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Math Academy, part 1: My eigenvector embarassment

frankhecker.com

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Re: Math Academy, part 1: My eigenvector embarassment

#4
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 asked myself the same thing. The article said “learn” Linear Algebra, not “review” Linear Algebra. Do some undergrad math programs not teach Linear Algebra?

Re: Math Academy, part 1: My eigenvector embarassment

#5
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 asked myself the same thing. The article said “learn” Linear Algebra, not “review” Linear Algebra. Do some undergrad math programs not teach Linear Algebra?

It was an optional senior level course at my college

Re: Math Academy, part 1: My eigenvector embarassment

#6
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?

Same boat as the author here, except I switched from physics to software after year three.

I had never heard of them until I was _years_ into software engineering. I think this is more common than you may think. I had never dealt with linear algebra in a formal setting, despite leveraging a lot of the concepts, until then.

Re: Math Academy, part 1: My eigenvector embarassment

#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 time -- but she did take their calc course and it helped her ace her CalcBC AP test.)

Re: Math Academy, part 1: My eigenvector embarassment

#8

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 if your kid loves math - my kid benefited from Math Academy (currently in college studying CS). Started with Math Academy as a HS freshman and finished BC Calc 2 years early with a 5 on the AP Exam. While he did Khan Academy for many years (which is a great resource) it didn’t really motivate him as much and seemed designed for a broader more generalist audience.

We also tried some other programs like Art of Problem Solving (great program, but required very synchronous classes which were hard to fit in)

My suggestion would be try it for a few months,

Re: Math Academy, part 1: My eigenvector embarassment

#9
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 undergraduate geometry texts from the 30s-60s and linear algebra was generally not an assumed prerequisite. There was a particular separation between the studies of "two and three dimensional vector spaces over R" (largely geometric) versus "finite dimensional vector spaces over a field" (entirely algebraic), and determinants were presented directly as volume computations. These days undergraduates mostly treat R^2 and R^3 algebraically, maybe at the expense of geometric understanding. (E.g. Euler's rotation theorem is easily proved when restated as a theorem about matrices over R^3 with determinant +1, but Euler's original statement and proof using spherical trigonometry is deeper.)

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