This guy is so charming and witty. It's like they took a slight-of-hands magician to give a math talk.
@TheDavidlloydjones
3 ай бұрын
sleight Completely different concept.
@crapadopalese
3 ай бұрын
@@TheDavidlloydjones Ah, thank you for the correction! English is not my native tongue so it's always good to be made aware of some recurring mistake I've probably made a million times without being corrected :)
@ruijunlin4574
4 жыл бұрын
what is the lecture notes or textbook?
@dimadima5298
Жыл бұрын
Allan hatcher , algebraic topology
@TheDavidlloydjones
3 ай бұрын
The backs of people's heads as the write n blackboards are not a fit subject for KZitem. It's been done already. Two of them was too many. If you want to teach a class, teach a class. If you want to make a video, sure, make a video. Just try to get it straight in your head that they are two different things, OK?
@dfs6575
Жыл бұрын
I don’t think organic chemistry tutor will save me this time
@candlemelt
Жыл бұрын
Am I watching this because a guy on tiktok said it was hard? Yes💀
@intrinsic9585
Жыл бұрын
Bro did u watch the topology edit also? 😭😭
@candlemelt
Жыл бұрын
@@intrinsic9585 yep💀
@avaii6205
Жыл бұрын
no shot 😂
@sniyahtate1585
Жыл бұрын
I’m here from the edit lmao
@Even_cats_smile
Жыл бұрын
Same here🗿
@llrecova
5 жыл бұрын
Algebraic topology is one of the most beautiful courses in mathematics.
@i_amscarface_the_legend9744
2 жыл бұрын
Really ? I have only general ideas what this of Mathematics is about ! But, u give me motivation to start this course ! Thank u!
@duzhu7719
5 жыл бұрын
Can you upload the next semester's Algebraic Topology?Thank you a lot.
@beback_
2 жыл бұрын
THIS
@DannyWitwer
Жыл бұрын
The same request.
@aeolidida3204
4 жыл бұрын
I really enjoyed your lecture! Thank you for what you are doing. I'm from Russia, and in my university I don't have such a course. I have to work through a lot of material on my own, and your lectures do help me.
@intensedeep777
Жыл бұрын
me too,i'm from china and my University didn't have these course too:) but my english is very poor......
@johnrickert5572
2 жыл бұрын
Outstanding lecture! Thanks for providing it. At 31:30, one may note that removing any point from the circle leaves a contractible space, while this is not the case with the annulus. Or more simply, the annulus has a nonempty interior, whereas the circle has empty interior.
@murasso2736
Жыл бұрын
This guy is one of the rare professors whose classes are enormously exciting
@TheDavidlloydjones
3 ай бұрын
Yes. Imagine if he transferred his intelligence to making a KZitem video! But the back of his head as he scribbles on the blackboard is pretty much like that of every other idjit out there who thinks that's an activity worth recording and rebroadcasting. Just nuts!
@pedromatzke2088
5 жыл бұрын
Pierre Albin was right to have some doubts, Mittag-Leffler is from Sweden not Norway.
@12maritere
3 жыл бұрын
Up to 1905 Norway and Sweden were the same kingdom, so he was right
@maestraccivalentin316
5 жыл бұрын
These are super cool! Waiting for semester 2! :)
@thelowlymathematician588
Жыл бұрын
Still waiting
@DannyWitwer
Жыл бұрын
I'm another one who is waiting. Please someone upload semester 2 :)
@aleksherstyuk8319
4 жыл бұрын
Timestamp 1:02:27 this is really nitpicky, but I think Freedman's result was that there are uncountablely infinitely smooth structures on R4, but it was known that for any n other than 4, there's only 1 unique smooth structure. He said 4 and higher though. The reality is much weirder: R4 is the only exception to the rule that "classifying Rn topologically or smoothly is essentially the same task". (And it's an exception in an unexpected, dramatic, big way) Really great lecture! I'm hooked
@aleksherstyuk8319
4 жыл бұрын
@Mohammad Maruf Mamun the same thing happened to me. I was a pure algebra and topology (and category theory) guy, but turns out, introducing differential structure just makes certain things mysterious and interesting
@definitelynotofficial7350
3 жыл бұрын
Is this guy part Greek or something? He said "γεωμετρία" (geometria) with perfect Greek accent and it really startled me because non-native speakers struggle with pronouncing words like it right, and he kinda looks Greek too.
@davidlozanocampillo2283
3 жыл бұрын
He probably speaks Spanish well (mentioned that he was brought up in Mexico). Greek and Spanish phonetics are almost identical.
@TheJoyLoveShow
6 ай бұрын
I wish I could ask questions! Does anyone know about the fundamental relationship between chaos theory and algebraic topology? I never knew chaos theory was necessary for forward movement in topology! Fascinating.
@SreeRama_20
2 жыл бұрын
thanks from India please upload some more topics like complex analysis, functional analysis
@medhatrabie3071
Күн бұрын
I did not understand Poincare approach
@Sidionian
3 жыл бұрын
Why hasn't Semester 2 been uploaded!?
@XrcyhikUbhdfbjdf
26 күн бұрын
Martinez James Jones Michael Jackson Sandra
@alessandragnecchi8767
4 жыл бұрын
when you're enjoying the nice introduction and then 8:38 arrives
@carloselfrancos7205
Жыл бұрын
Best course in algebraic topology so far
@sarita5294
4 ай бұрын
It was an awesome lecture with you sir on this channel here, just superb , the funny elements you added in the class were the best part as most professor just focuses only on giving an 1 hour boring lecture just by filling up the board the whole time. We need professors like you in our institutes.
@9Glaedr0
4 ай бұрын
This is fun to hear. But I don't understand a thing. Where do I do a foundation course?
@GEORGIOSMGEORGIADIS4
9 ай бұрын
Here from Aleph 0's vid, wish me luck 🤞
@umut3147
Жыл бұрын
In 31:52, I think we don't need the dimension theorem. If we subtract two points on S^1 becomes disconnected. However, This isn't the case in Ann.
@AkamiChannel
8 ай бұрын
Anywhere online to find the supplements he's referring to?
@themathguy3149
3 жыл бұрын
God how can so much cool fit in one person?
@DannyWitwer
Жыл бұрын
For me these are the most inciting lectures in the subject. Thank you, Professor Pierre Albin! And I am really eager to ask, are there videos of the second semester yet?
@tanmaymishra9576
4 ай бұрын
until 21:00 , history of topology
@forheuristiclifeksh7836
10 ай бұрын
6:42 riemman wants to go further
@RalphDratman
4 жыл бұрын
This is a wonderful presentation
@forheuristiclifeksh7836
9 ай бұрын
4:44 gauss bonet theorem
@kmd21886
Жыл бұрын
ابدع بمعنى الكلمة
@pascal3458
2 ай бұрын
اتفققق
@Dglinski2
4 жыл бұрын
I haven’t taken a college math course in about 5 years and even then didn’t get in to much conceptual math. What kinda prerequisites would someone need to know to understand topology? I’m very curious and this first lecture seemed fun even, I’ll attempt to keep following along but could anyone describe what fundamentals someone should know going in to this course that might make it easier to understand?
@aldogarcia6347
4 жыл бұрын
You will need algebraic and topological concepts. Good books in Algebra are Topic in Algebra by Herstein or Contemporary Abstract Algebra by Gallian. For topology, I can advise Munkers and Willard. Hope this helps.
@Jean-Berry
4 жыл бұрын
Perhaps you should look up abstract algebra lectures by Benedict Gross here on youtube. They are also very fun! (sometimes could seem like its going way too fast tho)
@Jean-Berry
4 жыл бұрын
Also, maybe you should also look up linear algebra, and for that I recommend lectures and book by Gilbert Strang on that subject. His lectures on linear algebra are lovely.
@spacetimemalleable7718
2 жыл бұрын
A GREAT lecture! Most impressed by his knowledge and wit.
@p_khale07
3 жыл бұрын
what book did he mention when he said chapter 0,1,2 ? thanks in advance !
@bellfoozwell
3 жыл бұрын
Allen Hatcher’s “algebraic topology “. Go to his website to get it.
@emanoelsouza8100
Жыл бұрын
@@bellfoozwell thank you!
@andrewdias2690
4 жыл бұрын
This is a great lecture! I really like this approach to topology as opposed to other videos I've seen. And the way he mispronounces all these mathematicians' names is kinda adorable.
@dehnsurgeon
2 жыл бұрын
how did no one notice the typo at @53:06
@haneenballan7337
4 жыл бұрын
Does anyone have a solution manual for the Allen Hatcher textbook?
@krakenmetzger
5 жыл бұрын
Please buy a better eraser
@jmxu0405
5 жыл бұрын
I couldn't help mistake him for Jimmy Carr
@joebloggsgogglebox
4 жыл бұрын
Jimmy Carr is his evil twin
@andydidyouhear
2 жыл бұрын
Is this a graduate course or a PhD-level course?
@chymoney1
Жыл бұрын
No
@fbkintanar
Жыл бұрын
I think that at top level research universities, algebraic topology is taught at the undergraduate level, and this presentation seems to be pitched to upper division undergraduates. However, in developing countries, many math departments, even the better ones, don't have an undergraduate algebraic topology course. You would only encounter algebraic topology as a special topics course at the graduate level, if there happened to be a professor interested in the field that year. This is true of my local university in the Philippines, even if its math department is one of the best in the country. No full-time algebraic topologist 😒☹
@1995amittai1
3 жыл бұрын
The algebraic topology Feynman
@aous5880
Жыл бұрын
What are the mathematical requirements that I must study before I learn topology as a beginner, given that I did not study mathematics after high school
@pseudolullus
Жыл бұрын
Set theory, proof writing, abstract algebra and point-set (standard) topology. This is a very advanced class, but also very enjoyable.
@karimshariff7379
Жыл бұрын
What is the textbook he mentioned? Thanks.
@Thehewhoviews
4 жыл бұрын
Timestamp 54:15
@rhaldryn7511
4 жыл бұрын
What university is this?
@martinmartinez4685
4 жыл бұрын
i think University of Illinois at Urbana-Champaign.
@soundslikemath860
3 жыл бұрын
@@martinmartinez4685 it is.
@farhanakausar4281
2 жыл бұрын
I want to show that Show O(p,q) is homotopic to O(p)×O(q) for p and q positive integers. Is there any hint or idea how to define homotopy?
@randalllionelkharkrang4047
Жыл бұрын
do u know where we can find exercises/ book to accompany these lectures?
@MoonBull13
Жыл бұрын
Why do they still use chalk boards. I cringe and get goosebumps hearing chalk or erasers on them
@samspeight4944
2 жыл бұрын
The answer is always no if you use infinity-categories ;)
@umergulzar4062
4 жыл бұрын
I need help with some typical questions can u help
@maciej12345678
2 жыл бұрын
11:47 this is nonsens what he saying -- saying first something else then something different and then that that answer to other question but to first is NO very twisted why to say something and try not say what realy neeed to say-- but still something new
@xerxes1871
3 жыл бұрын
So many holes to fill in......
@tcveatch
Жыл бұрын
Another dumb question. At 32:30 he explains a “continuous family” of maps and writes F:Xx[0,1]->Y “so” (X,t) |-> f_t(X) is continuous. I find this uninterpretable, unreadable. 1) clearly f_t(X) is a map, since it is a function of X,that is, *maps* values of X to f_t(X). But in what if any sense is (X,t) a map; it is NOT a map, but rather a continuous open range of numbers from X to t. An open line segment is no map at all, more like a dead thing, a mere piece of space,the input to a map perhaps but not a map. 2) Does the scope of this particular F end after X or ] or Y? Y, I’ll guess, but then how can Y be the output if it’s part of the input? 3) Is the idea of a family that members map from one to another, so both the inputs and outputs are members of the family? If so Xx[0,1] must be a continuous map which it isn’t since it is a subregion of R^2. And Y must be a continuous map which it could be but not necessarily by anything written or said here. And (X,t) must be a continuous map which it isn’t since it is an open line segment. And f_t(X) must be a continuous map which it could be by assumption from Y being a continuous map but then we don’t really have reason to believe that yet, do we? So in what sense is this a family of continuous maps? Apparently none. 4) Maybe the map is BETWEEN things in Xx[0,1] and things in Y, and as an example (X,t) which is in Xx[0,1] seems to map according to what he said to f_t(X) which could only be an element in Y, if Y were some kind of universe of FUNCTIONS and f_t(X) an element in that universe, which I wish he would explain since I never heard of a domain or a range being a world of functions, since functions take domains to ranges, that would be a mixing and a confusion of categories, where I grew up. I mean, you could MENTION that Y is not a normal numerical range, some subset of R^n, but a “space” of functions or continuous maps or something, just you know, so I (we?) could understand you. I’ll have to wrap my head around that. Then what would make this map to a function in Y a continuous map, is something also evidently unstated. Is it the openness of the segment (X,t)? If so, that could be made explicit and then be explained, why that follows, too. Please help this struggling, concrete minded follower understand what you are saying.
@pavlosurzhenko4048
9 ай бұрын
He wrote that the function acts like (x,t) |-> f_t(x) (x here is a small and represents a variable, not the space X), i.e. F is a function that maps Xx[0, 1] (with the product topology) into Y. Basically, you don't think of t as a parameter, but as another argument of the function F. The (x, t) |-> f_t(x) notation is the same as saying that F(x, t) = f_t(x).
@techconbd7661
Жыл бұрын
I'm from all over the place 😆
@johnstfleur3987
Жыл бұрын
"STEVE JOBS IS ALIVE."(AYANA)
@Israel2.3.2
4 жыл бұрын
Library doesn't have Hatcher. I like physical copies :(
@NotLegato
4 жыл бұрын
luckily hatcher is cheap as dirt. it's sub-30 pounds.
@Israel2.3.2
4 жыл бұрын
@@NotLegato oh cool I'll order it then. Fascinating subject so far.
@hassaannaeem4374
2 жыл бұрын
great!
@johnstfleur3987
Жыл бұрын
"17."
@suup4k75
9 ай бұрын
I wonder where he learned to pronounce poincare this way
@testchannel-pg5vd
11 ай бұрын
I am from all over place
@tcveatch
Жыл бұрын
Dumb question. How does the given definition of continuous (23:49) capture the meaning of “continuous”? Functions from an open domain to an open range have open BOUNDARIES (as in the open range (0,1) in contrast to the closed range [0,1]), but what continuity ACTUALLY means is continuous INSIDE the domain. A definition constraining the boundaries of set would not evidently constrain the interiors thereof. Maybe somebody could clarify, since the teacher didn’t. Thanks.
@gateronblackinksv2173
10 ай бұрын
I’m not exactly sure what you mean by “open boundaries”, but the intuition for this definition comes from analysis. In analysis, you can prove (from the epsilon - delta definition of continuity) that a function is continuous if and only if preimages of open sets are open sets. I believe Allen Hatcher also provides some intuition in his notes on point set topology, which you can find here: pi.math.cornell.edu/~hatcher/Top/TopNotes.pdf
My impression is that he is referring to the book Algebraic Topology by Allen Hatcher, even though he mentions it as Patrick's book.
@Gangstabob716
Жыл бұрын
This is one of the easiest classes I took at my university. I don't understand how people struggle with this subject
@fslakoh
Жыл бұрын
Math is Nice but totaly unuseful Profs are paid juste for fun 🎉
@98danielray
4 жыл бұрын
7:00 what gives the "locally resembles a plane" characteristic is curvature, not homeomorphism to planes. otherwise, thanks for the great lecture
@arismartinian3346
3 жыл бұрын
I know this is an old comment, but I'm not totally sure what you mean. An n-dimensional manifold is defined by its having a neighborhood around an arbitrary point homeomorphic to Euclidean n-space. Curvature is only defined on certain smooth manifolds.
@hamzehabuabed6333
4 жыл бұрын
Why you are laughing
@rookitchen
4 жыл бұрын
laughing should not be allowed in a math class. This should be a fundamental axiom of all math classes.
@UnderscoreZeroLP
3 жыл бұрын
not funny
@beback_
3 жыл бұрын
Not allowing things should not be allowed in a math class.
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