The Math Sorceror on Topology by Munkres

Here's my comment:

I studied an undergraduate course based on Sutherland's book An Introduction to Metric and Topological Spaces. For some reason I really liked that book, but I never understood what the course I was studying was actually supposed to be about. It was just a bunch of proofs of theorems that seemed kind of random to me. Like we were just making these definitions and proving theorems about them without having any real goal. Since then I've started to see that what it is really about is analysis on sets and Poincaré's and Dirichlet's attempts to make this rigorous. But the course I did didn't have any of this historical context, so it just seemed like a vague association of disconnected ideas all called "topology" and not always for the same reasons!

The other day I saw a really interesting Biography of Poincaré in a bookshop. It may have been this one: Henri Poincaré: A Scientific Biography by Jeremy Gray. The course I studied was Open University M435 An Introduction Metric and Topological Spaces and Geometric Topology.

Maybe students could try writing solutions to exercises as proofs in Lean, then they would at least know that they hadn't done anything really stupid in their solutions. See https://leanprover-community.github.io/undergrad.html and Daniel Tubbenhauer on Computer Aided Mathematics.

Here is a playlist of his videos about Topology.

Subscribe to The Math Sorceror.

Here's Norman Wildberger explaining why the Fundamental Theorem of Algebra is really a half-baked conjecture about point set topology.

Subscribe to Insights in Mathematics.

Here's what people are doing now: see Langlands program and Quadratic reciprocity. This is part of an interview with Edward Frenkel.

Subscribe to Theories of Everything.

Comments

Post a Comment

Popular posts from this blog

Live Science - Leonardo da Vinci's Ancestry

Image
... and his posterity too? See  On Communication in Linear Time And Hypertext And The Gospel of Sophia . So it looks like El Cielo of the cistine [sic!😂] chapel is not the limit anymore.  I think I just met one of his descendents. A guy called Versailles Toledo who is from Chiapas. That might explain the murals I mention in my recent untitled post , just before the post mentioning this video. I also just took this photo of Rafael Gonzales, born here in Tecate, B.C., who told me about a spring near here called Agua Fría , half way from Tecate to Loma Tova , where, a few decades ago, people used to go to have barbecues and stuff, but now he thinks it may be private land. If someone reading this has a Facebook account, please write a link to this post onto his FB page. To see why I took the photo, look at his T-shirt and the horse-shoes and ponder this: Subscribe to BeatrizER and her video(s?) about mathematical logic, ... Sounds like Edith (II) Rix has been online all the t...
Read more

David Turner Obituary by Sarah Nicholas Fri 24 Nov 2023

Image
This was in The Guardian: David Turner obituary , only eight days after I posted  David Turner Talking About Sixty Years of Functional Programming History : This talk was given in London in 2017: See  Turner, D. A. "Some History of Functional Programming Languages" also  John Hughes - Why Functional Programming Matters  and David MacQueen's talk at ICFP 2015 in  Numberphile - Sophie Maclean on the Catalan Numbers . At 10:30 This whole discussion abut combinator reduction is especially interesting. I didn't know Arthur Norman had tried building hardware for combinator machines. I'll look that up: maybe start here A.C. Norman  Faster combinator reduction using stock hardware  in LFP '88: Proceedings of the 1988 ACM conference on LISP and functional programming. At 26:25 on the ISWIM virtual machine implemented in the PAL compacting garbage collector?! This work Reynolds and others did was at MIT in Masecheusetts and Argonne National Laboratory ...
Read more