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Calculus distilled into hours
- sudont 16y agoWith such a wealth of information available, to dive in one only needs the hardest things: a path and a reason. Anybody have insight into how to actualize these nuggets into some semblance of a self-learning course?
- T_S_ 16y agoThe key step with math is to do the exercises. Videos can get you interested, and help explain what you read, but that's it. In the end, you need a textbook, judged according to the quality of its exercises and then a maybe a study partner to make it fun and maintain commitment.
- katovatzschyn 16y agoAnybody have insight into how to actualize these nuggets into some semblance of a self-learning course? Buy Calculus by Micheal Spivak. Solve at least one problem every day. Make it ritual and a daily requirement. Watch MIT lectures for corresponding chapter you are on. To learn this, don't trouble over the path and reason at present. Buy the book and start. Right now. http://www.amazon.com/Calculus-4th-Michael-Spivak/dp/0914098918/ http://www.amazon.com/Calculus-4th-Michael-Spivak/dp/0914098... Buy it. To learn this- buy it and start. Right now.
- cma 16y agoWhich MIT lectures would you recommend that use Spivak?
- pinchyfingers 16y agoStrang's Calculus book is available for free. Is the Spivak book a much better resource? I'm not familiar with either one, but I've seen both recommended before. http://ocw.mit.edu/resources/res-18-001-calculus-online-textbook-spring-2005/textbook/ http://ocw.mit.edu/resources/res-18-001-calculus-online-text...
- b_emery 16y agoHaven't read his calculus book, but Strang's linear algebra book is the best math book I've ever read. It's actually readable! Certain chapters are available on line. Based on it I would definitely try his Calculus book if I needed one.
- InclinedPlane 16y agoStrang's Calculus book is fantastic. I bought it long ago merely to have it (having already learned Calculus).
- CamperBob 16y agoSpivak's book is more of an analysis text. If you are interested in mathematics, go with Spivak. If you're more interested in engineering or physics, you may be happier with Strang.
- mickdarling 16y agoI 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. :-)
- dantheman 16y agoI believe there was some work done using small talk to teach children physics where they were able to do quite complex things without having to understand calculus... can't quite find the link right now.
- b-man 16y agoTry looking at the constructionist articles, specially Papert's works, as there are a lot of them online[1]. Basically, the idea is that you can introduce deep mathematical concepts very early by adopting a more intuitive media. Also, take a look at McLuhan[2] to understand how the media shapes the message if you really want to go deep into it. [1] http://www.papert.org/works.html http://www.papert.org/works.html [2] http://en.wikipedia.org/wiki/Marshall_McLuhan http://en.wikipedia.org/wiki/Marshall_McLuhan
- ThomPete 16y agoSeymore Paperts Mindstorms program. Read the book it's brilliant. http://www.amazon.com/Mindstorms-Children-Computers-Powerful-Ideas/dp/0465046746 http://www.amazon.com/Mindstorms-Children-Computers-Powerful...
- amix 16y agoWhile 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: http://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/index.htm http://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-... 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).
- seancron 16y agoThanks for reminding me of those lecture videos. I have a linear algebra test tomorrow, Wednesday, and these videos will certainly help me study for it.
- kxs 16y agoI've to second that, it was a bit slow at times but overall pretty decent and far better than my university class. Is there anything similar for Analysis I and/or II?
- xenophanes 16y agoIn his lectures on physics, volume 1, Feynman explains differential calculus in like 5 pages. It's really good.
- mbm 16y agoIt's too bad Newton wasn't as succinct.
- korch 16y agoWhile that seems like a bad idea now, there's a very necessary reason for Newton doing it that way. Newton presented Calculus exclusively in the more complex language of Euclidean geometry in order for it to be taken seriously by the intelligentsia, the royalty, and clergy of the era, as well as to make a bold statement about the historical magnitude of his discovery. In that era, Euclid and Newton were the book ends bounding all that was known of mathematics and natural philosophy(proto-science). So of course he had to write it the same way way Euclid would. Euclid's manner of logic and geometrical reasoning was lauded and unchallenged by both the church and the king, so there would be no way to refute a proof built upon the same language. I think there are two levels of refutations which Newton was guarding against. First, it's the typical peculiar trait of mathematicians to achieve perfectionism in a proof. The margin for error is zero-it's either all right or it's all wrong. Everything you are working on is either the most important thing in the world, or utterly worthless folly. So it's a point of immense personal pride to present a work that is complete, irrefutable, and entirely self-consistent. Second, considering the political & religious climate of the time, had Newton shown calculus without Euclid, the religious implications could have easily blown up into a scandal because his physics starts the ball rolling in formally challenging several major foundations of Christian theology. If you consider that Newton and all professors of the era at Cambridge had to be approved as official clergy in the Church of England, so his job and his future career success would depend highly on not outraging his superiors. Many men who spark revolutions by challenging ancient power structures end up tragic martyrs. But Newton navigated that problem with equal mastery. He ended up the Master of the Mint, was elected to parliament, grew immensely wealthy, had the ear of the Queen, and became so famous that visiting foreign celebrities would mark him as the first person to visit upon arriving-even before the Queen! For many decades after the publication of the Principia, Newton in fact concealed the derivation of the calculus using mathematical terminology we would now easily recognize as being similar to our own. But he did write it all down, he just never published it. There's an interesting story about this manuscript. Newton's friend, the secretary of the Royal Society kept this paper in safekeeping and private. Leibniz once visited England before he was famous and influential, and Leibniz knew Newton's secretary and visited him in London. The secretary allowed Leibniz to read Newton's private manuscript, describing the derivation of calculus, which no other people had ever seen. Not too much later, after Leibniz returned to the continent, he published his own book demonstrating calculus. Newton recognized the plagiarism, Leibniz denied it, and they maintained an intense personal feud for the next 40 years.
- tiki12revolt 16y agoMy 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: http://www-math.mit.edu/~gs/PIX/cupcakematrixtxt.jpg http://www-math.mit.edu/~gs/PIX/cupcakematrixtxt.jpg).
- pgbovine 16y agowow, GS is the man! he still looks remarkably similar to the way he did almost 10 years ago when i took his class. EDIT (to make this post not as content-free): Prof. Strang keeps the hope alive that some distinguished faculty in top research universities still place an emphasis on great undergraduate teaching
- jackfoxy 16y agoGS is the Man! Watching his calculus and linear algebra course videos overclocked in VLC is a beautiful experience. What a great teacher.
- whimsy 16y agoThanks for making him cupcakes =) He's on my list of top five favorite teachers ever, and he teaches on the other side of the country from me. Incidentally, what makes that his favorite matrix?
- tiki12revolt 16y agoNo idea actually, but it was something he mentioned the first day of class. He introduced it as "K, the second difference matrix, and my favorite". That was good enough for us.
- Emore 16y agoAny similar clear presentation regarding probability theory? A struggling student studying randomized algorithms would greatly appreciate :)
- mnemonicsloth 16y agohttp://www.youtube.com/watch?v=r1sLCDA-kNY http://www.youtube.com/watch?v=r1sLCDA-kNY (lecture #1) The Indian Institutes of Technology have full video for a lot of their engineering curriculum on youtube.
- Emore 16y agoWatching. Thanks a lot, seems really useful!
- SkyMarshal 16y agoI'd also like to recommend an oldie but a goodie: Calculus Made Easy, 2nd Ed (1914) http://www.gutenberg.org/ebooks/33283 http://www.gutenberg.org/ebooks/33283 One of the best explained calculus texts I've read.
- plainOldText 16y agoWow. I can't believe I've watched all those videos in one time slot. :))
- sliverstorm 16y agoI 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 show you, but you still come away unable to solve all but the most basic problems.
- yojimbo311 16y agoAnyone 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.
- juiceandjuice 16y agoEvery calculus based physics book.
- yojimbo311 16y agoThanks, that helped.
- jwr 16y agoProf. Gilbert Strang is a great teacher — I am amazed at how well he explains complex concepts in a simple way. 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.
- RyanMcGreal 16y agoI 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. 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. 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. And then, 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. 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. 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. [1] http://ocw.mit.edu/resources/res-18-005-highlights-of-calculus-spring-2010/big-picture-of-calculus/ http://ocw.mit.edu/resources/res-18-005-highlights-of-calcul...