An introduction to homology | Algebraic Topology | NJ Wildberger

[@oscarwal]

that's how math should always be taught, the down to top approach with lots of examples and easy to remember catchphrases is great. thank you !

[@arkapointer]

Oscar Roche I totally agree

[@StefanHoffmann84]

@@Gabbargaamada Abstraction is the result of seeing enough examples sharing a common concept. I can recommend you to read Halmos or Polya to see the value of it.

[@Gabbargaamada]

@@StefanHoffmann84 my math professor never really elaborated upon examples. For instance, we studied epsilon delta limits symbolically. When it's abstract rigor had finally made some sense, the professor went on to describe this concept by applying them to functions which are far more concrete.

[@Gesantel]

@@Gabbargaamada This just isn't true. And I'm saying this as a grad student at any Ivy League school.

[@cyberqirexx]

@@Gabbargaamada delta epsilon limits is pretty simple thing. Try learn smth abstract and difficult without examples, probably you will stuck

[@bogdandobondi9547]

I might not share your aversion towards the reals (or infinite sets), sir, but besides that this series of lectures contains perhaps the most useful videos on KZbin. I have great professors but they all have teachingstyles which differ from yours. And in this difference lie the much appreciated benefit for me. Thank you very, very much for the entire series and not only this lecture.

[@aaos75]

The best day of my life. too often I saw it without a proper introduction. huge and grateful thanks for the whole course

[@shilangyu]

This is the best introduction to homology I have ever seen. I had a hard time grasping this topic, books often skips some small (yet important) details. Watching this cleared everything up. Thank you, your style of teaching is very approachable.

[@dhaka_mathematical_school]

Professor N J Wildberger, you are one of finest teachers on this planet.

[@polopadic7954]

perhaps a perfect lecture, or as close to perfect as it gets

[@WildEggmathematicscourses]

Thank you

[@michelhenridevoret5184]

Amazing series of crystal-clear lectures on a difficult and complex topic. Prof. Wildberger is a mathematical pedagogy genius. This is the best introductory material on 20th century mathematics that I have ever seen on the web so far, and particularly on KZbin. I will follow any new series of lectures that Prof. Wildberger will put on KZbin!

[@njwildberger]

@Michel Henri Devoret Thanks Michel!

[@nidhirathi11]

Dear Sir, you have a gift of teaching in a wonderful way. Highly appreciate it. Keep making videos of whatever classes you teach. Thank you so much. I have seen the whole series.

[@siddharthjain2127]

Yes I'm agree with you 😊 😊

[@erelsgl]

Hi, nice to meet you in class :) I totally agree with you

[@alvaroballon7133]

Thank you! I was trying to learn this by myself but I was failing miserably. Now Im getting it so easily

[@TenzinLundrup]

I heard the term Khovanov homology in a lecture by the string theorist Ed Witten (also winner of the Fields Medal) so here I am as a layman learning some basics which Witten must also have had to learn at some point. Thank-you Prof. Wildberger. p.s. Intuition comes from examples (I would imagine) not abstract definitions and relations. Also, the structure of space in LQG (Loop Quantum Gravity) is all about vertices and edges; see the lectures by Rovelli on youtube. Spacetime is becoming relational and discrete in this description.

[@monicamir]

How you glue the edges and end up with a torus, or something with more holes .... this is very interesting.

[@Crasshopperrr]

I definitely appreciate whoever edited out some segments! Shorter is better!! =)

[@dirkdugan]

I'm so glad this series was posted. Unfortunately, my professor has the tendency to verbalize most of the details, and also to avoid writing coherent sentences. So this is really helpful.

[@AnnevanRossum]

What a great lecture! The difference between homotopy and homology is made intuitive already at the start. The lecture itself is very easy to follow. Even doing the matrix elimination step by step. It's so nicely self-contained that I didn't mind that it could be summarized. I'll definitely check out more of his lectures!

[@dukeyin1111]

The best down to earth, intuitive, soft intro to the subject

[@erelsgl]

What a wonderful talk. I tried to study from Wikipedia and it was so complex, but your talk make it seem so simple! Thanks a lot.

[@clearclearskies]

Your love for the subject really shows in THIS lecture. Beautiful stuff. Thank you very much.

[@bohu1122]

It was very helpful starting from a simple example and go to more general definitions step by step. Thank you for making this amazing series!

[@cristafractal4021]

Thank you so much for posting this lecture, it is a nice and intuitive way of understanding homology groups.

[@jacobchanda4405]

thankyou very much Dr/prof/sir, I was fearing Homology,but with this video ,it has really helped me a lot cause I can now understand what am studying

[@hamidrezakhajoei3344]

These lecture series save lives

[@laflaca5391]

That boundary operator reminds me a lot to the exterior derivative operator acting on forms, where cycles seem to be analogous to closed exact forms, I wonder in this connection goes further and if there is some kind of Stoke's theorem for theese objects. Great lecture btw!

[@900102xy]

A useful lecture. I would be also helpful to have some exercises, additional material supplied with it. I searched your university website, but could not find anything of that kind.

[@persistenthomology]

Hello Prof. Wildberger. My question is: how do you (can you?) make sense of singular homology if you don't believe in infinite sets? Do you accept that "the set of singular n-simplices" of a space exists?

[@jacobec12]

You my guy Wildberger. Keep doing what youre doing

[@MehdiRamezani]

Great teaching. Thank you for sharing.

[@scientiaetveritas40]

Dr. Wildberger, could you please do some videos on cohomology please?

[@ndmath]

44:35 There's an algorithm for finding 'bridges' in graphs by Robert Tarjan that uses something like this (not sure if it is the same fact). I think the name is "Tarjan's bridge finding algorithm".

[@qaysshakir7443]

Thank you very much for that valuable lecture.

[@filter80808]

Amazing presentation. Brilliant. Thank you!

[@enkii82]

Dear Professor, can you do a lecture on Sperner's Lemma, subsimplex, and Brouwer's Fixed Point Theorem? Please :)

[@Seastric]

very helpful indeed.💯💯

[@njwildberger]

Yes, all higher homotopy groups turn out to be commutative, but this is not entirely obvious, is not part of the definition (ie they are defined as non-commutative groups), and doesn't apply to the first homotopy group (the fundamental group). The homology groups however are already defined in the framework of commutative groups. So I think the statement is still valid.

[@shmalomemories5627]

where can I read more about the relationship between spanning trees and homology (I am especially interested in the higher dimensional homologies).

[@DanielStJohn-hc7mh]

Outstanding Lecture !!

[@CyberneticOrganism01]

Thanks so much, this is terrific and very clearly explained.

[@mahira3547]

Amazing explanation

[@f.zillinger6949]

Very informative and helpful video.

[@ac-dp3jk]

a superb lecture. thank you so much !

[@00tact]

This is so good. Thx!!

[@wdlang06]

it is so clear. But, can one assign the directions of the edges randomly?

[@Gmaraio7233]

Yeah

[@mip0]

gold GOOOOOOOOOOOLD!

[@arturwojciechowicz3124]

Thank You .

[@hippybonus]

great lecture. Thanks!

[@applemaniac0504]

I think it should be a + b+ d=a+b+c+(c-d),shouldn't it?

[@herosalhAssa]

Hello, Thanks for being here, i have a queston ? where can i get the pdf lecture notes of Algebraic topology ?

[@njwildberger]

You can get screenshot pdf's for many of my Playlists at my website wildegg.com, here is the link to the store: www.wildegg.com/wildegg-store.html

[@ja524309]

What textbooks are being used for this class?

[@njwildberger]

There is no set textbook, but I can recommend Hatcher's Algebraic Topology, available online.