51–60 of 66 posts
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For me, the main solution was to apply it to another problem that uses Linear Algebra as Application, which in my case was Introductory Quantum Course and implementing BLAS using Rust and C. That way you keep thinking and using this info. Otherwise, information in vacuum seems to abstract to care about.
I really like your approach. Any resource recommendations?
To be honest, I just read the introductory post, and it'stated there that the author wants to do MVC after finishing LinAlg, which is stated as their goal for end of 2025. As someone that has the same end goal (but probably 2026 for me) - isn't it maybe wiser to do MVC before LinAlg? Read the whole thing now, slightly disappointed OP doesn't try to tell us what an eigenvector is, based on his current progress.
I assume by MVC expands to multivariate calculus? In which case, I don't think it makes sense to do multivariate calculus before linear algebra. The derivative of a multivariate function f : R^ n → R^ m at a point x is a linear map L : R^ n → R^ m so that f(x + v) = f(x) + Lv + o(|v|) for small v . That means that multivariate calculus is about approximating nonlinear functions using linear ones in a small neighborho…
To be honest, I just read the introductory post, and it'stated there that the author wants to do MVC after finishing LinAlg, which is stated as their goal for end of 2025. As someone that has the same end goal (but probably 2026 for me) - isn't it maybe wiser to do MVC before LinAlg? Read the whole thing now, slightly disappointed OP doesn't try to tell us what an eigenvector is, based on his current progress.
MVC has depencies on LinAlg. Ex Jacobians.
Skip to last chapter. > The most notable of these are the synthetic division method for polynomials, the various trigonometric identities, and differentiation of products and quotients of functions. So he learned nothing you already know at 15. Or younger in Asia. I think he forgot his goals because it doesn’t even mention eigenvectors. I am surprised because it is not a difficult thing to understand? It is a vector…
Now, do the part with the explanation of what it actually means for a (physical) system to have eigenvalues, and what it tells you about the response of such a system to external or intensive inputs, or how to change such a system to targeted a certain response.
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…
3blue1brown is pretty good.
If you think linear algebra is something geometric, like "a 3x3 transform matrix is rotation and scaling; an eigenvector is something after transformation and parallel to its old self..." you will be surprised at how little LADR talks about these.
On the contrary, the most important part (imo) of 3b1b is that it helps you intuitively get these geometric interpretations.
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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 th…
In Europe (at least in certain countries, can't speak to all of them), maths lectures will typically be abstract and proof-based from day 1 - at least for maths majors (but frequently for CS and physics students too). Other majors, such as economics and maybe engineering, may get their own lectures that tend to be more hand-wavey because they don't necessarily need the axioms of real numbers to take a derivative here and there.
My linear algebra course was algebra and proof based to the extent that maybe a little bit more geometric intuition would have helped.
https://drive.google.com/drive/folders/1JrMp7R4j86tMzHn0Sfa_...
Skip to last chapter. > The most notable of these are the synthetic division method for polynomials, the various trigonometric identities, and differentiation of products and quotients of functions. So he learned nothing you already know at 15. Or younger in Asia. I think he forgot his goals because it doesn’t even mention eigenvectors. I am surprised because it is not a difficult thing to understand? It is a vector…
Hooray! You managed to explain it as dryly and as poorly as any other linear algebra book or course out there. Now, do the part with the explanation of what it actually means for a (physical) system to have eigenvalues, and what it tells you about the response of such a system to external or intensive inputs, or how to change such a system to targeted a certain response.
Eigenvalues in an oscillating system describe its resonant frequencies. Its eigenvectors can describe motion at that certain resonant frequency. Imagine a bridge. If wind or traffic match a resonant frequency (eigenvalue) it would be dangerous. Engineers can redesign it to change the corresponding eigenvector and shift the eigenvalue (its resonant frequency for that mode of oscillation) to a safer range. See that bridge in London.
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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.
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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…
I’m taking their Math Foundations 2 now. So far my only two complaints are:
1. Everything feels like a random grab bag of “tricks”. There isn’t a coherent presentation of why this works or why it’s important. 2. Geometry lessons just suck. I don’t blame MathAcademy for this, since they basically follow what would be considered standard American high school geometry curriculum. But after having gone through Euclid’s Elements, everything here just feels empty by comparison.
Overall I’m still very happy with the product. They do largely deliver on their promises.
https://worrydream.com/refs/Lockhart_2002_-_A_Mathematician'...