I wanted to learn more about Differential Topology. I was out of school as I already completed my Masters thesis and received my Masters in Physics from Ludwig Maximilians-Universität München (LMU) this past year (2014). I wanted more tools in my toolbox as a physicist and to include differential topology, from the mathematicians’ perspective, in it. I found the MIT OCW for 18.965 entitled Geometry of Manifolds, that was provided by you, in the Fall of 2004. The MIT OCW materials provided there are excellent. I’m a big believer in MIT’s OCW (Open CourseWare) and MOOCs (Massively Open Online Courses), in that for anyone who’s serious about learning should have access to free, open, and the best education materials and fellow students, instructors, scholars, researchers, regardless of age, nationality, or socio-economic circumstances. I do not seek to reinvent the wheel. What I want to try to do is to try to bring openly online what seems to be missing in the MIT OCW, but is integral in elite university education: the discussion class, the TA session (teacher’s aid), the student group collaboration, what I’ll term the Übundgruppen. This grows out of my own need for feedback, positive and negative, in my quest and struggle to learn Differential Topology on my own. I don’t know what the right form or formulae for this should be but I’ll do what I can by blogging, tweeting, typing up LaTeX notes open to anyone to read and edit. The format that I’m falling back on is a single pdf file, compiled from LaTeX, where I put all my notes, thoughts, references, exercises worked out, problems and solutions, in a single place, which I’ll make available openly online for anyone to read and edit, and I hope anyone who’s also serious about learning Differential Topology will benefit from an online, collaborative effort. I’ll blog and tweet pieces from this pdf/LaTeX file on a number of social media platforms, but I have not seen an internet platform that makes scientific publishing easy. It wastes my time to reformat my LaTeX file onto wordpress or tumblr. I will just point to my single pdf/LaTeX file which I’ll make available publicly and openly always on Google Drive. (links below) LaTeX file for my Übundgruppen “notes” for MIT OCW 18.965 pdf file for my Übundgruppen “notes” for MIT OCW 18.965 ernestyalumni Google Drive folder for materials on MIT OCW 18.965 I wanted to invite you to give me any and all positive and negative feedback on how I’m learning, what I should be learning, what books I should be reading, what I’m doing wrong, what’s the latest cutting edge that mathematicians are researching in Differential Topology, and where physicists and maybe even engineers could benefit in their own respective research from Differential Topology. Thank you for your time, any and all positive or negative feedback is welcomed. Note: I'm posting on wordpress concurrently; really I haven't found an internet platform that's perfect for scientifically writing; I work with what I can: https://ernestyalumni.wordpress.com/2014/11/27/on-mit-ocw-18-965-the-geometry-of-manifolds/
