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Math Academy, part 1: My eigenvector embarassment

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Re: Math Academy, part 1: My eigenvector embarassment

#21

Post by gmays »

insane_dreamer wrote: post #7

is MathAcademy that much better that KhanAcademy (which also has a Linear Algebra course and covers eigenvalues of course), which is free? Considering it for my youngest kids, but my eldest (now finished college with a degree in engineering) used Kahn Academy as a high school supplement and it was quite good (this was about 10 years ago). (She didn't take the KahnAc LinAlg course -- not sure it was around at that tim…

Yes, Math Academy is insanely good. It's a lot more intense, focused learning and less edutainment.

I'm an adult and not a kid, but wrote about my experience after 100 days of using it daily here: https://gmays.com/math

The Math Academy team (including the founders) are also active on X/Twitter: https://x.com/_MathAcademy_

And there's a Math Academy community on X here in case you want opinions from other users: https://x.com/i/communities/1833198423593431339

Re: Math Academy, part 1: My eigenvector embarassment

#23

Post by HPMOR »

emseetech wrote: post #19
HPMOR wrote: post #18

Earlier quoted context omitted.

MathAcademy really is fantastic. I've done 5300 xp so far (80+ hours), and am almost finished with their Math for Machine Learning. It's remediated a lot of things I've struggled with during my University ML classes. Seriously a wonderful pedagogical experience. I can integrate multivariate functions easily, know all my derivative trig identities, and I don't get confused by continuous random variables any more.

I'm working through Foundations specifically to do Math for Machine Learning and I'm very excited for that course. What were your thoughts on it? Also, if they ever did a Math for Computer Graphics course I'd never cancel my subscription.

I think Math for ML is __fantastic__. And based on the curriculum Jason has published for ML, it seems very __very__ promising. I've done a fair bit of ML @ Cornell, so I've had exposure to a lot of the material he plans on covering. However, I glossed over a lot of the theory because some weakness in my math. I feel like this has been remediated with M4ML and ML should expand and solidify my understanding.

Edit: Wrt to computer graphics, going through M4ML and the ML sequence will really help you understand what's happening there. Convolutional Neural Nets, Gaussian Splatting, all rely on these same principles.

Re: Math Academy, part 1: My eigenvector embarassment

#24

Post by FranklinChen »

beezle wrote: post #11
aithrowawaycomm wrote: post #9

Earlier quoted context omitted.

He is a bit older. Linear algebra is also very old, but it didn't really become the field we know today until the 1950s. I would add that in 2025 it is cheap to buy a computer that can solve large linear systems, but that certainly wasn't true in 1975, so linear algebra was less applicable in the real world. I am not too familiar with the pedagogical history of linear algebra, but I've been reading some advanced unde…

I was a double major, one in physics, in the 80s. After the three semester engineering physics classes, intro QM was taught spring sophomore year. We used Liboff. In addition, it was required for all physics, chem and engineering majors to take math 20(5?) which was linear algebra. And given that most of basic QM was formalized by 1930 and relies upon eigenvectors, hard to see any physics course taught since that tim…

Whoa, Liboff, that book... I only vaguely remember it now (took QM in 1988). I took "math for mathematicians" (Math 25) instead of "math for physicists" (Math 22?), but remember my classmates who took first year "math for physicists" got eigenvectors very quickly right off the bat in the pre-published book they used https://www.cambridge.org/core/books/course-in-mathematics-f...

Re: Math Academy, part 1: My eigenvector embarassment

#25

Post by teunispeters »

i2go wrote: post #3

he was a physics and math major and did not know eigenvectors and eigenvalues? i would like to know how is this possible. can someone explain it to me?

Speaking as a CS/Math dual major from the late 1980s, the explanations in the textbook were ... uselessly bad where I went (SFU). So while I know the math involved, I didn't know the terms until I retook it from a teacher who actually taught worth anything, years later. (I still don't use the terms, they're not very ... well, they're awkward and while my embedded work sometimes calls for the math, the terms ... meh. There are clearer ways to put things!).

Re: Math Academy, part 1: My eigenvector embarassment

#26

Post by resource0x »

As a math major, I scored a perfect 100 on my Linear Algebra exam in 1974. However, just two days later, I couldn't recall a single thing.

A few years ago, with ample free time, I decided to refresh my (nonexistent) memory by watching online linear algebra lectures from various professors. I was surprised by their poor quality. They lacked motivation and intuition. Khan Academy offered no improvement. Then, someone recommended Linear Algebra Done Right (LADR). I read it three times, and by the third iteration, I finally began to appreciate the beauty of the theory. Linear algebra is a purely algebraic theory; visual aids are of limited help. In short, if you have the time, I recommend reading LADR. Otherwise, don't bother.

Re: Math Academy, part 1: My eigenvector embarassment

#27

Post by gmays »

resource0x wrote: post #26

As a math major, I scored a perfect 100 on my Linear Algebra exam in 1974. However, just two days later, I couldn't recall a single thing. A few years ago, with ample free time, I decided to refresh my (nonexistent) memory by watching online linear algebra lectures from various professors. I was surprised by their poor quality. They lacked motivation and intuition. Khan Academy offered no improvement. Then, someone r…

Have you tried Math Academy? I think the difference is that it's actually made by a team of mathematicians creating the content manually.

Re: Math Academy, part 1: My eigenvector embarassment

#28

Post by rahimnathwani »

resource0x wrote: post #26

As a math major, I scored a perfect 100 on my Linear Algebra exam in 1974. However, just two days later, I couldn't recall a single thing. A few years ago, with ample free time, I decided to refresh my (nonexistent) memory by watching online linear algebra lectures from various professors. I was surprised by their poor quality. They lacked motivation and intuition. Khan Academy offered no improvement. Then, someone r…

I don't know whether LADR is good for someone who is new to linear algebra. I've seen it recommended so many times, so ~12 years ago when I was living in Beijing I bought two copies (one in English for me, and one in Chinese in case I needed to ask a colleague for help).

It took me time to study each page, to understand the examples, and then to attempt the exercises. It seemed very beautiful.

Then one day I came to a part I couldn't understand: I didn't see how something Axler said followed from the earlier stuff on the page actually followed. I scratched my head for a couple of hours, which is much longer than I'd spent on any previous page.

Eventually I asked a colleague for help. I showed him the page. He asked me to explain what I didn't understand. I started to explain what I knew, and how I didn't understand how this thing followed. As I was explaining it, that part suddenly clicked.

But I got stuck a few more times and didn't persevere.

I wonder whether it would have been better for me to have studied some numerical approach to linear algebra (like Strang's videos) first, rather than going straight into a book that's so abstract and proof-based.

I suppose it depends on your mathematical background.

(Your comment made me think about those folks who were once fit and muscular, then years later they are out of shape, and then they decide to get in shape say how easy it was to get back in shape. They don't realize that part of what made it easy is that they were once in shape, and they still more muscle cells or whatever.)

Re: Math Academy, part 1: My eigenvector embarassment

#29

Post by ATMLOTTOBEER »

emseetech wrote: post #19
HPMOR wrote: post #18

Earlier quoted context omitted.

MathAcademy really is fantastic. I've done 5300 xp so far (80+ hours), and am almost finished with their Math for Machine Learning. It's remediated a lot of things I've struggled with during my University ML classes. Seriously a wonderful pedagogical experience. I can integrate multivariate functions easily, know all my derivative trig identities, and I don't get confused by continuous random variables any more.

I'm working through Foundations specifically to do Math for Machine Learning and I'm very excited for that course. What were your thoughts on it? Also, if they ever did a Math for Computer Graphics course I'd never cancel my subscription.

It’s just ok. Certainly better than watching some random yt videos or passively reading a tb. For context I did ~11k pts to finish M4ML. It’s a little frustrating to see them chase the money and make ML/programming courses while the core differentiator (lesson quality) is still lacking in the later math topics. There are persistent issues that annoyed me so much that by the end it was like pulling teeth go grind out the points every day.

It has you overfit on the style of questions they ask, and I never felt like I got a good grasp of lots of the later topics despite passing my reviews and quizzes no problem.

Re: Math Academy, part 1: My eigenvector embarassment

#30

Post by resource0x »

gmays wrote: post #27
resource0x wrote: post #26

As a math major, I scored a perfect 100 on my Linear Algebra exam in 1974. However, just two days later, I couldn't recall a single thing. A few years ago, with ample free time, I decided to refresh my (nonexistent) memory by watching online linear algebra lectures from various professors. I was surprised by their poor quality. They lacked motivation and intuition. Khan Academy offered no improvement. Then, someone r…

Have you tried Math Academy? I think the difference is that it's actually made by a team of mathematicians creating the content manually.

Not yet, but now I will, just out of curiosity. There's a problem with mathematicians teaching the subject. After all, the youtube lectures were also given by mathematicians. In attempt to make things "accessible", they de-emphasize the algebraic part of the subject and replace it with... I don't know what. The common theme is to consider only R^n. That's not what it's about. Maybe Math Academy course is different though.
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