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What is a point of Linear Algebra Tutorial which does not even attempt to properly define what a vector is? >A vector has: >A symbol (we might call it v, w, o

What is a point of Linear Algebra Tutorial which does not even attempt to properly define what a vector is? >A vector has: >A symbol (we might call it v, w, or even →AB in geometry). >Components (the individual numbers, like 2 and 3 in [2, 3]). >An arrow picture (a geometric way to see the vector as a directed line segment). None of these are properties of all vectors. They are properties of how vectors are represented in numpy.

voidhorse 1y ago
And precisely this is the risk of teaching "mathematics" using a programming language. Unfortunately, I think quite a few people don't actually know the abstract mathematical definitions and use concrete implementations as definitions in their heads in the first place. At least using a theorem prover would get you closer to doing actual maths and proving. It's probably more accurate to say courses like these teach mechanics/calculation more than they teach the theory.
- CamperBob2 1y ago
  There are already an uncountable number of linear algebra textbooks on the market. This is not meant to be a formal math textbook, but is instead aimed at those looking to pick up practical application-level insights and skills. (The "Why this matters" sections in the book are a worthy improvement on the state of the learning art by themselves, IMHO.) This collection of lab exercises seems far better suited to the purpose than the abstract proof-based resources that some of you seem to have in mind. Fortunately, those resources are still available to those who want to go further into the theory. And if you feel you have something to add to linear-algebra pedagogy yourself, well... what's stopping you?
__MatrixMan__ 1y ago
You are quoting the lab which is all about doing stuff in numpy. Probably if you want to critique the definitions used you should switch to the book. That said, it doesn't lead with a notion of vector that is as general as I'd like. Readers might be later surprised to find that there are vectors which are not lists of numbers. But I only looked at the first few pages so I assume the vector space axioms show up eventually.
- constantcrying 1y ago
  The book is even worse: "A vector, by contrast, is an ordered collection of numbers." This is a terrible definition and makes talking about proper linear algebra proper impossible.
  - dvrj101 1y ago
    here you go mate, exactly what you are looking for : https://github.com/little-book-of/linear-algebra#contributing https://github.com/little-book-of/linear-algebra#contributin...
    - tamnd 1y ago
      Every contribution is welcome: whether it's criticism, fixing typos, or even completely rewriting a section! Writing this book has been a real challenge for me, since all the books I enjoy reading are very formal ones :)) Anyone here into Grothendieck's SGA or EGA? (Sorry, a bit off topic!)
  - tamnd 1y ago
    I tried to build intuition before going into the formal definitions. Personally, I've always liked Bourbaki's books, but they're too formal for learning - especially in linear algebra, which I see as something meant for applications rather than pure math research. Maybe I just oversimplified things or made them feel less "math".
- hirako2000 1y ago
  I find it very disrespectful towards a project with such popularity to contributors ratio. It takes long hours to produce a working notebook, a synergy between concept descriptions and theorical explanations alongside code, comments of code and markdown for the theory here and there is an artistic coupled with engineering stunt you should try to accomplish yourself before criticizing. Perhaps you have, in which case a contribution as the other comment points out is the courteous thing to do. That book must have taken months to author and is one of the best read on the subject I've ever come across. Edit: removed incorrect fact about scalars.. they don't have a direction they have polarity.
canthonytucci 1y ago
What is the point of a comment saying something doesn’t properly define something that doesn’t share the proper definition? (Posted in good fun, no harm intended)

voidhorse 1y ago

And precisely this is the risk of teaching "mathematics" using a programming language. Unfortunately, I think quite a few people don't actually know the abstract mathematical definitions and use concrete implementations as definitions in their heads in the first place. At least using a theorem prover would get you closer to doing actual maths and proving. It's probably more accurate to say courses like these teach mechanics/calculation more than they teach the theory.

CamperBob2 1y ago
There are already an uncountable number of linear algebra textbooks on the market. This is not meant to be a formal math textbook, but is instead aimed at those looking to pick up practical application-level insights and skills. (The "Why this matters" sections in the book are a worthy improvement on the state of the learning art by themselves, IMHO.) This collection of lab exercises seems far better suited to the purpose than the abstract proof-based resources that some of you seem to have in mind. Fortunately, those resources are still available to those who want to go further into the theory. And if you feel you have something to add to linear-algebra pedagogy yourself, well... what's stopping you?

__MatrixMan__ 1y ago

You are quoting the lab which is all about doing stuff in numpy. Probably if you want to critique the definitions used you should switch to the book. That said, it doesn't lead with a notion of vector that is as general as I'd like. Readers might be later surprised to find that there are vectors which are not lists of numbers. But I only looked at the first few pages so I assume the vector space axioms show up eventually.

constantcrying 1y ago
The book is even worse: "A vector, by contrast, is an ordered collection of numbers." This is a terrible definition and makes talking about proper linear algebra proper impossible.
- dvrj101 1y ago
  here you go mate, exactly what you are looking for : https://github.com/little-book-of/linear-algebra#contributing https://github.com/little-book-of/linear-algebra#contributin...
  - tamnd 1y ago
    Every contribution is welcome: whether it's criticism, fixing typos, or even completely rewriting a section! Writing this book has been a real challenge for me, since all the books I enjoy reading are very formal ones :)) Anyone here into Grothendieck's SGA or EGA? (Sorry, a bit off topic!)
- tamnd 1y ago
  I tried to build intuition before going into the formal definitions. Personally, I've always liked Bourbaki's books, but they're too formal for learning - especially in linear algebra, which I see as something meant for applications rather than pure math research. Maybe I just oversimplified things or made them feel less "math".
hirako2000 1y ago
I find it very disrespectful towards a project with such popularity to contributors ratio. It takes long hours to produce a working notebook, a synergy between concept descriptions and theorical explanations alongside code, comments of code and markdown for the theory here and there is an artistic coupled with engineering stunt you should try to accomplish yourself before criticizing. Perhaps you have, in which case a contribution as the other comment points out is the courteous thing to do. That book must have taken months to author and is one of the best read on the subject I've ever come across. Edit: removed incorrect fact about scalars.. they don't have a direction they have polarity.

canthonytucci 1y ago

What is the point of a comment saying something doesn’t properly define something that doesn’t share the proper definition? (Posted in good fun, no harm intended)