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Math Academy, part 1: My eigenvector embarassment

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Re: Math Academy, part 1: My eigenvector embarassment

#31

Post by resource0x »

rahimnathwani wrote: post #28
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…

Very true. But the same applies to teaching. Mathematicians don't know where even to begin - for some of them, it's all too obvious. But the same happens with any subject. Someone proposes a certain design - but after many (20... 30... 40) years in business, you feel the design won't ever work, and try to explain, and fail because you don't know where to begin.

Re: Math Academy, part 1: My eigenvector embarassment

#32

Post by dboreham »

aithrowawaycomm wrote: post #9
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?

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…

Hmm. He'd have to be over 90 years old to have studied before the 1950s.

Re: Math Academy, part 1: My eigenvector embarassment

#33

Post by trentnix »

Jason Roberts, the founder (and primary coder) of Math Academy, has been podcasting for over 15 years and has been talking about Math Academy and its inspiration, origins, business fundamentals, financial realities, and ambitions on the podcast for many years. A lot of that discussion is distilled in the Math Academy about page (https://www.mathacademy.us/about). If you want to check out the podcast, it's here: https://techzinglive.com/

Jason also coined the term "Luck Surface Area" which has since been popularized by a number of others.

I haven't used Math Academy myself (although it's something I intend to try one of these days), but I can safely vouch that Math Academy isn't a fly-by-night shallow edtech grift. They've spent a small fortune and thousands of hours developing and refining content and curriculum. Math Academy is a thoughtful, intentional, well-manicured solution.

Re: Math Academy, part 1: My eigenvector embarassment

#34

Post by LudwigNagasena »

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?

I was surprised too. I thought Linear Algebra and Real Analysis are the foundation of any math degree.

Re: Math Academy, part 1: My eigenvector embarassment

#35

Post by viraptor »

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…

If your goal is to practice and be able to pass tests perfectly - yes, it's much better. If you just want an overview of some area for a specific task, probably not. MA's approach is "you're going to learn it and you're going to learn all the foundations for it and you'll perfect the tests", which is great for many people - especially if you're actually going to be tested on things in the future. And being 99% practice, 1% reading really leans into that idea.

Re: Math Academy, part 1: My eigenvector embarassment

#36

Post by cgriswald »

rahimnathwani wrote: post #28
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…

I got a B in my linear algebra course which was basically only numerical. I’d have gotten an A but the professor thought mountains of homework was teaching and I refused to do it all. Suffice it to say I aced every test and all the homework I actually did. None of it helped in understanding and like the grandparent I remembered none of it at the end and turned to LADR.

I don’t think any of that numerical approach helped when I read LADR. LADR isn’t about “doing the work” it’s about “doing the work to understand”. Similar to your experience I remember reading the first chapter and then among the first chapter questions I saw questions that looked like they had no basis whatsoever in what I thought I had just learned. Then, eventually, it clicked. That’s, frankly, the only way it works with Axler, so if you want it, you’ve got to do it.

My advice is to not waste time with the numerical approach and just do it.

I had a professor who used to say “being a student is suffering” but he used it to justify a bunch of bullshit. In this case, though, I’d agree with him. LADR is suffering d followed by satisfaction (and rinse and repeat).

Re: Math Academy, part 1: My eigenvector embarassment

#37

Post by thaumasiotes »

LudwigNagasena wrote: post #34
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?

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.

Re: Math Academy, part 1: My eigenvector embarassment

#38

Post by adhamsalama »

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…

3blue1brown is pretty good.

Re: Math Academy, part 1: My eigenvector embarassment

#39

Post by pinoy420 »

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 that when multiplied to a matrix (which in almost all cases would change the direction of the vector), in fact only scales it - and does not change its direction.

The scale factor is its eigenvalue.

So if you hav [[2,0],[0,3]] this should when multiplied to a vector give you [2x,3y]. But if you supply the vector [1,0] or [0,1] you see that the result multiplies that vector by two. So any multiple of these eigenvectors (e.g. [10,0]) will result in a doubling of the vector.

This is not a difficult concept. By any means.

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