Check out our second video on @TomRocksMaths's channel where he teaches me some Fluid Dynamics, it is some pretty awesome stuff. Great to do this pair of videos with you Tom! ►►►kzbin.info/www/bejne/mKHIdJmtjpmkl5I&ab_channel=TomRocksMaths
@aashsyed12773 жыл бұрын
wait......he said it was part 1....
@TomRocksMaths3 жыл бұрын
This was such fun! Can you teach me more topology please? :)
@aashsyed12773 жыл бұрын
@@TomRocksMaths of course( he can)
@DrTrefor3 жыл бұрын
@Tomrocksmaths Omg yes please
@elltwo83933 жыл бұрын
If you swap the words in algebraic topology, you get topological algebra, which is also a topic worth checking out! One of my favourite kinds of theorems in math are duality/representation theorems, and Pontryagin duality is one particularly cool example.
@theflaggeddragon94722 жыл бұрын
Indeed Pontryagin duality gives, (S^1)^PD = Hom_{cts}(S^1,S^1) = Z, while in algebraic topology, pi_1(S^1) = [S^1,S^1] = Z where [X,Y] denotes homotopy classes of maps from X to Y. It's somehow the "same" formula!
@MCLooyverse2 жыл бұрын
Is this a thing that mathematicians do a lot? Having the field "Xic Y" be distinct from the field "Yic X"? "Algebraic Geometry" is very different from "Geometric Algebra". Or is this just a thing with "Algebra"?
@Dr.Cassio_Esteves3 жыл бұрын
I loved this lecture! I'm quite impressed that I was able to follow along with it knowing only a little bit of group theory. Sir you did a excellent job at presenting this topic. Sorry any mistakes, my english is a work in progress.
@peacefulchildofjesus64842 жыл бұрын
Thank you both of you so much. I was confused in Topology a lot. Now, my messy loops are untied. Bravo, brilliant !
@eulersfollower71403 жыл бұрын
This is like a highly anticipated crossover 😎😎
@DrTrefor3 жыл бұрын
Math Avengers:D
@aashsyed12773 жыл бұрын
@@DrTrefor mathevengers check that channel :)
@chandankar50323 жыл бұрын
After a ton of request finally prof will cover some snippets from his area of research. Feeling blessed.
@michaelzumpano73182 жыл бұрын
Love that you and Tom hooked up on this. Great topic too. Both of you are great teachers.
@wargreymon20247 күн бұрын
This is very good intro to algebraic topology!
@TheTessatje123 Жыл бұрын
This is fun: its somewhere in between a question requiring user input (maybe youtube will develop that feature in the future) and a fixed presentation :-).
@pseudolullus Жыл бұрын
Not going to lie, it took me 2-3 watchings and some notebook action to actually understand it, but it was certainly worth it!
@HungDuong-dt3lg3 жыл бұрын
Can’t wait, Dr. Trefor!
@fatemekashkouie36622 жыл бұрын
Thanks a lot for the vivid explanation 🙏
@MikeLeed2 жыл бұрын
The audio is much better in this video, great work!
@DrWillWood3 жыл бұрын
That was really great! thanks so much to you both :-D
@DrTrefor3 жыл бұрын
Glad you enjoyed!
@bockmancheung3 жыл бұрын
Worth binge watching!
@interest21stcentury743 жыл бұрын
Hey dr!! Very Interesting!! Im thinking of getting a minor in mathematics and I still have Abstract Algebra, so I would like to ask you when you will do a course on that? Thank You so much, you never fail to impress us! And Im pleased to be an alumni of yours, you taught me Discrete Maths, Calculus and Differential Equations and Markov Chains and Graph Theory and now Game Theory
@DrTrefor3 жыл бұрын
That's cool! I do want to do a series on Abstract Algebra one of these days:D
@aashsyed12773 жыл бұрын
cool! me cant wait too!
@AlessandroZir2 жыл бұрын
very useful, insightful, & kind: thank you!! ❤️❤️
@matejcataric22593 жыл бұрын
Topology is the best!
@casualphysics8403 жыл бұрын
I’d be upset if tom doesn’t discuss the topology of rocks
@TomRocksMaths3 жыл бұрын
... future video idea :)
@orvarl-o25542 жыл бұрын
If you include non capital letters there is also a two-point with i and j.
@interest21stcentury743 жыл бұрын
Great Video Dr!! I would like to take abstract algebra maybe this spring or fall 2022, and I will self tutor myself first, so I would like to ask you if you will post anything related to that at the end of 2021 or in 2022. Thank You so much for your effort and god bless you.
@DrTrefor3 жыл бұрын
Cool! I do mean to do some abstract algebra at some point!
@farrukhsaif1083 жыл бұрын
Damn I am really here procrastinating studying by studying huh
@broccoloodle Жыл бұрын
In the proof at the end, I think it's not clear that f continuous implies that r f_t also a homotopy
@Spacexioms3 жыл бұрын
Awesome!
@BlackPillHurts Жыл бұрын
Great
@jimmyt_19883 жыл бұрын
Awesome! Loved it!
@DrTrefor3 жыл бұрын
Glad you enjoyed it!
@subhadipsarkar76923 жыл бұрын
♥️♥️♥️♥️
@aryansaxena49788 ай бұрын
31:00 so if I loop around twice in S^2 (north pole to south to north), it is the same loop as looping around once. But if I do that in S^1, these are different loops? Why in the living hell is that!
@TrinityTwo3 жыл бұрын
Love the shirt, professor. Where can I buy it?
@yonathan41943 жыл бұрын
So if I get this right in the Proof of Brouwer's Fixed Point Theorem you're saying that if every x is not equal to f(x), then there is a mapping from the disk to the s1 right? but I still don't understand where the contradiction is. Is it because the mapping changes the fundamental group?
@DrTrefor3 жыл бұрын
I’ve shown a way that every path on the circle can in fact be sent to the trivial loops through the composition of the two maps. But that is impossible as the fundamental group is Z
@yonathan41943 жыл бұрын
@@DrTrefor In 1 dimension, the proof of Brouwer's Fixed Point Theorem is easily proven by the Intermediate Value Theorem. Is there an analog of the Intermediate Value Theorem in a higher dimension? and thanks for the reply Dr. Bazett.
@writerightmathnation94812 жыл бұрын
@@yonathan4194 I think what you may be looking for as a generalization of the intermediate value theorem is the fact that a continuous image of a connected set is connected. This is a theorem of topology.
@KaliFissure2 жыл бұрын
I love seeing functions as they exist. forms in the field of mathematics. Q? Surface(cos(u/2) cos(v/2), cos(u/2)sin(v/2),sin(u)/2) 0>u>4π 0>v>2π Klein or not? it requires 4pi to complete the surface (electron half spin) but the node is problematic. opinions? proofs?
@chandankar50322 жыл бұрын
Ok, I feel like it's a dumb question. I guess we didn't prove the fixed point theorem on arbitary metric, or did we? If that's the case then why are we using only the fundamental group of S1, is it because ultimately metric gives a real output and the generalisation balls and spheres correspond to a real number.
@DrTrefor2 жыл бұрын
Ya we have some work to do to understand something in arbitrary metric spaces, but the basic arguments ultimately will work out the same
@GastroenterologyPINNs2 жыл бұрын
You 2 are my favorite
@luih3673 жыл бұрын
This is going to be epic 😎🤙
@TomRocksMaths3 жыл бұрын
@camac79883 жыл бұрын
Nice video guys 😍
@obscurus13443 жыл бұрын
Why is pi1(S^2) = 0? You can loop in the opposite direction or stay put, wouldn't it be equal to Z also?
@DrTrefor3 жыл бұрын
Imagine you had a rope around the equator. You can sort of pull that rope up up up to towards the north pole making a smaller and smaller circle all the time. THat is the sense in which it collapses to that constant path at the north pole every time.
@sdsa0072 жыл бұрын
@@DrTrefor if i loop the loop at the equator will it still collapse to the north pole? or do i get a unique construct?
@akrishna17292 жыл бұрын
@@sdsa007 it can still be "slid", or continuously deformed into a trivial loop on the surface of the sphere
@dimadima5298 Жыл бұрын
But what we want to determine the fundamental group of line
@DrTrefor Жыл бұрын
It’s just 0!
@dimadima5298 Жыл бұрын
@@DrTrefor I understand that it's not necessary to the figure to be closed if we want to find it's fundamental group?
@jurrich2 жыл бұрын
Late to the party, but while capital letters only have three forms, "letters" (English ones at least =) have four: there's one circle, two circles, one point, but also two points (e.g. "i" or "j")
@writerightmathnation94812 жыл бұрын
This adds a level of topological complexity, in that these letters firm disconnected spaces.
@ガアラ-h3h Жыл бұрын
20:09 multiplacruon can always be viewed as repeated adding like 1 * 200 = 200 = sigma k[0;200] k
@mohamedababou36963 жыл бұрын
The theories of correct Mathematical communication are represented in the presence of the sender, who is the Mathematics teacher, who believes that Numbers have an end, and the receiver, who is a Mathematics student who receives a Mathematics education free from the illusion of infinity.
@aashsyed12773 жыл бұрын
Numbers have NO END....... !!!!! INFINITY IS THE NUMBER OF NATURAL NUMBERS!!! THERE ARE INFINITELY MANY INFINITIES OF INFINITIES AND SO ON........;!!!!!!!! STOP IT U WHO KNOW NOTHING ABOUT MATHEMATICS!!! YOU CANT APPROXIMATE USING TAYLOR SERIES!!!! U KNOW NOTHING ABOUT MATHEMATICS AND WILL NEVER SUCCEED YOU BEAT THE JEWISH PEOPLE .......
@Helalll2943 жыл бұрын
قفلتوني من أم الفيديو
@mohamedababou36963 жыл бұрын
True and scientific Mathematics is Mathematics devoid of the illusion of infinity...Mathematics is an exact sciences, not an abstract one.
@aashsyed12773 жыл бұрын
Go away. Comment on another channel. Don't spam. I just needed to reply cause how idiotic you were .
@writerightmathnation94812 жыл бұрын
I've been told by scientists that mathematica isn't science because it is not falsifiable. I prefer my mathematics to not be falsifiable...
@geraltofrivia9424 Жыл бұрын
Everyone here forgot how involuntarily funny you can be...
@mohamedababou36963 жыл бұрын
It is not possible to build a correct Mathematical educational framework without abandoning the illusion of infinity and its symbol.
@aashsyed12773 жыл бұрын
Get out of here . If u believe it then don't comment. Don't tell others. Tell yourself .
@geraltofrivia9424 Жыл бұрын
You're infinitely ridiculous.
@DavidSmerkous9 ай бұрын
Why do you say that? Do you take issue with Cantor's thm?
@mohamedababou36963 жыл бұрын
The unwillingness to believe that Numbers have an end and and the denial ofillusion of infinity, cannot be a natural characteristic emanating from an ordinary human being... Rather, it is a condition that expresses the existence of either a deliberate desire to spread Mathematical ignorance or a psychiatric condition.
@aashsyed12773 жыл бұрын
Numbers don't have an end. Infinity is the number of integers there are. You don't even understand mathematics .
@writerightmathnation94812 жыл бұрын
Please, sir, what's the largest positive integer?
@geraltofrivia9424 Жыл бұрын
These comments of yours are the dumbest thing ever.
@DavidSmerkous9 ай бұрын
It's no denial of infinity. We can both argue it's existence but one is more probable and useful than the other. The concept of counting via integers alone is an abstract concept created by humans. For what is the number 1? We find it useful to describe some groups of objects. Math is always an approximation of our reality, not reality itself. As a mathematician you're living in an "illusion," and infinity is a useful/proper tool that helps describe spaces/thms in a useful and predictable way.