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.
Looked it up... It's a bit difficult for my level. What do you think of M. Henle's "Combinatorial topology" Dover book? Thanks for uploading your lectures on YT. I really like them :)
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.
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!
_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!)
Yes and no. The term "Topology" by itself can refer to a quite different subject more properly called "Point set topology" which is more analysis oriented, or to Algebraic Topology, which is more geometric and algebraic, and what we are learning here. I do not consider Point set topology a prerequisite for this subject, although it can be useful to shed light on certain concepts.
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.
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).
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.
i just found your channel, i read alittle about Algebraic Topology. Im definitely interested in it, i have a real love for mathematics. i have studied Complex Analysis, Advanced Real Analysis, Advanced Mathematical Analysis, Advanced Calculud 1&2, Advanced Engineering Mathematics, Locally convex Spaces, Abstract Algebra, Topology. As well undergraduate and graduate level mathematics.
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.
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?
Hello sir, thanks for your help...... 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 me.......
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.
You should have some mathematical maturity, that is to say, have done some undergraduate mathematics courses at a higher level. You should have seen some abstract algebra, although I will be reviewing most of what you need, but not developing it. In particular having had a course in group theory, or being able and willing to learn, is desirable.
Hello Sir, I am a Ph.D candidate....want to work on topological field in the topics of 2D and 3D image processing.........Whether these lecture videos are sufficient or rather i have to go a book....but which one please help me?? I am very fascinated to work on this topic
You should make sure to also learn some geometry besides topology. Probably a good idea to go through the WildTrig series on rational trigonometry, and the UnivHypGeom series, which will give you a good grounding on projective geometry. As for a book on Alg Top, I recommend Hatcher's Algebraic Topology, available online.
Professor. Are 'Set theory' and 'Point-set topology' prerequisite courses for studying this course, 'Algebraic topology'?? (I have watched and studied the courses of yours like 'Rational trigonometry' and 'Hyperbolic geometry'.) If 'Set theory' and 'Point-set topology' are the subjects which i have to learn, would you recommend some books or videos for self-study(cause i'm a engineering students who really loves theoretical physics and mathematics so i can't attend the mathematics classes of my university.) Thank you for your videos.:)
+Christopher SIMON Not a chance. That is not even a proper mathematical object. See my MathFoundations series for a discussion, and in fact in the next dozen videos I will be talking a lot about big numbers and the meaninglessness of considered in "all" natural numbers as a completed set.
+njwildberger well that's a new set of videos to watch ! I'm not convinced for the moment, but i ll come back once i'll have seen them all. Great job anyway, thank you !
Which ones? I removed some of the earlier shorter videos as the same content is now in the longer full lecture series. The Playlist is Algebraic Topology, or AlgTop for short.
Let's assume the hole is big enough in which case we would slide it through the loop, then through the hole, other side, then along the loop, then again the other side, the hole again, loop again and we would have two balls together. But the hole is too small. The only transformation that is possible but I cannot visualize it would be to make the loop bigger and tilt one side of the wood through it. It does not look promising. Or to push the whole wood through the loop (and hope for the best). Who can visualize all of this he is a true topologist.
@jovan jelic It is not easy but by continuing to think about it you can understand it better. Another thing to try is to actually make a model : tape a piece of string firmly to the end of a pencil --making sure the loop is not long enough, and then try it out yourself on an old shirt!
@@njwildberger yes, but that would be a Poor Man James Bond approach. I think topologists see everything in their head, even higher dimensions. A friend who had all 10 marks in Math undergraduate once told me he could see 11 dimensions (but at about the same time I found out he got schizophrenia - he was teaching a class once and then started to draw little flowers after equations as he lost touch with reality - , so I was never quite sure if this was realistic or his imagination). I'll continue to visualize it but I am 99% sure I won't be able to solve it visually in my head. Are you referring to the 3rd problem (torus made of wood)?
@@njwildberger oh, I was referring to Problem 3. I was thinking to tilt and push the wood through the loop or slip the loop on the wood all the way down like putting sockets on, but I cannot visualize any of that or what the final result would be i.e. it is a pure guessing, but it looks like the only possible transformation.
