While in university I took linear algebra and didn't understand much of it, especially on a deeper level. Then I stumbled upon Gilbert Strang's linear algebra lectures and watched them... After watching his explanations I got all of it and actually understood things at a much higher level. It was a sweet revelation and today I find linear algebra beautiful. I highly recommend watching his linear algebra lectures: <a href="http://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/index.htm" rel="nofollow">http://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-...</a><p>Edit: I also find linear algebra to be useful and much more important for programming/CS than calculus, especially for implementing various ranking algorithms (e.g. Google's PageRank algorithm is mostly rooted in linear algebra).
My friends and I love Gilbert Strang. So much so, that last year during his 18.085 class we made him cup-cakes for his birthday. (see: <a href="http://www-math.mit.edu/~gs/PIX/cupcakematrixtxt.jpg" rel="nofollow">http://www-math.mit.edu/~gs/PIX/cupcakematrixtxt.jpg</a>).
I struggled with high school calculus. I just couldn't wrap my head around the concept. My teacher kept making noises about "rate of change" but it made no sense. Luckily for me, I was taking physics at the same time, and we ran an experiment to calculate acceleration due to gravity.<p>So we ran the experiment with a weight and a ticker tape and a little hole punch tool and we got these data sets measuring the distance between each consecutive hole on the tape. Plotting distance against time on a graph, we produced a curve somewhat reminiscent of a y = x^2 function.<p>Then, given d2, d1, t2 and t1, we were able to calculate a set of velocities between each point. Plotting velocity against time on a graph, we produced a sloped line somewhat reminiscent of a y = 2x function.<p>And <i>then</i>, of course, given v2, v1, t2 and t1, we were able to calculate a set of acceleration rates between each point. Plotting acceleration against time on a graph, we produced a horizontal line somewhat reminiscent of a y = 2 function.<p>Then it hit me. Looking at the three graphs, in a flash I suddenly understood exactly what "rate of change" meant. I understood why d(x^2) = 2x, and why d(2x) = 2. Calculus made perfect sense, and I plowed through all the exercises that had plagued me since the start of the year.<p>So when I clicked on the first video in this OCW set [1] and watched Professor Strang put distance/speed and height/slope side by side as his two canonical examples, a big smile spread across my face.<p>[1] <a href="http://ocw.mit.edu/resources/res-18-005-highlights-of-calculus-spring-2010/big-picture-of-calculus/" rel="nofollow">http://ocw.mit.edu/resources/res-18-005-highlights-of-calcul...</a>
I have been intermittently trying to teach my 6 year old niece calculus graphically. She can visually tell what the slope of the curve is and filling in the area under the curve is, well child's play. :-)
I'd also like to recommend an oldie but a goodie:<p><i>Calculus Made Easy, 2nd Ed (1914)</i><p><a href="http://www.gutenberg.org/ebooks/33283" rel="nofollow">http://www.gutenberg.org/ebooks/33283</a><p>One of the best explained calculus texts I've read.
With such a wealth of information available, to dive in one only needs the hardest things: a path and a reason.<p>Anybody have insight into how to actualize these nuggets into some semblance of a self-learning course?
Prof. Gilbert Strang is a great teacher — I am amazed at how well he explains complex concepts in a simple way.<p>Does anybody know of a similar resource on probability, especially the Bayesian approach? All I could find were lectures of significantly worse quality than prof. Strang's teachings.
Anyone happen to know a good resource that takes a single problem to show how Geometry, Algebra, and Calculus can each be used to solve it? I'm hoping for something that can quickly demonstrate how each builds on the other to get better and faster results.
I haven't watched the videos, but be wary of anything that claims to simplify math into some awesomely brief time frame. In my experience you come away with a conceptual understanding, but no ability to apply it. Convolution, for example. 99% of pages on convolution spend a long time describing what it represents, and using nifty animations to <i>show</i> you, but you still come away unable to solve all but the most basic problems.