I love your channel I would considered it to be one of the best math channels on youtube, like you have so many awesome videos like real analysis series, functional analysis, and now complex analysis. Will you do a series on operator theory and harmonic analysis?
Integration is dual to differentiation. Convergence is dual to divergence. Decreasing the number of dimensions or states is a syntropic process -- homology. Increasing the number of dimensions or states is an entropic process -- co-homology. Homology (convergence, syntropy) is dual to co-homology (divergence, entropy). Syntropy is dual to increasing entropy -- the 4th law of thermodynamics! Imaginary numbers are dual to real numbers -- complex numbers are dual. "Perpendicularity in hyperbolic geometry is measured in terms of duality" -- universal hyperbolic geometry. Ellipsoids are dual to hyperboloids -- linear algebra, matrices. Duality creates reality! From a converging, convex or syntropic perspective everything looks divergent, concave or entropic -- the 2nd law of thermodynamics. All observers have a syntropic perspective according to the 2nd law of thermodynamics! "Always two there are" -- Yoda.
I can't believe I just found this channel a day ago. I plan to binge all your playlists, def need a refresher on Real Analysis. But love the videos and the explanations, thank you so much for this excellent resource!!!
Thanks for presenting these topics in such a clear way. Very helpful. This is the point of the explanation of Complex Analysis I usually try to compare differentiability in C1 vs in R2. C1 is more restrict and there many ways to show that. Perhaps you could come with a nice way to show that, as your approach is to present C as a metric space from the beginning with a proper distance measure function d = sqrt( aa* )
Hi, thank you very much for your videos they are amazing! I want to ask you, what kind of software you use in order to write all of this things? seems very helpfull in order for me to explain math and physics to my students
@@brightsideofmaths Hi do you realize that you are using duality! Integration is dual to differentiation. Convergence is dual to divergence. Decreasing the number of dimensions or states is a syntropic process -- homology. Increasing the number of dimensions or states is an entropic process -- co-homology. Homology (convergence, syntropy) is dual to co-homology (divergence, entropy). Syntropy is dual to increasing entropy -- the 4th law of thermodynamics! Imaginary numbers are dual to real numbers -- complex numbers are dual. "Perpendicularity in hyperbolic geometry is measured in terms of duality" -- universal hyperbolic geometry. Ellipsoids are dual to hyperboloids -- linear algebra, matrices. Duality creates reality! From a converging, convex or syntropic perspective everything looks divergent, concave or entropic -- the 2nd law of thermodynamics. All observers have a syntropic perspective according to the 2nd law of thermodynamics! "Always two there are" -- Yoda. The 4th law of thermodynamics is hardwired into mathematics. Energy is duality, duality is energy and everything in physics & mathematics is made from energy.
Integration is dual to differentiation. Convergence is dual to divergence. Decreasing the number of dimensions or states is a syntropic process -- homology. Increasing the number of dimensions or states is an entropic process -- co-homology. Homology (convergence, syntropy) is dual to co-homology (divergence, entropy). Syntropy is dual to increasing entropy -- the 4th law of thermodynamics! Imaginary numbers are dual to real numbers -- complex numbers are dual. "Perpendicularity in hyperbolic geometry is measured in terms of duality" -- universal hyperbolic geometry. Ellipsoids are dual to hyperboloids -- linear algebra, matrices. Duality creates reality! From a converging, convex or syntropic perspective everything looks divergent, concave or entropic -- the 2nd law of thermodynamics. All observers have a syntropic perspective according to the 2nd law of thermodynamics! "Always two there are" -- Yoda.
Hi, for a set to be considered open, all members of the set must satisfy epsilon ball in which only consists z of the same set, but what about the members z that are at the edge of the set ? The epsilon ball would include z that are outside of the set, am i right ?
Hi this is a really good video. I have a few questions. Do we consider a singleton set to be closed or open? And does the set U in the definition have to also be connected?
@@brightsideofmaths Thank you for the answer. I feel so stupid about the singleton question like you literally just gave the definition of an open set in the video and it clearly does not meet the condition for it to be open. But I really appreciate the respond. Thank you.
@@SaranaeJang There are no stupid questions. You are very welcome! My answer shouldn't sound harsh or impolite. I just quickly type answers for a lot of questions the whole day and try to keep it short and clear :)
these notations or math lingo are incomprehensible, dont you wanna tell people with high school math operators, while removing much subtleties which just hinder the main points for beginners.
i also meant advanced math as well but with high school kind of operators, i keep forgetting flipped E or upside down A, one notation after another, they are like reading braille deciphering for which i need matching tables, so to speak.
Kind Regards, as desperately as I may sound, I am a desperate aspirant who was accepted to study Medicine in russia 🇷🇺, but requires financial assistance, Any help of any sort will be highly appreciated
![Complex Analysis 18 | Complex Contour Integral [dark version]](http://i.ytimg.com/vi/pA_jfc2RCUM/mqdefault.jpg)
![Complex Analysis 3 | Complex Derivative and Examples [dark version]](/img/n.gif)
Please do the quiz to check if you have understood the topic in this video: tbsom.de/s/ca
I love you!!!
You are teaching me sacred maths, the sacred part of it - and the crazy thing is that I understand almost every single bit of it!!!
You are so welcome
I love your channel I would considered it to be one of the best math channels on youtube, like you have so many awesome videos like real analysis series, functional analysis, and now complex analysis. Will you do a series on operator theory and harmonic analysis?
Complex differentiability? More like "Complete amazing videography!" Thanks again so much for making and sharing all of these videos.
You makes this complex subject simple!
I was losing hope in this course but I'm glad I found you
Glad I could help! :)
Looking forward to seeing more of this series. It’s very well organized and logically ordered.
Integration is dual to differentiation.
Convergence is dual to divergence.
Decreasing the number of dimensions or states is a syntropic process -- homology.
Increasing the number of dimensions or states is an entropic process -- co-homology.
Homology (convergence, syntropy) is dual to co-homology (divergence, entropy).
Syntropy is dual to increasing entropy -- the 4th law of thermodynamics!
Imaginary numbers are dual to real numbers -- complex numbers are dual.
"Perpendicularity in hyperbolic geometry is measured in terms of duality" -- universal hyperbolic geometry.
Ellipsoids are dual to hyperboloids -- linear algebra, matrices.
Duality creates reality!
From a converging, convex or syntropic perspective everything looks divergent, concave or entropic -- the 2nd law of thermodynamics.
All observers have a syntropic perspective according to the 2nd law of thermodynamics!
"Always two there are" -- Yoda.
I can't believe what kind of coincidence this is , my exam is the day after tomorrow, and your video is fresh
Now you're lecture videos are more sharp, clean and crisp as you progress....thank you Sir.
So nice of you :)
I can't believe I just found this channel a day ago. I plan to binge all your playlists, def need a refresher on Real Analysis. But love the videos and the explanations, thank you so much for this excellent resource!!!
Can't wait to see the next videos.
I'm intrigued :)
Thanks for presenting these topics in such a clear way. Very helpful. This is the point of the explanation of Complex Analysis I usually try to compare differentiability in C1 vs in R2. C1 is more restrict and there many ways to show that. Perhaps you could come with a nice way to show that, as your approach is to present C as a metric space from the beginning with a proper distance measure function d = sqrt( aa* )
Just being curious here, why do you want to compare C1 and R2? That they share a cartesian image on paper is just a coincidence.
Such a precise and clear explanation. I wish I would have learned analysis from you!
Thank you :)
thankyou this is so good for revising
Merci ! Vivement la suite. 👍😎
Go mate go!
Good job 👍
Hi, thank you very much for your videos they are amazing! I want to ask you, what kind of software you use in order to write all of this things? seems very helpfull in order for me to explain math and physics to my students
Thanks! I use Xournal :)
@@brightsideofmaths Hi do you realize that you are using duality!
Integration is dual to differentiation.
Convergence is dual to divergence.
Decreasing the number of dimensions or states is a syntropic process -- homology.
Increasing the number of dimensions or states is an entropic process -- co-homology.
Homology (convergence, syntropy) is dual to co-homology (divergence, entropy).
Syntropy is dual to increasing entropy -- the 4th law of thermodynamics!
Imaginary numbers are dual to real numbers -- complex numbers are dual.
"Perpendicularity in hyperbolic geometry is measured in terms of duality" -- universal hyperbolic geometry.
Ellipsoids are dual to hyperboloids -- linear algebra, matrices.
Duality creates reality!
From a converging, convex or syntropic perspective everything looks divergent, concave or entropic -- the 2nd law of thermodynamics.
All observers have a syntropic perspective according to the 2nd law of thermodynamics!
"Always two there are" -- Yoda.
The 4th law of thermodynamics is hardwired into mathematics.
Energy is duality, duality is energy and everything in physics & mathematics is made from energy.
Awesome video! Thank you!
Integration is dual to differentiation.
Convergence is dual to divergence.
Decreasing the number of dimensions or states is a syntropic process -- homology.
Increasing the number of dimensions or states is an entropic process -- co-homology.
Homology (convergence, syntropy) is dual to co-homology (divergence, entropy).
Syntropy is dual to increasing entropy -- the 4th law of thermodynamics!
Imaginary numbers are dual to real numbers -- complex numbers are dual.
"Perpendicularity in hyperbolic geometry is measured in terms of duality" -- universal hyperbolic geometry.
Ellipsoids are dual to hyperboloids -- linear algebra, matrices.
Duality creates reality!
From a converging, convex or syntropic perspective everything looks divergent, concave or entropic -- the 2nd law of thermodynamics.
All observers have a syntropic perspective according to the 2nd law of thermodynamics!
"Always two there are" -- Yoda.
Outstanding!
Hi, for a set to be considered open, all members of the set must satisfy epsilon ball in which only consists z of the same set, but what about the members z that are at the edge of the set ? The epsilon ball would include z that are outside of the set, am i right ?
If the boundary point is an element of U, then U is not an open set :)
Thank you for all your efforts.
Question: which program do you use to present the course? And your figures with which program do you plot them?
Thanks! I use the free program Xournal!
Hi this is a really good video. I have a few questions. Do we consider a singleton set to be closed or open? And does the set U in the definition have to also be connected?
Singletons are closed and not open. Connectedness is not necessary here but will be later.
@@brightsideofmaths Thank you for the answer. I feel so stupid about the singleton question like you literally just gave the definition of an open set in the video and it clearly does not meet the condition for it to be open. But I really appreciate the respond. Thank you.
@@SaranaeJang There are no stupid questions. You are very welcome! My answer shouldn't sound harsh or impolite. I just quickly type answers for a lot of questions the whole day and try to keep it short and clear :)
Excellent presentation. What are using to do the presentations?
Best Regards
Thank you! I use the nice free program Xournal :)
👍
The definition of differentiable in the quiz and video doesn't match - I think the one given in the video is correct.
In the quiz I made a mistake that I fix now. Thanks for telling me :)
@@brightsideofmaths I'll keep pointing out small stuff if I catch it - just let me know if it gets obnoxious. Thank you for great content! 🙂
these notations or math lingo are incomprehensible, dont you wanna tell people with high school math operators, while removing much subtleties which just hinder the main points for beginners.
Good point. I have a whole series for starting with mathematics: tbsom.de/s/slm
So you should watch that first :)
i also meant advanced math as well but with high school kind of operators, i keep forgetting flipped E or upside down A, one notation after another, they are like reading braille deciphering for which i need matching tables, so to speak.
Yes, you have to learn the language to speak :)
Kind Regards, as desperately as I may sound, I am a desperate aspirant who was accepted to study Medicine in russia 🇷🇺, but requires financial assistance, Any help of any sort will be highly appreciated
thankyou this is so good for revising
Thanks for your support :)