These series just keeps getting better and helping me understand topological data analysis and geometric deep learning. Have a wonderful Easter Sir.
Aahh! Finally a lecture on cohomology! Really excited to learn this from you! Thank you professor ♥️
This series has been helping me ton with my PhD oral exam preparations! I just hope a couple more get released before Tuesday... :D
Unfortunately we won't have the next lecture until later next week. All the best on your oral exam and PhD. You'll rock it! 👊🏼
How many more videos will there be in this series? I hope we get to see more of chapter 3 (and 4), these lectures are gold..
Around 3 more. We'll spend the next couple lectures on the cup product.
I have an additional question, how is your boardwork so clean? Do you have a rough idea of how much you are going to fit in one board? I just wing it and it ends up being very messy.
I sketch notes on my iPad ahead of the lecture, giving me a rough idea of how I'll arrange the content on the boards. But I also do plenty of winging it.
I am from India and have advanced topology along with Algebraic Topology in my MSc last year . Your videos are amazing and helping me a lot to overcome the difficulties in Algebraic Topology .
absolutely love these lectures!
Finished it! It was an amazing lecture! ♥️
Great Video! But what does it mean for the group hom(Z,Z) to be isomorphic to Z? Aren’t they groups of maps to groups of functions? Sorry if this is a dumb question, as I have a weak abstract mathematical background
hom(Z,Z) is the group of homomorphisms from Z to Z. As explained in the video each homomorphism f in Hom can be characterized by an integrer via f(1) =n. Therefore there is a bijection n f between Z and Hom(Z,Z).
Not a dumb question; they’re isomorphic but certainly not ‘equal’. One consists of a set of integers, the other a set of maps from the integers to the integers. To add to the above comment: they’re not just in bijection (non-isomorphic groups can certainly be in bijection); the natural map that bijects them is a homomorphism since f_(n + m) = f_n + f_m since they agree on 1 (they both send it to n + m).
Much appreciated thing. Thank you Professor! 🙂
Sorry professor late this time not gonna watch this video right now currently enjoying my vaccation travelling vietnam. My favourite hobbie after math is travelling. To this date i have travelled 2 countries internationally thailand and vietnam. Being in vietnam i feel like a billionare. Also thanks for the lecture in advance.
Thanks for this!
Anthony 🙇
Waiting for The Sun, waiting for next lecture😊
30:48 Yes, you can check it if you like… but you can instead just remember that contravariant represented functors preserve coproducts 😉 (a fact I learnt only very recently!).
really, its unexpected.
I start watching your series here. I learnt the relationship of cohomology and homology. I will watch the whole series because it helps a lot and saves me some time to read books later. Good work!