Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

Immersive Linear Algebra – A free interactive online book

immersivemath.com

Post reply on HN
Print view View original

71–80 of 80 posts

Re: Immersive Linear Algebra – A free interactive online book

#71

Post by rectang »

wingerlang wrote: post #52
sudo_bang_bang wrote: post #12

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 t…

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.

I'm in a similar situation, not getting much math in college while pursuing an unrelated degree and only teaching myself programming later. I've subsequently addressed my math deficit through extension courses at local universities, Coursera and Udacity MOOCs, Khan Academy, etc.

There two areas where I've felt the need for advanced math most keenly during my software development career are: 1) Similarity scoring in information retrieval and recommendation engines. 2) DSP.

Re: Immersive Linear Algebra – A free interactive online book

#72

Post by noobie »

cabinpark wrote: post #24

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 cour…

What's challenging to me is my inability to develop intuition about LA simply because most of the time I have no idea what (the purpose) I am doing.

How does one build intuition about LA?

Re: Immersive Linear Algebra – A free interactive online book

#73

Post by jamessb »

thyrsus wrote: post #34

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 corne…

HN previously had some discussion on an article that used IamgeMagick to do this correction on a video: https://news.ycombinator.com/item?id=8713070

Re: Immersive Linear Algebra – A free interactive online book

#74

Post by cokernel »

cabinpark wrote: post #24

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 cour…

At my (American, liberal arts, flyover country) university, linear algebra was my first real mathematics course. (The prior classes were calculus and a "proof" class, AKA intro to intro to number theory.) I'd been introduced to the determinant, Gauss--Jordan elimination, and so on, in high school, but all in a very mechanical way.

I think this transition between mechanically generating solutions to problems using pattern matching and some basic algorithms on the one hand, and the more mathematically mature approach of exploring problem spaces using pattern matching, some basic algorithms, and intuition can be difficult for many people.

It's not necessarily the material -- you can get used to almost anything, and even convince yourself it's easy or obvious with enough familiarity -- but the lack of intuition. When you're first learning linear algebra, its fundamental unity is not obvious, especially if the instructor does not take pains to point it out. (And even if the instructor does take pains to point it out -- well, it's hard to understand why the instructor is saying we could do this computation this way or that way.) So in the absence of existing intuition or any perception of unity, linear algebra becomes another target for pattern matching and basic algorithms.

As it happens, I've never, ever felt like I didn't "get" linear algebra. However, I almost always feel like I "get" it now and all my prior conceptions of it were a confused muddle.

Re: Immersive Linear Algebra – A free interactive online book

#75

Post by cokernel »

cabinpark wrote: post #65
dalke wrote: post #36

Earlier quoted context omitted.

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.

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 wi…

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.

Re: Immersive Linear Algebra – A free interactive online book

#76

Post by jimhefferon »

immersivemath wrote: post #63
jimhefferon wrote: post #42

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

This service is free of charge!

Are you involved with the project?

If so, thank you. What is the license?

Re: Immersive Linear Algebra – A free interactive online book

#77

Post by ThrustVectoring »

cabinpark wrote: post #24

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 cour…

It's a global vs sequential learner thing. Linear Algebra is usually taught as a giant pile of tricks, techniques, and terminology. This is tractable for sequential learners like myself - I really enjoy picking up new tools in a narrow context just for it's own sake. Highly global learners basically can't learn anything this way.

So, in short, my advice is "add more context."

Re: Immersive Linear Algebra – A free interactive online book

#79

Post by krat0sprakhar »

RockyMcNuts wrote: post #15
krat0sprakhar wrote: post #3

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-...

shoutout to LAFF as well - https://www.edx.org/course/linear-algebra-foundations-fronti... - 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).

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

Re: Immersive Linear Algebra – A free interactive online book

#80

Post by immersivemath »

shurane wrote: post #78

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.

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