I wanted to learn 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’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 found the MIT OCW for 18.965 entitled Geometry of Manifolds, that was taught by Prof. Mrowka in the Fall of 2004. The MIT OCW materials provided there are excellent. 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.
I invite anyone who’s serious about learning or engaging in Differential Topology to share in my discussion and struggle.