By: Jonathan Leirer
This past Fall I was enrolled in a course on Linear Algebra. It was one of my first experiences with abstract, proof-based math courses and the initial adjustment was difficult. I was unsatisfied with my own performance and competency in the material, so I started looking for outside sources to supplement my in-class experiences. Eventually I stumbled on to MIT’s OpenCourseWare. As luck would have it, OpenCourseWare had a Linear Algebra course complete with video lectures filmed in the Spring of 2005. Expectedly, the material from the MIT course did not perfectly correlate with the material from my course; however, the videos were broken down lecture by lecture with topic summaries, thereby allowing me to select the videos which covered the topics I wished to reinforce. I found this extremely helpful, especially since textbooks can often be unnecessarily terse and formal, while lectures tend to be more intuitive and informal. Once discovered, I used MIT’s OpenCourseWare on a semi-regular basis, not only to complement the courses I was currently enrolled in, but also to brush up on materials I haven’t seen in a few years, like Differential Equations.
For better or for worse, I am the type of student who likes to see material presented in more than one fashion. I feel as though my knowledge is more robust if I can understand the material from several different platforms rather than solely from the direction offered in class. As a result, it is not uncommon for me to go to the library and read other books on the same subject. I personally view it as a diversification of my knowledge and find that it leaves me with a greater degree of understanding. With the development of technology, I now have another arsenal of educational material to turn to – online lectures and lecture notes. Not only can I decide to crack open a book, but now I can watch a video lecture or download a lecture in PDF.
While the usefulness of the former has already been discussed, I have yet to praise the lecture PDFs. As loyal readers of this blog may know, I am preparing for a PhD in Economics. In doing so I have taken many math classes – in fact my other major is math- and while I find the material interesting, I often wonder how I will end up applying it to higher level economics. Again I turned to the internet and found my answers. Websites designed by and/or for perspective Economics PhDs are replete with online lecture notes from graduate courses in Microeconomics, Macroeconomics, Econometrics, and Mathematics, all written by economists. These resources fill a valuable niche that isn’t necessarily filled by textbooks. First they often tend to be more conversational than a textbook, lending themselves to readability without loss of rigor, much like the online lectures. Second the material is often specialized and adaptable. While textbooks can quickly become out of date, not to mention the time lag between the writing and the publication, PDFs are quick and easy to update and specifically tailored to that individual course. I know I have used lecture notes for material in Topology, Bounded Rationality, and Macroeconomic Theory, some for class and some for personal interests. My access to these PDFs helped give me a realistic idea of what will be expected from me mathematically in my graduate courses as well as inform my education today.
I think these resources are extremely valuable assets that can be made available with an attractively low marginal cost. In the case of video lectures, all you need is someone to man the camera every lecture for a term. Once you bear that sunk cost, the marginal cost of posting it on the internet is zero (assuming no one watches the video in lieu of attending MIT) while the marginal benefit is greater than zero. As for the lecture PDF’s, most, if not all, professors write out lecture notes already, maybe even already in PDF form (especially if they are used to writing in LaTex.) Again, the marginal cost is nearly zero (assuming no one reads the lecture notes in lieu of attending University X) while the marginal benefit it indeed greater than zero. I commend these efforts towards a more democratic approach to learning, and wonder what will be the effects on higher education.