
Immersive Linear Algebra – A free interactive online book - samlittlewood
http://immersivemath.com/ila/index.html
======
Scottopherson
This looks awesome. The popup-help's are a little jarring though since there's
no indication as to which words will trigger a popup. Also:

"Oh come on, you should know what a vector, v, is by now. Check out Chapter 2,
for crying out loud."

seems kind of harsh to say to the reader while they're reading the first
sentence of Chapter 2..

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cokernel
"Kind of harsh" is an understatement. Insulting the reader like this is not
acceptable. Mathematics is already difficult enough to learn by its very
nature. Authors, you don't need to help make it more difficult. We already
have a hard enough time convincing people that they _can_ learn something this
difficult.

~~~
immersivemath
Thanks for the feedback. We have removed the popup for "vector".

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cabinpark
I always see linear algebra on HN and many people comment on how they never
understood the subject. This makes me ask: what exactly is it that people
don't get about linear algebra? What makes it appear to be a difficult
subject?

As someone who has used linear algebra almost every day in some form over the
last decade, it's hard to get a perspective of what aspects are challenging to
the beginner. And since I TA courses that involve linear algebra, it is good
to know where the problems are.

~~~
dalke
I see that chapter 10, on eigenvalues/eigenvectors, is "Coming soon!".

Eigenvectors never made intuitive sense to me. As with the various
decompositions (Cholesky, LU, etc), I could apply the math as algorithms to
follow, but never got to the point where felt I could apply them to new
problems.

Then again, in practice, I've only needed eigenvectors once since college, and
it was more a rote implementation described in a paper. (In other words, don't
feel like you should educate me on them here.)

Since you are a TA, don't you get some idea of where your students struggle
with linear algebra?

~~~
cabinpark
Interesting. I used linear algebra with quantum mechanics where eigenvectors
represent quantum state of the Hamiltonian which is how I initially understood
them.

And as for TAing, have you ever TA'd? You definitely get a feeling but I can
count numerous times when I've stood in front of the tutorial class and asked
if there are any questions only to get no response back. I think it's a
symptom of first years. I've TA'd calculus as well and I get similar
responses. It's very frustrating sometimes.

~~~
dalke
I have TA'ed. Asking for questions in public doesn't help much. Students
rarely like to admit they don't know something.

I was thinking more of when you look at their assignments. There are often
multiple ways to approach a problem, and the route chosen can reveal something
about one's level of comfort.

It doesn't help that university TAs get almost no training in how to be a TA.
At least, I didn't.

~~~
cabinpark
Yeah I know. It's hard to squeeze information out of them. I actively tell
them to please, please come to me if they don't understand something and I
have office hours for a reason. Yet no one takes advantage. At a certain
point, you can only do so much since I'm a grad student and not a lecturer and
my time is finite.

The problem I've found with assignments though is that people copy and cheat.
Many times someone will do very well on assignments and then do absolutely
terrible on midterms and finals. It's very frustrating. I remember one course
where everyone did nearly perfect on the assignments and yet the final and
midterm followed the standard bell curve.

~~~
cokernel
It's worth devoting a portion of classroom time (in my opinion, a substantial
portion) to discussion of the topic, perhaps focusing on particular problems
and generalizing from there. For example, you might select random students
each day to present problems from homework. If you've ever noticed that you
learn something better once you teach it to someone else -- well, it works for
your students, too.

Moreover, if you create a non-judgmental environment in which people are free
to talk about their approaches to problems and get feedback not only from you
but from other students as well, then just by watching carefully, you will
learn some of the more common gaps in understanding. (Note that some students
will not talk in these situations unless forced, but that does not mean they
do not benefit from following the discussion.)

If you're anything like I was when I was first TAing courses like this, you
might think that if you do this, you won't have enough time to "cover the
material". But I put it to you that a lecture that is not absorbed doesn't
cover anything.

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sudo_bang_bang
I never studied math in college, in fact I barely studied math in high school.
It was always daunting to try to parse the notation and figure out how the
abstract symbols corresponded to some piece of reality.

When I became a self-taught developer I found my math skills continuously
lacking. I started teaching myself on Khan Academy and really picking it up a
lot better because of the simplicity of the language and the good examples. I
finally realized I learned math best visually.

Interactive lessons like these are great. There are things that can be
improved about this book (load times and enhanced interactivity) but all in
all this a great resource for people that learn best visually. I'll come back
to this soon in my future self-education.

~~~
wingerlang
What exactly do you do when you need math skills in developing? What do you
develop with it? Some specific examples?

I've done math while developing 3D stuff, physics simulation and a lot of
things - yet I never felt like my math skill mattered that much. And I really
dislike theoretical math like in school.

~~~
EvanKelly
Math is certainly not for everyone, but I actually found that once I started
diving into pure math (NOT what was taught in my school's math curriculum) it
was a whole new world.

Did your school actually teach pure math?

I bet a lot of programmer types had similar frustrations to the
computationally intensive version of math taught in many high schools when
they knew that these processes could simply be automated.

~~~
wingerlang
I don't even know what pure math is to be honest. The courses I specifically
lost interest in was linear algebra, discrete mathematic and statistic-
something. I did however use linear algebra just after while writing a simple
collision/physics engine prototype and found that to be very fun.

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cptvideo2
I'm sure that this a wonderful book, but please note the error right off the
bat in equation 1.3 The tangent of the angle in question is b/a NOT a/b as
stated. Probably a good idea to keep an sharp eye on the math as you go along
in this thing.

~~~
immersivemath
Send me your name to immersivemath@gmail.com and we will add you to the
acknowledgements section!

~~~
cptvideo2
That's o.k. I'm usually the one making boo-boos like that. Glad we caught it.

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krat0sprakhar
This is actually pretty cool! I spent the last few weeks going through Gibert
Strang's popular OCW course[0] & I'm sure this would serve as a great
companion. I can't wait for the chapter on Eigenvalues to be published as that
is something I don't yet grasp intuitively. Great work and thanks for making
this free and accessible!

[0] [http://ocw.mit.edu/courses/mathematics/18-06-linear-
algebra-...](http://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-
spring-2010/video-lectures/)

~~~
RockyMcNuts
shoutout to LAFF as well

\- [https://www.edx.org/course/linear-algebra-foundations-
fronti...](https://www.edx.org/course/linear-algebra-foundations-frontiers-
utaustinx-ut-5-03x)

\- [http://www.ulaff.net/](http://www.ulaff.net/)

might be good for you if you're motivated by a deadline, graded progress, some
Matlab/Octave implementation, and certificate of accomplishment, vs. self-
paced Strang (AFAIK).

~~~
krat0sprakhar
Had no clue about this course! Thanks a lot for the recommendation!

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nicklaf
Similar project, but for multi-variable calculus:

[http://mathinsight.org/thread/multivar](http://mathinsight.org/thread/multivar)

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generic_user
Is this available in an off-line bundle? I am becoming increasing wary of
online books/training/applications that can not be read locally. If I am going
to take the time to read through a full book (possibly weeks of reading) I
want to be able to use/reference it in 5 years like my paper books.

most of the value of a good math book is that years after reading it you can
use it as a reference to look things up you will inevitably forget.

~~~
thaumasiotes
While I don't disagree with your comment, I think once you've learned this
material you could reasonably look it up in a different book. Put another way,
going through this course might greatly increase the value (to you personally)
of having any other linear algebra text available. It's not necessary to look
things up in the same textbook you learned them from.

~~~
generic_user
This issue has come up with MOOCS also. If you look at the MOOC sites they
offer there class content including videos as downloads. Even tho most of the
MOOCS are introductory courses and you probably would need to get a good book
to go along with them lots of people were requesting downloads of the content.
There is a variety of reasons why people want off-line bundles. Its just
something I have gotten use to with this sort of content.

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something123
In terms of programming and linear algebra - please consult someone who is
actually knowledgeable about the subject if you're implementing it in code.

Linear algebra without error analysis is very dangerous. Many many things are
theoretically useful, but can't be used in practice. You can't calculate
determinants, you can't count unique eigen values, you can't use certain
decompositions.

Unfortunately this isn't really topic you can do a quick tutorial on and start
writing new algorithms

~~~
memming
and also don't compute the inverse if you don't have to!

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nstart
Slow to load (possibly due to HN traffic), but once it does, it seems like
it's got the makings of a great learning tool. Waiting for matrix chapter
since that's where I stopped learning Linear algebra on both my past two
attempts (Gilbert Strang made my mind explode as I tried to comprehend past 4
dimensions. And then I just got lazy). Really want to pick this up because
without linear algebra it's easy to get lost in all the major streams of
Machine Learning. At least that's what I felt when I tried to skip linear
algebra and move on to ML.

Sigh. I sometimes wish I paid more attention to my studies while I was in
school instead of goofing off and playing card games :'(

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thyrsus
At some point, I'm hoping to get enough of this to solve this problem: you've
taken a picture of, say, the Mona Lisa in its rectangular frame, but because
of crowds you weren't in line with dead center, instead you were 5 meters
back, 1 meter high, and 2 meters to the side, and not even pointed at the
center. Your photo now contains some quadrangle that is a _projection_ of the
rectangle. I'd like to tag the four corners and have an algorithm map the
photo to its original rectangle - I intuit there's enough information in the
photo and the four tagged points, given that the original is actually a
rectangle.

~~~
gjm11
A word of warning about solutions to this problem. The "easy" version states
it this way: the mapping you want takes (x,y) to
((ax+by+c)/(gx+hy+i),(dx+ey+f)/(gx+hy+i)) for some a,b,c,d,e,f,g,h,i -- a
general "projective transformation". If you decide ahead of time exactly what
rectangle you want to map to, you have 8 constraints on a..i (two coordinates
for each of four corners) and one irrelevant degree of freedom (if you
multiply all of a..i by the same constant, nothing changes) so you have
"exactly enough" information to find those parameters. So you solve the
equations and you're done.

This works, provided your measured positions are perfectly accurate, but it
isn't the best you can do. The reason is that a single projection actually has
one degree of freedom less than a general projective transformation. (Three
parameters to say where your camera is located. Three to say how it's rotated.
One scaling factor. Total is 7 rather than 8.) This means that there's an
extra (slightly hairy) constraint on the parameters a..i, which turns out to
mean that the aspect ratio of the rectangle you're mapping to is determined
for you.

Imposing that constraint will give you (1) more information -- you won't have
to know ahead of time what aspect ratio you have -- and (2) a more accurately
estimated transformation.

You can find more details of this stuff in, e.g., this PDF document:
[http://people.csail.mit.edu/bkph/articles/Harmful.pdf](http://people.csail.mit.edu/bkph/articles/Harmful.pdf)
.

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snake117
I was thinking of working in a lab that does research in the field of
computational biology. However, I never took a linear algebra course before so
I always felt like it would be a waste to make an attempt. I did a quick skim
and this looks very promising. If I can comprehend this, then maybe I will be
of some use in the lab. Thanks for sharing :)

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krohling
This looks amazing and well timed as I've been attempting to learn Linear
Algebra on the side. However, everything after Vector Products is "coming
soon". I will definitely use this once it's all there, which i hope is soon.
Heck I'd be willing to pay for it if it were ready now.

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jesicamila
Is this available in an off-line bundle?

~~~
immersivemath
At this time, it is not available as an off-line bundle.

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Voltbishop
Really great site. It's clean, look forward to seeing the complete interactive
book.

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shurane
Does anyone know if there's source code or a github page associated with this?
It would be nice to submit fixes to errors, typos and maybe make suggestions.

For starters, there might be a way to do away with the loading screen for
shorter pages.

~~~
immersivemath
At this moment there is no github available, but bugs reports are welcome at
immersivemath@gmail.com!

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adam12
This is the first time I've ever heard someone say algebra with a hard g
sound.

[https://www.youtube.com/watch?v=TIcSnsmitHw](https://www.youtube.com/watch?v=TIcSnsmitHw)

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orange_county
Thanks for this! I am currently taking linear algebra with Serge Lang's book
and I feel that this is a good addition to my studies. When do you expect to
have the other chapters done?

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jjangsangy
Cool, well doesn't work on my mobile device, but I'll definitely check this
again later since I need to review more Maths before going back to uni

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jimhefferon
Not Free? That's fine, but I couldn't see a statement of that. If so, I wonder
how they plan to do DRM.

~~~
immersivemath
This service is free of charge!

~~~
jimhefferon
Are you involved with the project?

If so, thank you. What is the license?

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mrcactu5
Are there any ways to contribute?

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wehadfun
To bad that teachers rarely have the freedom to teach using tools of their
choosing

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neovive
From a technical aspect, this is an excellent implementation of MathJax.

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70seconds
70 seconds to load a chapter? That's a terrible benchmark for even for some of
the heaviest websites out there!

This may not be a popular opinion but I (and many ordinary readers like me)
see that link as a website. Not a book.

It feels heavy and overwhelming to see a large number of 3D diagrams and
visual depictions on just one web-page. Having to scroll down to read the full
chapter with all that animation and "motion" is probably a bad move too. Given
that this is supposed to come off like a book you can probably ditch the
scroll.

Ideally, you'd want to give away few concepts in small easy-to-understand
chunks with just 1 or 2 figures per page. And let the reader flip/click over
to the next section like it happens with an ibook or kindle book or even a
real physical book.

IMHO the idea of ripping apart a book at its spine and forcing the loose
design of websites over it is a complete no-go for avid book readers.
Especially for the mobile and tablet users (probably even for the desktop
users!, why else would everyone insist to download PDF, ePub or other
artifacts?). But I'm sure that a section of developers over here wouldn't
agree with my opinion. So take it all with a pinch of salt.

Also just the place where I'd let the designers take over.

~~~
rubiquity
> _70 seconds to load a chapter?_

The full note says "up to 70 seconds on tables." On my computer it took less
than 2 seconds.

~~~
70seconds
It took over a minute on mine; but I'm sure they're hammered right now.

