
Calculus distilled into hours - peterbotond
http://ocw.mit.edu/resources/res-18-005-highlights-of-calculus-spring-2010/
======
amix
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:
[http://ocw.mit.edu/courses/mathematics/18-06-linear-
algebra-...](http://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-
spring-2010/index.htm)

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
Thanks 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.

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tiki12revolt
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: <http://www-
math.mit.edu/~gs/PIX/cupcakematrixtxt.jpg>).

~~~
pgbovine
wow, 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
GS is the Man! Watching his calculus and linear algebra course videos
overclocked in VLC is a beautiful experience. What a great teacher.

------
RyanMcGreal
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.

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-
calcul...](http://ocw.mit.edu/resources/res-18-005-highlights-of-calculus-
spring-2010/big-picture-of-calculus/)

------
mickdarling
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. :-)

~~~
dantheman
I 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
Try 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> [2]
<http://en.wikipedia.org/wiki/Marshall_McLuhan>

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xenophanes
In his lectures on physics, volume 1, Feynman explains differential calculus
in like 5 pages. It's really good.

~~~
mbm
It's too bad Newton wasn't as succinct.

~~~
nitrogen
There is another post in response to this comment containing four full
paragraphs explaining why Newton wasn't succinct, but the post is now marked
as dead. If anyone familiar with the Leibniz vs Newton history wants to turn
showdead on in their HN settings and read the post, I'd appreciate commentary
on its accuracy and origins (and, perhaps, an explanation of why it was
killed).

~~~
mhartl
Based on my reading of Jim Gleick's biography _Isaac Newton_ and my background
as a theoretical physicist, I believe your comment is essentially accurate. In
particular, Newton's desire to connect calculus with Euclidean geometry is
certainly correct. As you note, the _Principia_ eschews calculus in favor of
geometric arguments: Newton used calculus for his private calculations and
then translated the results into more conventional geometry to meet his
audience's expectations. I'm not sure about the religious aspect, but Newton
was privately a heretic (he believed in a unitary god—an awkward belief for a
professor at Trinity College), so he definitely knew how to placate the
religious authorities. Finally, the Leibniz anecdote is new to me, but it
sounds plausible.

In any case, I don't think your comment should have been killed.

~~~
nitrogen
_I believe your comment is essentially accurate._

I can't take credit for the comment. It was posted by HN user korch. I only
wanted to know if it was correct.

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SkyMarshal
I'd also like to recommend an oldie but a goodie:

 _Calculus Made Easy, 2nd Ed (1914)_

<http://www.gutenberg.org/ebooks/33283>

One of the best explained calculus texts I've read.

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sudont
With 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?

~~~
katovatzschyn

       Anybody 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/0914098...](http://www.amazon.com/Calculus-4th-Michael-
Spivak/dp/0914098918/)

Buy it. To learn this- buy it and start. Right now.

~~~
pinchyfingers
Strang'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-
text...](http://ocw.mit.edu/resources/res-18-001-calculus-online-textbook-
spring-2005/textbook/)

~~~
InclinedPlane
Strang's Calculus book is fantastic. I bought it long ago merely to have it
(having already learned Calculus).

------
Emore
Any similar clear presentation regarding probability theory? A struggling
student studying randomized algorithms would greatly appreciate :)

~~~
mnemonicsloth
<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
Watching. Thanks a lot, seems really useful!

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jwr
Prof. 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.

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yojimbo311
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.

~~~
juiceandjuice
Every calculus based physics book.

~~~
yojimbo311
Thanks, that helped.

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sliverstorm
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 _show_ you, but you still come away
unable to solve all but the most basic problems.

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plainOldText
Wow. I can't believe I've watched all those videos in one time slot. :))

