Mathematics and Physical Sciences Education
It's been quite a while since I've made a blog post. The cliche excuse would be to say that I've been snowed under with real life tasks. This is only partly true. Regardless, I thought it was time to update you all on some of my recent musings involving education.
It is quite clear that I am passionate about education, particularly in the fields of mathematics and physical sciences. My blog post on learning theoretical physics has turned out to be my most viewed post so far. Given that my background is in the physical sciences, I thought it was time I did something to contribute to the world's pool of knowledge beyond writing a few blog posts and handing in a thesis.
Having spent a lot of time on communities such as Hacker News and Slashdot I have come to realise that there is a growing thirst for online learning materials, particularly in the scientific arena. Organisations and movements like Khan Academy, MIT OpenCourseWare and Open Culture are pioneering a new era in education.
At this stage, I still don't feel like it is possible for autodidacts to achieve the same level of knowledge as that achieved by a graduate student finishing a masters-level science degree. The reasons are clear: It is a "niche market", the effort involved in providing a similar experience is substantial and crowdsourced methods at these levels would probably devolve into frivolous discourse and petty argument.
Thus I have taken it upon myself to correct this problem. I have decided to undertake the rather ambitious task of writing an entire set of lecture notes, question sheets, exam-style handouts and video lectures for a top-tier undergraduate mathematics and physics degree. Depending upon my free time availability, this task will not likely be "complete" for a long time. This does not matter. Every day adds a new sentence to the project and hence more knowledge than yesterday.
I won't pollute this post with an extensive map of all subjects with their hierarchical relationships, but I will provide a brief overview of my short term plan and the progress made so far. My rationale is that there are plenty of courses on Calculus/Linear Algebra 101 around the net. Khan Academy provides a great set of Linear Algebra videos as does Gilbert Strang at MIT. I do not want to reinvent the wheel just yet.
On the other hand, 200+ level courses are severely lacking. Thus it seemed appropriate to apply my areas of expertise to write some notes on the more advanced undergraduate subjects. Topics that I can provide solid information for include Vector Calculus, Partial Differential Equations, Fluid Dynamics, Numerical Linear Algebra, Classical Mechanics and Relativity. This is where I have decided to begin.
Fast-forward two months from my initial foray into online education and I have almost finished my first chapter of "Vector Calculus", discussing vector differential operators (grad, div, curl, Laplacian). The experience has been extremely insightful. I've written it from the perspective of a mathematician, rather than an engineer or physicist, and I had (almost!) forgotten the necessary level of precision required. It has forced to me fully understand a concept before committing it to text.
The notes will eventually reside at a domain I purchased a couple of years ago. I intend to output them both in PDF and in HTML/JS form, using the brilliant MathJax library. I also hope to gain a large number of "long tail search" visitors via SEO, as many of the niche mathematical terms are not competitive. If I gain enough in donations, then I may be able to purchase one of these to film video lectures!
I will stress now that the resources will always remain free in the sense of beer and speech. There will be no restrictions on usage or downloads - this is a core component of the idea. It is my way of returning the favour for all of the open source software and educational resources I have utilised over the years. This is not a startup - it is an educational resource that everyone can access and it will always remain so.
If anybody is keen to get involved with this project, particularly if they have extensive subject expertise in Pure Mathematics (Topology, Algebra), Statistics, Computer Science or Engineering, then I would be very keen to hear from you. Let's see what we can do to educate the world!