3 ms·

What are colleges teaching these days if not this??

by MiroF 6y ago

beefield 6y ago
I don't know, my college days were a couple of decades ago, so I have already forgotten plenty. But if you can point to a good source in the internet that explains this, I could try to see why my research efforts failed.
- MiroF 6y ago
  Here's wikipedia. Granted, the mathematicians behind wikipedia seem to be focused on making everything as notationally obscure and hard to understand as possible, but it outlines the concept https://en.wikipedia.org/wiki/Linear_map#Matrices https://en.wikipedia.org/wiki/Linear_map#Matrices
  - beefield 6y ago
    Well, I have to say that if that is the most approachable and easily googled content in the internet to figure this out, I am not too surprised I had to figure it out on my own...
exabyte 6y ago
For me I think the difficulty was just reconciling reality with the concept of a coordinate system. I think it was just some abstract concept that I considered to be out of my cognitive reach of understanding. I just had no way to anchor anything being said to me to a concept I had in my head at the time. I remember this poor teaching fellow where I went to Lehigh University where I studied Mechanical Engineering. He was foreign and had the honor of teaching us Linear Algebra. He must have noticed that none of us had even the slightest damn clue what he was talking about. So, the class before every exam, he would literally just give go over the exam problems nearly verbatim and solve them. I came out of that class with a good grade and not the slightest fucking understanding of Linear Algebra beyond the very superficial algebraic laws of multiplying tensor objects (i.e., scalars (0-D tensor), vectors (1-D tensor), and matrices). I'd like to thank Grant Sanderson (3Blue1Brown) and Mike Cohen (Udemy Linear Algebra course using Matlab and Python) for teaching me linear algebra. And don't forget Gilbert Strang, of course!! (find his course on MIT OCW) The visualizations of the tensors transforming provided by the first two are what really made Linear Algebra start to click for me. I want to go back to Gilbert Strang's course now that I have a better geometric understanding of what is happening and appreciate all his wisdom on the subject.
- MiroF 6y ago
  As a physics major at the time, I think that learning physics in addition to multivar and linear algebra is so handy in terms of providing reference material for intuitions. Also, learning it as part of a numerical computing stack (like python) where you can experiment and visualize is huge for building intuition.
kd0amg 6y ago
How to compute a matrix product, how to compute the solution to a system of equations, how to compute a determinant (inefficiently), how to compute eigenvalues Lots of how, not enough why

What are colleges teaching these days if not this??

by MiroF 6y ago

What are colleges teaching these days if not this??

I don't know, my college days were a couple of decades ago, so I have already forgotten plenty. But if you can point to a good source in the internet that explains this, I could try to see why my research efforts failed.

MiroF 6y ago
Here's wikipedia. Granted, the mathematicians behind wikipedia seem to be focused on making everything as notationally obscure and hard to understand as possible, but it outlines the concept https://en.wikipedia.org/wiki/Linear_map#Matrices https://en.wikipedia.org/wiki/Linear_map#Matrices
- beefield 6y ago
  Well, I have to say that if that is the most approachable and easily googled content in the internet to figure this out, I am not too surprised I had to figure it out on my own...

exabyte 6y ago

For me I think the difficulty was just reconciling reality with the concept of a coordinate system. I think it was just some abstract concept that I considered to be out of my cognitive reach of understanding. I just had no way to anchor anything being said to me to a concept I had in my head at the time. I remember this poor teaching fellow where I went to Lehigh University where I studied Mechanical Engineering. He was foreign and had the honor of teaching us Linear Algebra. He must have noticed that none of us had even the slightest damn clue what he was talking about. So, the class before every exam, he would literally just give go over the exam problems nearly verbatim and solve them. I came out of that class with a good grade and not the slightest fucking understanding of Linear Algebra beyond the very superficial algebraic laws of multiplying tensor objects (i.e., scalars (0-D tensor), vectors (1-D tensor), and matrices). I'd like to thank Grant Sanderson (3Blue1Brown) and Mike Cohen (Udemy Linear Algebra course using Matlab and Python) for teaching me linear algebra. And don't forget Gilbert Strang, of course!! (find his course on MIT OCW) The visualizations of the tensors transforming provided by the first two are what really made Linear Algebra start to click for me. I want to go back to Gilbert Strang's course now that I have a better geometric understanding of what is happening and appreciate all his wisdom on the subject.

MiroF 6y ago
As a physics major at the time, I think that learning physics in addition to multivar and linear algebra is so handy in terms of providing reference material for intuitions. Also, learning it as part of a numerical computing stack (like python) where you can experiment and visualize is huge for building intuition.

kd0amg 6y ago

How to compute a matrix product, how to compute the solution to a system of equations, how to compute a determinant (inefficiently), how to compute eigenvalues Lots of how, not enough why