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All of the mathematics listed above is on the short list of what anybody following the Khan academy or the MIT open courseware would teach themselves. It's alr
by xiaoma 16y ago
All of the mathematics listed above is on the short list of what anybody following the Khan academy or the MIT open courseware would teach themselves. It's already been shared and organized into a curriculum, for free, by a number of different sources. In fact, I'd say the process of learning the software would be the bigger challenge for an independent learner.
But even before the availability of those sorts of really convenient tools a lot of people have self-taught themselves past that level. In fact, I remember my abstract algebra prof telling us an anecdote to illustrate the importance of working through things on our own instead of waiting to see what was presented to us in our courses. He talked about a grad level course that he had been teaching for the past 10 years. Clearly, he knew the material inside and out, but the interesting thing is that he had never taken it himself as a student. How did he do it? He read a couple of books about the topic! It's a time-tested method.
I'd say if people aren't learning the math it's because they underestimate its importance. Either that, or people like me (and maybe you) overestimate its importance.
- 9oliYQjP 16y agoI'm a university dropout, but the level of linear algebra, multivariable calculus, and discrete math that I did take before leaving school is so far above and beyond what Khan academy currently offers. With the exception of Calculus, Khan academy is up to about where my public high school curriculum left me. Its calculus offerings are impressive and definitely cover my first year calculus courses. I've never been able to make much use of OpenCourseware because it doesn't fit my learning style. Don't get me wrong, I'm not holding anything against Khan academy. But it's quite impressive that it will eventually cover all the material in university that I had to pay to learn. There is a huge collision that's about to happen: increasing costs for post-secondary education; a middle class that will no longer be able to afford said post-secondary education for their kids; and free, quality, ubiquitous educational content like Khan academy. I'm not quite sure how things will play out. But things like Khan academy could pop the educational industry bubble, at best forcing lost cost quality formal education, and at worst, resulting in ubiquitous access to informal education to those that put in the effort.
- neovive 16y agoGreat points. There is definitely a shake-up in Education on the way. The high-cost, middle-tier, universities are already feeling this and it will only expand. The key to self-education is effort. It's much easier to be forced to take classes, do assignments, sit through lectures and take exams. It's much harder to have the self-discipline to do this on your own.
- zenocon 16y agoSelf-education, discipline, etc. require passion. This could apply to your coursework at MIT or downloading copyrighted technical textbooks off USENET for free to teach yourself mathematics and programming, etc. The internal drive is the differentiator...not so much where you came from.