Today, yet another question was posted on Math.Stackexchange (this time by the new user avatar) asking for topology references. This has been asked a few times before, but somehow the answers are a little bit different. So, as if I were responding to Ramana Venkata’s post on the meta about a consolidated topology resource, based upon the answers at MSE, and to facilitate topology references in the future, I am writing this blog post.
To be clear, this is a compilation of much (not all) of the discussion in the following questions (and their answers): best book for topology? by jgg, Can anybody recommend me a topology textbook? by henryforever14, choosing a topology text by A B, Introductory book on Topology by someguy, Reference for general-topology by newbie, Learning Homology and Cohomology by Refik Marul, What is a good Algebraic topology reference text? by babgen, Learning Roadmap for Algebraic Topology by msnaber, What algebraic topology book to read after Hatcher’s? by weylishere, Best Algebraic Topology book/Alternative to Allen Hatcher free book? by simplicity, and Good book on homology by yaa09d. And I insert my own thoughts and resources, when applicable. Ultimately, this is a post aimed at people beginning to learn topology, perhaps going towards homology and cohomology (rather than towards a manifolds-type, at least for now).
Posted in Math.AT, Mathematics, SE
Tagged algebraic topology, general reference, math, math.stackexchange, mathematics, mathoverflow, reference, reference-request, topology
I’ve come to realize that I’m always tempted to start my posts with “Recently, I’ve…” or “So and so gave me such and such a problem…” or “I happened across this on…” It is as if my middle school English teachers (all of whom were excellent) succeeded so well in forcing me to transition from one idea to the next that I can’t help it even today. But, my respect for my middle school teachers aside, I think I’m going to try to avoid that here, and just sort of jump in.
Firstly, as announced at Terry Tao’s Blog, two new polymath items are on the horizon. There is a new polymath proposal at the polymath blog on the “Hot Spots Conjecture”, proposed by Chris Evans, and that has already expanded beyond the proposal post into its first research discussion post. (To prevent clutter and to maintain a certain level or organization, the discussion gets cut up into 100-comment size chunks or so, and someone summarizes some of the key points in the header each time. I think it’s a brilliant model). And the mini-polymath organized around the IMO will happen at the wiki starting on July 12.
Now, onto some number theory – (more…)
Posted in Math.NT, Mathematics, Open, Polymath
Tagged abc conjecture, euclidean algorithm, goldbach conjecture, helfgott, math, mochizuki, number theory, polymath, tao, ternary goldbach
The Math.Stackexchange (MSE) is an extraordinary source of great quality responses on almost any non-research level math question. There was a recent question by the user belgi, called A list of basic integrals, that got me thinking a bit. It is not in the general habit of MSE to allow such big-list or soft questions. But it is an unfortunate habit that many very good tidbits get lost in the sea of questions (over 55000 questions now).
So I decided to begin a post containing some of the gems on integration techniques that I come across. I don’t mean this to be a catchall reference (For a generic integration reference, I again recommend Paul’s Online Math Notes and his Calculus Cheat Sheet). And I hope not to cross anyone, nor do I claim that mixedmath is to be the blog of MSE. But there are some really clever things done to which I, for one, would like a quick reference.
Please note that this is one of those posts-in-progress. If you know of another really slick bit that I missed, please let me know. And as I come across more, I’ll update this page accordingly.