Prof. Borcherds was joking but I’ll explain if someone wants to know. Because we choose i to be in the upper half-plane we get the complex numbers rotated 90 degrees counter-clockwise when multiplying by i. If you plot exp(ix) series you will get the counter-clockwise spiral because of this. Seems good enough reason to me
Good that REB spent some time on the differing (but equivalent) ways of defining the complex integral. In my opinion, the older writers do it best -- principally Titchmarsh in "Theory of Functions" and Copson in "Theory of Functions of a Complex Variable." Stewart and Tall also spend some effort on it, defining it in terms of the Riemann-Stieltjes integral.
Well, explained. Thanks you so much, it helped enormously !
7:03 greatest integral sign i have ever seen.
Field medalist not giving serious consideration to signs and notations. He is more excited to teach useful stuff than signs. Thanks for pointing out.
richard stop you are spoiling us
20:20 dz=i e^{ix}dx
Is there exists any type of double integral in complex analysis? Please answer. With regards
So cool
Should I already know group theory before this course
Hello sir. Could you please help me? I wonder if you can answer me, why don't we have double integral in complex analysis. With regards.
The complex integral definition is reminiscent of the real arc length approximation by linear segments.
I can‘t even make out what is written in that yellow ink 😅
For “Complex Linear” read “h = 0.”
yee
I will never understand why mathematicians are so keen on saying that things are obvious. Even if one thinks that something should be obvious, it doesn't do much for a struggling student to tell them that something is obvious. In fact, I think it can be quite frustrating. I sometimes wonder if it's so that mathematicians can inflate their own ego. If not, I can't really see why
Integration is dual to differentiation.
Infimum is dual to supremum.
Points are dual to lines -- the principle of duality in geometry.
Convergence (integration, syntropy) is dual to divergence (differentiation, entropy).
Reductionism is dual to holism.
Limits, boundaries, barriers = duality.
"Always two there are" -- Yoda.
“I don’t want you actually to read this . . . “
i thought this was a 4chan greentext from the thumbnail
Every path leads to Rome :)
I love your lectures, but I think a microphone with less distortion might be an easy and worthwhile investment.