great video! Do you have a good reference book for this? I started reading Peter Walters Intro to ergodic theory but wondered if that's still up to date?

If chose research then what is the job and how to earn money by it? Please answer. Because I don't know actual job?

This was the most helpful video ever. thank you

The problem exists in trying to manage a proposition in which infinity is being paired with finite concepts because they cannot be joined. There is no such thing as infinity within materiality. The concept cannot be realized as complete, i.e., a complete infinity within the context of an instant in time of its consideration. It can only be considered a progression to continue on forever, but quantifiable at any point along that infinite line/progression of time. All the business about bijection is irrelevant when we are considering infinity in its application. Hilbert proposed an hotel with infinite rooms and infinite guests BUT with all the rooms full. This means that there can be no shifting of guests to make room from others for as the unending nature of the rooms is considered that new guests might be accommodated, the same consideration must be exactly made for the infinite guests for “all the rooms are full”. This qualification couples each room in the infinite progression to a guest which precludes the proposed shifting. As for all the bugle oil about bijection, consider, if these two infinites are supposed to be the same size (conceptually a ridiculous notion) as per the proposition (if not, all the rooms could not be full) then by definition if the infinity of rooms is employed to make room for new guests then the infinity of existing guests would have to correspond to the manipulation of the infinite rooms that it might remain that “all the rooms are full”. One cannot have it both ways, including Hilbert. His paradox is sophomoric and a contradiction of his own making. Its piffle. Any thoughts?

What's the name of the differential forms book? Are they lecture notes?

Do you remember all that

This may have been true 40 years ago, but from my experience if you don't have a degree in Mailroom Science you can't even get a job working in the mailroom anymore

Ο τύπος έμαθε Ελληνικά για να διαβάσει τα Στοιχεία στο πρωτότυπο κι εγώ εύχομαι να ξερα καλύτερα αγγλικά γιατί όλα τα ελληνικά βιβλία στηρίζονται σε αγγλική βιβλιογραφία.

How does this video have so little views?? Its fantastic

I am looking at doing fractal biology for my grad thesis. Do you have fractal references you could point me to.

Very good explanation. Thank you

Hi

5:30 is it possible to define an entropy for the mass localization? as in the average number of bits necessary to find the open set

Very helpful video :)

I hate the book throwing, it’s so annoying

Why you used this nonsense music 😢

I just don't like when we are required to have the newest edition of a textbook. I always buy my textbooks used; the notes or underlining may be helpful and they are usually only very lightly used.

Thats crazy. You look like your insomnia has insomnia

Q: let X=R^3\{O}, the complement of a point O belong to R^3. then X can be partitioned into Euclidean lines. sir kindly make video on this Q

I was literally just working on this problem! Although my main question was what is the expected value of x given some bound on the length and a set of probabilities.

That was wonderful, i was only able to take up to multivariable calculus and second year linear algebra so i was really curious what came after thanks for this video. Looking forward to the post grad version! <3

So I’m guessing ur smart … right?

😅😅😅

Also known as "the weirdest thing math has come up with, ever".

I'm here because I'm thinking quit the boring medicine and go to studying the lovely mathematical

how do I choose what do research? I would really appreciate an answer

I took 35 and I actually wanted to take more: Proofwriting Single variable calc Linear algebra Discrete math (graph theory + combinatorics) Python Mathematical modelling Multivariable calc Group theory Real analysis Probability theory Mathematical modelling of dynamical systems Fourier analysis Numerical methods Ring theory Statistics Mathematical modelling of stochastic systems Complex analysis Dynamical systems Topology Geometry (bits of Euclidean, projective, hyperbollic and algebraic) Measure theory Number theory Computer assisted proofs (for algebraic geometry) Galois theory Ethics History of science Functional analysis PDEs Differential topology Differential geometry Biomedical mathematics Representation theory Module + category theory Set theory Automata + complexity theory

You ought to see what doing this on binary numbers does! You do it the same way, pairing digits up. For the doubling, that simplifies to appending 0 to the right end. For the multiply & test, there is only 1 test: a 1 digit. You append 1 to right of the doubling. You multiply by 1 (don't need to do as it is the same number), do the subtract, discard if too large & append 0 to answer, else append 1 & keep the subtract. So for the test, you take answer (so far) & append "0 1" to the right of it, subtract, append either 0 or 1 to the answer, etc. A few iterations of square root of 2 illustrated. 1 . 0 1 1 √10.00 00 00 00 01 < first subtraction 1 00 < remainder, bring down next 2 digits 1 01 < this is answer with 01 appended, too large, discard difference, next answer digit 0 1 00 00 < unchanged remainder, bring down next 2 digits 10 01 < answer with 01 appended, not too large, next answer digit 1 01 11 00 < remainder subtracted from, bring down next pair 1 01 01 < answer with 01 appended, not too large, next answer digit 1 etc.

Why do so many really smart people talk so ludicrously with their hands?

You can go even higher abstract! Integration on a locally compact topological group with a left-invariant Haar measure! (Abstract Harmonic Analysis)

My strong mathematics background (Bsc mathematics special degree , University of Ruhuna in Sri Lanka). I am a mathematics teacher. I am iteresting maths jobs then go to abroad or online. Help please.

seems that there is a much clearer way to explain the maths visualization of the sqrt long division algorithm but thank you for this vid, and your interest in the subject

❤❤❤

Just one thought (before even finishing the video): Man you never fail to prove yourself (at least to my humble mathive self) as legendary as 3B1B and Numberphile here on YT. i remember i once embarked on a lonely journey to find out why this works, and sure got many lovely insights along the way; that's why i personally see how elegantly you nailed it. Well done.

Hey there, do you have programming in a maths degree. Like C++ or Rust? Anyways, amazing content, subscribing

In korean, 'cee bar' means f-words lol

The square of the formula for the sum of integers, I think, lol, but that's memory...[n(n+1)/2]^2, etc...

please never stop making videos, youre great <3

Can you give me resources for learning coding that you have shown in this video?