
Need to refresh your math skills? From basic algebra to calculus and beyond. - chaosmachine
http://www.khanacademy.org/#Linear%20Algebra
======
NyxWulf
For most people, they come out of high school not just poor at math, they come
out "Math Broken" as one of my friends puts it. The second you mention
anything to do with Math, their eyes glaze over and their brain completely
disengages. I think there are a lot of things that contribute to that, but
generally Math is not taught in a very approachable way. The KhanAcademy is I
think a very good start in solving that problem.

I came across this site through an article that was on HN sometime last year,
around November or December IIRC. Since then I've watched roughly 100 videos
on that site. Some of the Finance videos, Trig, and Pre-algebra as a
refresher, and I'm now roughly 60 videos into the Linear Algebra videos. Even
though I'm in the midst of my master's program now, I've set a goal to watch 2
video's every day as time permits.

I am so impressed with this site, and with Salman Khan. The math is very well
done, but it's also very approachable. Most of the videos are roughly 10-15
minutes in length and are highly topical. That makes it easy to jump in and
pick up a refresher on something you haven't seen for a while. It's also great
for getting into something you haven't ever seen before. Personally I haven't
ever had Linear Algebra before, and if you've looked at many of the textbooks,
they are pretty dense, particularly if you are self learning. I've found this
site to be a great resource in getting oriented and it has really helped me
get some traction.

I have recommended this site to dozens of people, and while most of them don't
share my love of mathematics, they have been able to get some traction in
various problems by using this site as a supplement.

Anyway, as a daily user of the KhanAcademy, I can't say enough good things
about the site. I don't think it's a stretch to say it has the potential to
revolutionize how math is taught.

The one downside to the site I've noticed is the lack of problems sets. There
is a tester that will walk you up through the different topics, but unlike the
video's you can't just start where you feel you need to, you have to work up
through the early material, and that's fairly time consuming. I have a number
of other resource's I'm using for problem sets, but it would be nice to have a
few problems to work through for each video.

Overall an absolutely fantastic resource. Rating: 10/10

~~~
RiderOfGiraffes
I agree with everyone else that it's a fantastic resource and the material is
brilliantly presented, but I don't think it will help with the "Math Broken."
I'm absolutely not knocking the resource or the site, I can't say enough good
things about it, but if someone is already glazed over at the very mention of
math, I don't think the videos here will help.

If you think otherwise then I'd really appreciate a suggestion, as I have
someone I'd like to point at it ...

~~~
NyxWulf
I agree, I don't think it's the panacea for that problem. It's a start though.
The toughest things to get over imo, are the meme's that people will never use
math and/or that math is not useful in the real world. The KhanAcademy handles
the problem of insecurity about math and a gentler introduction to the topics
once someone is interested enough to consider learning it. How you instill
that initial desire and overcome their deep seated biases and insecurities
about it are a much harder problem.

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edw519
_With just a computer and a pen-tablet-mouse, one can educate the world!_

I'll say. Someone's been very busy. Thank you, Khan.

This appears to be an excellent resource. The 10 to 15 minute "bite-sized"
pieces make it easy to check something out in your spare time. Most definitely
bookmarked.

I also like how he has added a lot of business/finance stuff, which should
probably interest a lot of people here. Looks like a slight change of plans
today - I have to check more of this out.

[EDIT: I watched several videos in the Venture Capital and Capital Markets
section. Definitely worth my while. This teacher appears to be able to make
any topic, regardless of complexity, easy to understand. He even has a "happy
cursor", which reminds me of football quarterback Peyton Manning's feet when
he's getting ready to throw a pass. Funny how you can tell when an expert is
in the zone. I'm going to put together a schedule to watch a whole bunch of
these videos.]

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3dFlatLander
I'd like to add a very personal comment to this discussion. I have very bad
vision. So much so that in school, I couldn't see the board even when sitting
as close as possible. As a result, I'd end up creating notes from a synthesis
of what the teacher was saying and what I read in the book as the lesson was
going on. This usually didn't work out, and my math skills suffered.

This website helped me fill in the gaps of knowledge I had. Actually being
able to see the problem being done while given instructions was a great help.

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pixcavator
I like the style and I appreciate the idea. In fact, I’ve been working on
something in the same direction. So, here are a couple of things that I prefer
to do differently. First, these are video _lectures_ but without actual
students present. As a result, he is essentially talking to himself. I noticed
that this causes him to skip some details that students might be wondering
about. I prefer to start with actual lectures and initially put them on the
web as pdfs
([http://users.marshall.edu/~saveliev/Teaching/Fall09/m430/upd...](http://users.marshall.edu/~saveliev/Teaching/Fall09/m430/updates.html)).
Then I transcribe them to an online version
([http://inperc.com/wiki/index.php?title=Introductory_algebrai...](http://inperc.com/wiki/index.php?title=Introductory_algebraic_topology:_course)).
This is the second problem I have with his approach. Video just isn’t enough.
I don’t’ have to explain to you what video doesn’t have and html does:
searchability, cross-linking, speed of download, the ability to _read_ and
work at your own pace, etc. Certainly, my way is much slower.

~~~
pyre
One thing that video has that HTML doesn't: single-file archive ability. Sure
you can have a single HTML file as long as you keep it text-only, but most of
these topics are going to be diagram (and math figure) heavy. There's just no
good way to archive the content for later perusal. (Granted YouTube doesn't
want you to directly download the videos, but it's not like it's that hard to
circumvent -- and once you have the video you can easily find a player for it
on any platform)

[Note: I don't count .webarchive or .mht files as 'good enough'. .webarchive
files are Safari-only, and I don't even know of a tool to be able to extract
data from them. .mht files are 'sorta' supported (IE, Opera, Firefox w/ an
extension), but I don't like the idea that the data is Base64/MIME-encoded.
Personally I like .maff (Mozilla Archive File Format). It's only supported in
Firefox with an extension (and nowhere else unfortunately), but it's basically
a Zip file with the HTML/CSS/images inside of it.]

~~~
pixcavator
Well, the site runs on MediaWiki, so you can save the printable version of
each article. Even if you print the whole thing, the end result wouldn't be
that much different from a bunch of video files for each 15-min lecture.

~~~
pyre
The point being that as long as there are external files (css,images,etc) in
the page you will have to save it as 'Webpage (complete)' (or the equivalent
in your browser) which saves the HTML file and creates a directory for the
external files. If you are saving a bunch of sites/pages this way you end up
with _a lot_ of directory/html-file pairs. And were you to ever move these
around, you would need to make sure that the directory/file pair moved
together. It makes much more sense to have it all in one file (and as with
MAFF a file that doesn't necessarily need a browser to extract the contents).

Linking to this to the subject matter, most of the lessons have to do with
math and science, in a way that requires diagrams and specific notations. Both
of which cannot be represented in plain-text or HTML without external files.

~~~
pixcavator
Good point. I wish the printable version would automatically create a pdf.

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coffeemug
I found that the best way for me to internalize a particular subject in hard
science is to follow its history by reading the original papers. It's a hard
way to do it, but it helps you understand the motivation, the progression of
ideas, and the rigor that went into it. Anything else doesn't quite work for
me - I feel like I "sort of" understand, but five minutes after I close the
textbook (or the YouTube video) the understanding goes away with it.

I watched some of these lectures - they're excellent, but a bit too hand-wavy.
Without getting through the rigor there's no hope to gain a complete
understanding of the subject matter that stays with you forever.

~~~
plinkplonk
"I found that the best way for me to internalize a particular subject in hard
science is to follow its history by reading the original papers."

I've often wondered why math programs (and books) aren't structured this way,
explaining the historical context, reproducing the original papers (or
explaining the arguments or proofs in the paper if the original happened to be
in Latin or whatever), with a section on how the paper helped move the field
forward and so on. It doesn't necessarily have to sacrifice rigor to do this,
and a s amatter of fact I suspect a "walk the path (taken by the innovators)"
approach coupled with strict rigor would make for some awesome books (and get
more people interested).

~~~
RiderOfGiraffes
Frequently the historically motivated path is too long or creates too much
baggage. It's not always the case, granted, and sometimes the historical
development does give you the motivation, but you're still asking for a gifted
teacher, and that's rare.

A gifted teacher can teach with or without the historical perspective, and in
my experience a clean, direct presentation _with appropriate motivation and
context_ is usually better.

Again, not everything works for everyone.

~~~
teeja
Agreed. I'd have appreciated physics more if it had been taught with a more
historical approach. When I asked the profs why, the general answer was 'takes
too much time'.

(I 'spect part of it is that history is a 'humanity' ... but also that it's
because they didn't get the history either, and didn't have time to learn it
well enough to teach it.)

The physics department (major US university) actually hired a history of
science scholar, and I heard grumbling that he should be paid for by another
department.

------
ivan_ah
Salman Khan is an extremely talented teacher. I would go as far as to say he
is Feynmanesque in his ease with the subjects and ability to come up with good
examples for abstract concepts.

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ahlatimer
I used their videos on youtube while taking a linear algebra course last
semester when I needed an extra lesson on a particular topic. I highly
recommend them. Everything I saw was presented in a clear, well articulated
matter that made it much, much easier to understand than just reading
something out of a book.

~~~
SandB0x
_His_ videos. They were all created by one guy.

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morphir
I feel the need to point out that when I submitted a link to khan academy, no
one up-voted it. Why is this?

ref. <http://news.ycombinator.com/item?id=911882>

~~~
onoj
I did not see it that time? May also be the title given to the post. Humans
are fickle. ( will up vote you now ;)

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chaosmachine
I found this while doing some research on collision detection algorithms. All
math classes should incorporate game programming, I sure would have paid more
attention.

~~~
RiderOfGiraffes
Isn't this a classic case of "What works for me _must_ work for everyone." ??

Not everyone is interested in games, not everyone is interested in
programming. One source of motivation should not be forced on everyone, there
should be a wide range.

~~~
chaosmachine
Possibly. Any "real world" application would have been better than just
theory. But games seem like a natural extension of math lessons, and who
doesn't like games?

~~~
RiderOfGiraffes
Well, just to provide a single example, my wife is totally disinterested in
games. Absolutely doesn't care, to the point where if someone tries to
motivate topic X via games she ends up feeling that topic X cannot have any
value to her at all. By contrast, she is very interested in math, and wishes
that at school it had been presented as other than a collection of facts to
memorize and processes to learn and apply.

I know of others who have a similar attitude to games, and now, as I approach
50, I can't care much about them either.

Games aren't "Real World."

If you want "Real World" motivation then find some stuff from the real world.

To add some context, I am _passionate_ about putting things in context and
making them relevant. I visit schools to talk about uses of math, and
explaining how these subjects are anything but isolated and irrelevant stuff
to learn and hoops to jump through. I've given talks in venues such as the
West Yorkshore Playhouse, the Royal Exchange in Manchester, the Criterion
Theatre in the West End of London, Navy Pier in Chicago, and others around the
world. I give examples from GPS and SatNav through intercepting drugs couriers
and on to gene splicing and DNA analysis. I talk about finding cliques and
connections in social networks, and then apply that to detecting plaigarism
and ranking web sites. I talk about weather forecasting, roulette, life
assurance and debt management.

I mention them in passing when relevant, but I don't talk much about games.

~~~
Tichy
How do you motivate basic maths, though? Not everything can be directly
connected to drug couriers and what not.

Ultimately I suspect the only way to succeed in maths early on is to consider
it to be a kind of game. That is, puzzle solving for fun.

~~~
RiderOfGiraffes

      > How do you motivate basic maths, though?
      > Not everything can be directly connected
      > to drug couriers and what not.
    

So far I've always succeeded, and I don't even think I'm especially gifted. On
current experience, if you name a topic or technique, even in basic math, I
can probably relate it to and motivate it by (comparatively) real world
requirements at an appropriate level.

    
    
      > Ultimately I suspect the only way to succeed
      > in maths early on is to consider it to be a
      > kind of game. That is, puzzle solving for fun.
    

I agree entirely that people who are going to go and do science or math
probably have an element of problem-solving enjoyment, and for them, such
motivation not only will work, but is the most appropriate. Getting such
people to puzzle over why something happens, and getting them curious about
how it works is probably the best thing you can do for them.

When I'm talking to people I show them a couple of things and gauge their
reactions. Here are two:

<http://www.fieggen.com/shoelace/ianknot.htm>

<http://news.ycombinator.com/item?id=604347>

Any given person will react in one of two ways. One is to half-shrug as if to
say "who cares?" and then move on, the other is to look closer and say "Do
that again." People in the former group are most likely to need motivating
with things that matter to them _which might (but might not!) include games._
The others can just have their curiosity poked and you're off and running.

YMMV, personal opinions only, _etc, etc._

~~~
Tichy
If you can make it happen, I am only glad for it. I think it is a shame that
so many people miss out on maths. I haven't tried to teach it yet, so I can't
really say. I've tried at times to come up with real world applications for
the maths taught at school, but didn't come up with much.

I think one exercise I would give my pupils would be to determine the real
prices of mobile phones.

Enjoyed the shoelace link, will try it the next time I tie my shoes.

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jasonlbaptiste
I make this comment every month:

There needs to be a comprehensive site that aggregates all the educational
videos on the net (lectures, conference talks, screen casts, simple
instruction,etc.).

~~~
hexis
For better or worse, that site is google.com

~~~
jasonlbaptiste
It's a start, but there needs to be 1000x better organization and curation.

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Slashed
My math skills were always bad. I mean, even though I had one of the best
scores in school, I could never explain why it works, e.g. why _9^1/2_ is the
same as _sqr(9)_.

Since I want to self-study the _Quant Finance_ , I decided to refresh and
develop my math skills up to the Calculus. This website is amazing! Not only
it's a good refresher, it's the best source of knowledge created by one man.

~~~
eru
Interesting. I usually learn best by explaining / teaching.

------
rubyrescue
How sad that people pay up to 40k to the University of Phoenixes out there,
or, worse, take on 40k of unforgivable and practically un-repayable federal
student loan debt, when this type of material is available for free!

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oPerrin
Unfortunately decimals seem to be harder for computers than people :)

<http://screencast.com/t/ZjUwOWRl>

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scrrr
Excellent website, I'm impressed.

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rick_2047
This thing really could have helped me prepare for chemistry for exams in
school. I matches my curriculum to the mark. definitely going to share with my
juniors.

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sscheper
Wow, that's some deep material. Thanks for the link, Chaos.

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billswift
Buying good textbooks to learn from is a lot more cost effective than spending
on the high-speed internet connections that is needed to download even a short
video in any reasonable time. This "resource" is only useful to already have
high-speed internet access.

~~~
chaosmachine
A month of high speed internet is cheaper than a single text book in many
countries. Considering there's probably 40 textbooks worth of material on this
one page alone, nevermind the rest of the internet, I'd say priorities should
be on providing internet access.

~~~
pbhjpbhj
OLPC + Khan Academny videos = win.

~~~
GFischer
Only if they were in Spanish - here in Uruguay we have the OLPC deployed for
all schoolchildren, but most students don't have the level of English required
:)

~~~
pbhjpbhj
Well your Spanish is good ...?!

It's not a huge stretch to imagine someone sitting and redubbing one of these
though is it?

~~~
GFischer
Well, it sounds like a long project to me :) .

It would be a nice project, though, maybe I'll propose it (and contribute to
it).

Guess the first step would be contacting Khan.

PD: Spanish is my mother tongue.

~~~
pbhjpbhj
Good on ya!

I was thinking more akin to having a site that would facilitate the redubbing
allowing you to upload a dub via the site which would then be patched onto the
video. You'd need some verification and voting on best dubs.

~~~
GFischer
You're right, I'm dumb :) .

Even some subtitles might help, and that's a much smaller project :)

