Delta complexes, Betti numbers and torsion | Algebraic Topology | NJ Wildberger

[@gopalsurya]

Dear Prof. Wilderberger, thanks a lot for this series. It was very informative just like all the other series of videos that you have posted. Your contribution to society is much appreciated.

[@njwildberger]

You are welcome. Remember that I do have a Patreon page where you can join up and become a Patron of my channel if you like. The link is: www.patreon.com/njwildberger

[@mittaltushant]

When I had to to learn homology (out of the blue, just the torus's group), I thought it would take time as I had never taken a course in topology let alone homotopy. But watching just 5 videos, I learnt everything I needed very clearly in just a day !! Thanks a lot, Professor Wildberger.

[@njwildberger]

There is an intimate connection between parts of algebraic topology and differential geometry. However to describe that requires first some work setting up differential geometry. I will be teaching some of that later this year, might add some lectures on that topic, will see how it goes.

[@lixianghe-tf4ro]

Maybe the most beginner-friendly video in algebraic topology all over the world.

[@dhaka_mathematical_school]

Professor N J Wildberger, you are a life savior.

[@markborz7000]

I could listen to Your lessons endlessly. You have a god given talent to explain complicated things in a simple way. It's really a pity that You stopped here. There are so many themes in algebraic topology, especially in connection to manifolds, cohomology etc.... Physicists like me would be very grateful. Thank you very much for these marvelous lectures.

[@njwildberger]

I probably will talk about homological algebra in the MathFoundations series at some (more distant) point. But a course on group theory is certainly something I will consider down the road--it's one of my personal favourite subjects, especially when extended to hypergroup theory, which is really fascinating.

[@ziaafzal]

Excellent lecture series. Great teacher!

[@postbodzapism]

Time really flies! Thanks to this video a year ago I finally could have the intellectual permit into the great algebrotopologic world and understand related literatures. But will you do any video on homological algebra (probably in a group theory series?) in future? That would benefit many a math enthusiast like me.

[@AdrienLegendre]

Excellent lectures, and well organized. The examples provide a better understanding than is commonly provided by textbooks on the subject.

[@njwildberger]

The Klein bottle is hard to visualize in our three dimensional space, but it is not too surprising that the computation of its homology shows that there is no two-dimensional hole---this corresponds to the fact that we can go from this inside to the outside of the bottle in the space. The 2Z component of the first homology shows there is a loop/cycle which does not bound a disk, but if you traverse it twice, then it bounds a disk. Thinking of the middle loop of a Mobius band might help.

[@tmc03186]

I have watched the whole series and benefited a lot as a non-math major. Thanks a lot and I couldn't wait to see AlgTop35+

[@張展豪-s9l]

Thank you Professor Wildberger. Your lectures on algebraic topology are clear, inspiring and well-linked. I learn a lot from this set of lectures and I am looking forward to your lectures on 3-d manifolds. Thank you!

[@Crasshopperrr]

Oh wow, thank you so much! Very clear exposition of some things I've wanted to understand for some time.

[@njwildberger]

It is a very complicated issue. There are combinatorial methods, as well as algebraic ones: the fundamental group plays a big role, as does homology and homotopy. Geometric methods are important--in particular hyperbolic geometry. Analytic methods have dramatically changed the subject in the last decade. Basically though we are still very far from understanding 3 manifolds anywhere near as well as 2 manifolds (surfaces). Hopefully I will talk about this direction in a future year!

[@2pizen]

Dear Sir, it has been 10 years since your wonderful series! Self propelled topologists are forever grateful! Did the followup series on manifolds make it to youtube?

[@mistershoujo1235]

Thank you for the wonderful series, Prof. Wildberger! I learned so much!

[@WildEggmathematicscourses]

You are welcome!

[@vainoshaumbwa7556]

These lectures gave me the better understanding of computational homology. Thanks to the Prof

[@francescoapg]

Thank you very much for sharing this series

[@yurihe4978]

Thank you very much prof. Njwildberger. I really love your lectures, it help me understand homology much better. Waiting for >36~

[@shubhamnamdeo6280]

Excellent lectures for understanding the basic ideas behind the of Homology of topological spaces. Thanks!

[@johnstroughair1972]

Great course, I really learned an incredible amount. I am really looking forward to the continuation if it is going to appear.

[@njwildberger]

Thanks John, I am too busy with other projects right now to continue this one. But you can join the Algebraic Calculus One course, which is also very exciting. The videos are at Wild Egg mathematics courses (my sister KZbin channel).

[@haminatmiyaxwen]

Thank you professor for your advice, i have a excellent ground in Calculus and Linear Algebra, with matrices and eigenvalues etc.

[@baharjafarizadeh9464]

Perfect, I really enjoy it when you explained the projective plane. Thanks

[@Cm-cv4bk]

Sir, your lecture series is excellent. I have attended all lectures of topology up to 40 lectures but for 3 dimensional topology, I did not found the lecture series, Please let me know, whether you have uploaded the lectures for 3 dimensional topology?

[@ghazan555]

I learn a lot from your lecture series and I will say you are my teacher , please send me some exercises on these lecturer series every thing is fine but I want to do exercises to warm up myself .Thanks

[@World-of-Delusion]

After many years of being your student, I have finally watched and understood almost everything in this series. Alg. top. is very beautiful. Are you still planning on continuing with higher dimensional manifolds?

[@debajyotichoudhuri7896]

Excellent work! I was wondering if any of your videos anywhere has a bit about the Poincare polynomial?.

[@haminatmiyaxwen]

Thank you so much Professor for these lectures, i am 16 years old a junior in high school and i myself is studying Algebraic Topology, it is a very interesting subject. I believe mathematics is beautiful. Also professor, what would you recommend for me, continue my learning in Algebraic Topology or Algebraic Geometry?

[@s.krishna1036]

These lectures are wonderful and really helpful!! Thanks so much for posting them! Is it possible for you to post some lectures on cellular homology? Thanks again!!

[@AnastasisKr]

Thank you very much for the great lectures :)

[@LuisFontes]

Excelent lectures. Thank you very much

[@irshadmangetti8928]

Thank you, this set of lectures was really useful. Do you have lecture/s which discuss cohomology and cup product?

[@Pygmygerbil88]

So generous of you sir.

[@ghazan555]

Very nice lecture series and hats off sir ,

[@Science4allOrg]

Thank you for this lecture. It was fantastic.

[@ayan849]

Wonderful lectures. :) Thank you so much for posting.

[@tanchienhao]

amazing series! thanks alot!!

[@vivekshaw2437]

Awesome Lectures

[@JayadeepShitole]

Really Nice lectures Professor!

[@njwildberger]

At your age, probably you should get a good grounding in calculus and linear algebra. But of course otherwise you can just study whatever interests you!

[@kabayakawa]

Thank you for lectures

[@brendawilliams8062]

Thank you

[@njwildberger]

That won't be for another year or two, probably!

[@herosalhAssa]

is there any lecture about cohomology groups?

[@TheKatiePv]

@Insights into Mathematics: sir, please correct me if I misunderstand, but I don’t think that diagram of torus is a delta-CW because of the orientation failed. The edge c should be go the opposite way?

[@ursashiroy6149]

extremely helpful videos

[@RaghadAlNouri]

I got it, Thanks.

[@explo727]

thank you so much!!!

[@khardaniali7061]

thank you. i need this.