Introduction to Algebraic Topology | Algebraic Topology 0 | NJ Wildberger

This is the full introductory lecture of a beginner's course in Algebraic Topology, given by N J Wildberger at UNSW. The subject is one of the most dynamic and exciting areas of 20th century mathematics, with its roots in the work of Riemann, Klein and Poincare in the latter half of the 19th century. This first lecture will outline the main topics, and will present three well-known but perhaps challenging problems for you to try.

The course is for 3rd or 4th year undergraduate math students, but anyone with some mathematical maturity and a little background or willingness to learn group theory can benefit. The subject is particularly important for modern physics. Our treatment will have many standard features, but also some novelties.

The lecturer is Assoc Prof N J Wildberger of the School of Mathematics and Statistics at UNSW, Sydney, Australia, well known for his discovery of Rational Trigonometry, explained in the series WildTrig, the development of Universal Hyperbolic Geometry, explained in the series UnivHypGeom, and for his other YouTube series WildLinAlg and MathFoundations. He also has done a fair amount of research in harmonic analysis and representation theory of Lie groups.

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[njwildberger]

An excellent text is Allen Hatcher's book Algebraic Topology, available online for free. While it differs considerably from this course, it probably complements parts of it in a good way.

[iwakira]

Professor Wildberger, I watched all the videos in this series of Algebraic Topology. I thought that I would never understood the subject, but now I feel that I know the subject very well! I would like to thank you for that. Please keep unloading great videos like this. Sincerely.

[RenormalizedAdvait]

Without doubt Prof. Wildberger is the best math professor in this platform, what a crystal clear insight!

[mechwarreir]

Thanks for uploading these! My search in finding a topology lecture series was actually very difficult.

[ClickLikeAndSubscribe]

I have to say this is the first online lecture I have ever seen on the internet machine that is well explained and illustrated, and properly paced.

[CultMechanicus]

Thank you for the lecture I'm quickly finding mathematics a sanctuary.

[pby]

Thank you for sharing this. You explain things really well. Greg, from Arizona.

[waynedick]

I am going to watch your course. It will help my matroid studies. I think the tetrahedron is the most interesting solid because of it is the minimal enclosure. Finally, the Euclidean plain is pretty interesting too.

[aretwodeetwo]

What a great professor. I'm jealous.

[jmafoko]

great introduction to difficult subject with nice puzzles. great motivation. the only motivation I had was I heard topology may help understand manifolds(classification of manifolds).

[xy]

I have watched two hours of these lecture series and can say that they are a good introduction to a subject for a general interest. They also do not require any remarkable prerequisites. Amateur mathematicians with a common sense should be able to follow easilly. However, in my opinion, the definitions and proofs are not rigorous sufficiently. So if you want to learn Algebraic Topology seriously I recommend a deeper material, even if you just want to start learning it.

[saucytommy]

How fascinating. One shape can be any with Topology.

[davlatkamoliddinov]

Very good lecture because professor very very best

[Shahalilchi]

U R amazing, i wish U give more lectures in manifolds or more general in geometry.

[_GrayBear_]

_Outstanding._  And I couldn't be more grateful for this wonderful resource you've shared with us!

(But I have to admit, I am praying that the camera work improves.  2.5 minutes into this and the cameraman is skilling me.  Zoom _out, _ please!  And stay still!)

[sanjursan]

Good Stuff!! Maybe second (Loyd) puzzle would be easier to explain backwards. I mean have the pencil/loop assembled with the shirt FIRST. The puzzle then is to remove the pencil from the shirt etc.

[drivanovich]

Thank you for commenting back and the AMAZINGLY clear lecture. I know how to cut and bend the paper to make it look like the problem. I don't know which lecture to watch to have the topology behind it explained. Everything I have read about topology says an object can be bent, stretched, or twisted but not cut or torn. In problem one you are cutting the paper. Is it still the same shape as the original paper?

[gdiwakar]

Hello sir, thanks for your
As in continuation to our previous talk i wanna to add one more fact i have elctronic engineering as my background knowledge.  And interested to work in image / signal processing....Does the help that you have suggested ( WildTrig series on rational trigonometry, and the UnivHypGeom series ) will be easily understandable to

[njwildberger]

No it is not the same shape. The problem's aim is to get you to think geometrically in three dimensions, and to appreciate the potential richness in studying objects in space. Well done if you have solved it, I hope it was fun. Perhaps you can try it on your friends!

[alapandas]

The shirt problem is amazing. We have to fold the shirt around the hole and pass the hole over the pencil through the string loop and then unfold the shirt.