14 күн бұрын
21 күн бұрын
Ай бұрын
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@alexscofield1198 2 күн бұрын
Just here to say, it’s really nice that you changed the AI voice for your real one. Very much appreciated!
@XXX-zi5in 3 күн бұрын
what?
@joshualeopior9019 3 күн бұрын
I have a grasp on what your explaining but I don't really understand what your doing with all these function thats a bit hasty for me. I am familiar with sets, boundarys and descrete sets. But that was still a bit much especially if you havn't heard of Mero/Holomorphic sets and there respective functions in the complex plain.
@ooolivers-iqp 3 күн бұрын
this is much better than listening to the TTS reader
@clemenswild4523 4 күн бұрын
your content is a delight. I would love to see a video about Picards Great Theorem in your style.
@oceansofmath 9 күн бұрын
These are some of my favorite videos on youtube thank you!!!!!!
@M.Z.M.N. 11 күн бұрын
That's elegant btw can u provide formal proof for this theorem
@oceansofmath 11 күн бұрын
Really good video. Thank you so much!
@BenDover-eh5zw 13 күн бұрын
You deffo see Stokes' Theorem contained/addressed in the Fundamental Theorems of Lebesgue Integration. Good vid!
@quantumsoul3495 14 күн бұрын
Nice! Could you do distribution theory, differential forms on manifolds and geometric current theories ?
@cofiber 13 күн бұрын
Great suggestion!
@RickyRicky-002 14 күн бұрын
❤
@quantumsoul3495 15 күн бұрын
You should have given examples of singular random variabels, so which are neither continuous nor discrete
@Jim-be8sj 16 күн бұрын
This is a great video getting at core concepts of the topic. A measure theory class I had when I got my PhD was the most difficult class in all of my education. The professor was quite good and even wrote a real textbook for it, but I would have really appreciated a roadmap like this immensely. It would have helped to synthesize the learning and provide a better context of where all the pieces of the puzzle go. Thanks for making this.
@shinn-tyanwu4155 16 күн бұрын
The quality of logic is overwhelm ing😊😊😊
@Miguel_Noether 16 күн бұрын
I didn't understand anything because it was just a resume of things...
@ВалерийГайнанов-и5г 17 күн бұрын
Thank you for not oversimplifying things! Would be cool to include more examples of these used in physics
@comic_sans_ 17 күн бұрын
This is literally everything I learned in probability theory last semester lol. Thanks for the nice and high-quality video!
@pacificll8762 18 күн бұрын
Great !
@wtt274 18 күн бұрын
Excellent video ❤
@uchindamielia2399 18 күн бұрын
Is anyone else dizzy, or it's just me. I could benefit from a longer video
@TheCrmagic 18 күн бұрын
Do you know of an intuitive way to explain matrix p,q norms?
@aditya234567 18 күн бұрын
Ive been following many math and science channels over last 6 years but this channel quickly became the best. Thank you sooo much for the great work. I owe u alot!
@Spix_Weltschmerz-Pucket 18 күн бұрын
I always tell people, when you find some pedantic physicist, ask them why does the wave equation has to be defined in an infinite Hilbert space? 😅 Great video! Thanks for sharing!
@pedrosso0 19 күн бұрын
Your voice sounds AI-generated and the unusual and incorrect intonations make it difficult to follow along with the content.
@thelocalsage 14 күн бұрын
yeah i’m not messing with this because of the AI-generation. bummer.
@rysw19 14 күн бұрын
It sounds like AI because it is AI
@ccriztoff 7 күн бұрын
yeah pass
@TALCOHOME 19 күн бұрын
Your chanell is really good!! Shoutout from Brazil 🇧🇷 !
@DrMcCrady 19 күн бұрын
Great video!
@TheNumberCruncher0913 19 күн бұрын
How do you compute the lebesgue decomposition?
@Technoyote 15 күн бұрын
I don't know how to do it in the general case but here's a simple one. Say you have a random variable that, 50% of the time, is a coin flip between -1 and +1. The other 50% of the time, it's a standard normal. The absolutely continuous measure is the 50% normal distribution. The singular measure is the 25% mass on +/-1.
@luchesartomov 20 күн бұрын
Great explanation!
@joeeeee8738 20 күн бұрын
No examples?
@michaeln.8185 20 күн бұрын
Amazing video! I look forward to what you will post next!
@thatdude_93 20 күн бұрын
A small correction: the operator L you defined is symmetric, not necessarily self-adjoint. For this you would either have to show that L is bounded or that the domain of L coincides with the domain of L*
@sensorer 16 күн бұрын
I would love for this to be stressed more often. Physics professors usually gloss over the difference
@studywithjosh5109 20 күн бұрын
Very nice. Subscribed and I will be watching all of your videos in the coming weeks.
@Victor-ss5bg 20 күн бұрын
I just discovered your channel and I am pleasantly surprised by the quality of the content! Thank you for the effort put into the creation of the videos, and keep up the good work!
@ewthmatth 21 күн бұрын
I can't believe the highest rated comment here is someone complaining about this benign text-to-speech engine that sounds fine and is perfectly clear.
@imnimbusy2885 21 күн бұрын
I love mathematics and all that jazz but I can’t be the only one who chuckled at 1:25
@DarthJarJar10 17 күн бұрын
Indeedily, you aren't alone... Has that lemms ever heard of even and odd functions 😂
@sensorer 21 күн бұрын
I would love a similar video for other sets of orthogonal functions. As well as a unified overview of techniques that work for many such sets of functions. They usually are orthogonal with respect to some scalar product, they are solutions to some kind of differential equation(eigenfunctions of some differential operator) and so on Even though I knew everything presented in the video, I really like the way it is structured. Deep enough, but consise.
@Emadmn700 21 күн бұрын
Wish i could understand this
@orsongodyns2333 21 күн бұрын
Wonderful channel ! So clear and efficient
@TheMauror22 21 күн бұрын
This channel is pure gold!!
@loganreina2290 21 күн бұрын
Think you need a (-1)^n at 3:57, but it doesn't interfere with the next step. Really sleek arguments all around. What sources did you use?
@cofiber 21 күн бұрын
You're right, there should have been a (-1)^n. In generally adapted the approach in math.stackexchange.com/questions/4941449/derivation-of-legendre-polynomials-from-only-orthogonality and the filled in the details.
@nazishahmad1337 21 күн бұрын
Which AI voice you are using please tell.
@jaysn1683 22 күн бұрын
Thanks again for a masterpiece, this AI voice is a major improvement!
@paulwilliams4371 22 күн бұрын
your channel has been a goldmine for me, amazing explanations and the graphics are suburb.
@tirthrajsinhchauhan5481 22 күн бұрын
Superb. Pure gem. I am speechless. In 9 and a half minutes this video sums up at least an entire chapter worth of mathematical methods text in Physics. I have yet to come across a material this concise and yet in depth enough
@bennyloodts5497 22 күн бұрын
World class quality! My compliments.
@SchienexScience 22 күн бұрын
Wow, I found this treasure channel! Thank u very much❤
@SonVu-rw9hh 22 күн бұрын
Why on earth does anyone would want to know about raise to the p power of a function. I see it has no application unless complicated holder inequalities technique used for them make my mind blown away.
@cofiber 22 күн бұрын
Actually, Lp spaces do have much application. For instance Lp spaces are used to define Sobolev spaces, which in turn are often used in the study of partial differential equations, as they allow us to analyse pdes in a more general settings and find weak solutions.
@antronixful 22 күн бұрын
In quantum mechanics you use this notion all the time. In your average undergrad level quantum mechanics, the lectures will skip all these definitions, but they are there. If you take more advanced courses, the amount of applications this and other topics related to real/complex analysis and linear algebra will blow your mind away even more.
@thatdude_93 20 күн бұрын
L^p-spaces are heavily used in functional analysis, which is the mathematical language of quantum mechanics. They also play a huge role in defining certain notions of solutions to partial differentail equations, which again is very useful in physics, since most of the physical theories are formulated as partial differential equations. L^p-spaces also appear in probability theory and the theory of stochastic analysis, which is the foundation of modern financial mathematics.
@estebanvasquez-giraldo5770 23 күн бұрын
It is indeed intuitive if you have enough background. I am really happy that someone is doing things carefully and for somewhat advanced public. Thank you so much. There is a question I have always had for many years and I would really appreciate it if you could answer: You mention that an orthonormal basis is not a basis. But the u_α are elements of the vector space, and then you say that we can represent any vector as a series, a linear combination of the orthonormal basis elements. How does the orthonormal basis fail to be a basis? Is it because of the uniqueness requirement, can you give a example? Also related, then you show how the Fourier series is built, and in that case the u_α's are complex exponentials and in that case they are elements of the vector space because we are considering them in a period. But what happens with the Fourier transform. Why can we justify expanding elements of the vector space as linear combination of functions which do not belong to the space, and therefore are not vectors?
@cofiber 22 күн бұрын
An orthonormal basis generally fails to be a basis, as not every element in the vector space can be represented as linear combination of finitely many elements. Instead we have to sum over infinitely many elements. In a general vector space, this is not possible as there is no concept of convergence. The uniqueness does not fail, as an orthonormal basis is linear independent. For example in the space of continuous functions on [-1,1], the Legendre polynomials form an orthogonal basis, but sin(x) can not be written as a sum of finitely many polynomials.
@geraltofrivia9424 23 күн бұрын
Beautiful.
@bpr214 23 күн бұрын
Very clearly explained.