41–50 of 66 posts
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.
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?
I was introduced to eigenvectors in a math course on linear algebra. They seemed esoteric but I could prove theorems and stuff… cool but kind of forgettable.
Then I took quantum mechanics. That’s where I learned eigensystems. That’s where their utility and beauty were beaten into me, problem set by problem set. In quantum mechanics, eigensystems are ubiquitous: from using ladder operators to solve the harmonic oscillator in an elegant way, to what quantum numbers actually are, to the reason behind the Heisenberg uncertainty principle, and to the so many different ways to use perturbation theory to explain atomic and molecular spectra.
You can do the basics of quantum mechanics without explicit linear algebra, and many intro physical chemistry texts aren’t able to assume the math as a pre-requisite and have to do that. But it’s tedious and awkward, like trying to learn physics without calculus.
Going back through the foundations courses on Mathacademy (I started halfway through Math Foundations II, currently nearing the end of III) has been great. It's been surprising how much I've forgotten, but also reassuring how quickly it comes back. My plan is to move on to the more advanced courses with firmer foundations.
The focus on answering questions constantly helps me focus, although the multiple choice structure is kind of limiting, if inevitable. It's frustrating to have it throw a whole load more questions at you because you missed a minus sign, where a proper teacher would have seen your working and been able to tailor their feedback.
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…
I'm a self-motivated adult learner, so I don't know what it's like for kids. Though the program was originally designed for them, so I suspect their experience would broadly be similar to mine.
As other commenters have mentioned, you need to be okay with grinding through problem sets with no videos or UI pizzazz -- maybe this doesn't work for everybody. I'd compare it to the difference between trying to learn a language through scattered YouTube videos and Duolingo versus tandem and grinding on a good Anki set.
NB: I'm taking it for the Math for ML track and am currently most of the way through the Math Foundations III course. So I can only comment on the lower level courses.
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.
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.
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 neighborhood, which enables you to apply tools from linear algebra to it.
You can kind of do multivariate calculus without linear algebra by essentially treating f as a collection of m × n univariate functions that you do ordinary calculus with (lots of partial derivatives) but I doubt it would be very enlightening.
Earlier quoted context omitted.
I was surprised too. I thought Linear Algebra and Real Analysis are the foundation of any math degree.
Topology is also considered a staple of a modern math degree.
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…
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…
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.