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Immersive Linear Algebra Book with Interactive Figures (2015)
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Re: Immersive Linear Algebra Book with Interactive Figures (2015)
#32Earlier quoted context omitted.
Have you opened the book? There are both theorems and proofs there.
Maybe I should’ve been more clear: what I meant is that these programmers-oriented resources are all about applications…maybe a bit too much. For instance, In this book I cannot find the algebraic structure of vector spaces, theorems about how certain linear operators such as the kernel or the image led to subspaces (which is a very important result) or a proper introduction to the spectral theorem, for both Euclidea…
I get where you're coming from but linear algebra is one of the most applied branches of mathematics out there. It's easy to visualize and easy to teach the computational side of it so it makes sense that some books focus more on that and these are popular among people whose main interest is in how to apply it - like programmers. You don't need to know what a ring is to learn how to multiply numbers.
I wouldn't say this one is programmers-oriented either - it was posted to HN, sure, but maths and physics students could benefit from some visualizations too as a supplement to a more rigorous text.
As for the things you mentioned as omitted, I think if you want to do a complete treatment you have to introduce more mathematical prerequisites which limits the audience of your book. For a mathematician, I'd say classical linear algebra in itself is not particularly interesting - it's very well-behaved and pretty much "solved". What you care about is how it relates to other structures (groups, modules, fields), how it develops into other topics (functional analysis) and how it's used to study other objects (representation theory, tangent spaces of manifolds). In isolation, most of what's left is the computational aspect which is what non-mathematicians mostly care about.
Re: Immersive Linear Algebra Book with Interactive Figures (2015)
#333Blue1Brown[1] has opened my eyes on the intuitive understanding of linear algebra, many, many years after taking a first course in linear algebra, which left me completely mystified.
[1] https://www.youtube.com/watch?v=fNk_zzaMoSs&list=PLZHQObOWTQ...
Re: Immersive Linear Algebra Book with Interactive Figures (2015)
#34Earlier quoted context omitted.
I am kinda this person, any good resources/texts on this? I'm very slow but I have no deadlines.
Slow is fine, and I do. My personal favorite is a former NASA employee who recorded a series of lessons for students to use to supplement their normal undergrad studies, prepare for exams, that kind of thing. He has a YouTube channel which has all sorts of topics (for free), but his site has paid videos on math, chemistry, electricity, some electronics, statistics, and a few other topics. You can find it on the high…
Such a helpful comment, much appreciated.
Re: Immersive Linear Algebra Book with Interactive Figures (2015)
#353Blue1Brown[1] has opened my eyes on the intuitive understanding of linear algebra, many, many years after taking a first course in linear algebra, which left me completely mystified. [1] https://www.youtube.com/watch?v=fNk_zzaMoSs&list=PLZHQObOWTQ...
I teach linear algebra in college, and during our first class, I urge all my students to watch this series as soon as possible. It's great at giving them a geometrical understanding of what's going on, so they feel more motivated to learn the theorems and do computation (and already develop some intuition as to why the theorems are true).
Re: Immersive Linear Algebra Book with Interactive Figures (2015)
#363Blue1Brown[1] has opened my eyes on the intuitive understanding of linear algebra, many, many years after taking a first course in linear algebra, which left me completely mystified. [1] https://www.youtube.com/watch?v=fNk_zzaMoSs&list=PLZHQObOWTQ...
I teach linear algebra in college, and during our first class, I urge all my students to watch this series as soon as possible. It's great at giving them a geometrical understanding of what's going on, so they feel more motivated to learn the theorems and do computation (and already develop some intuition as to why the theorems are true).
Have you read this post on incorporating spaced repetition into teaching linear algebra?
https://bentilly.blogspot.com/2009/09/teaching-linear-algebr...
Re: Immersive Linear Algebra Book with Interactive Figures (2015)
#37Earlier quoted context omitted.
I teach linear algebra in college, and during our first class, I urge all my students to watch this series as soon as possible. It's great at giving them a geometrical understanding of what's going on, so they feel more motivated to learn the theorems and do computation (and already develop some intuition as to why the theorems are true).
Have you read this post on incorporating spaced repetition into teaching linear algebra? https://bentilly.blogspot.com/2009/09/teaching-linear-algebr...
I hadn't, thanks! Spaced repetition is certainly a useful tool. I always try to start every lecture with one or two review problems (that I call "brick problems", making sure the previous brick row is solid before building on it).
I don't assign homework anymore because I have no interest in grading AI output (and even less interest in asking AI to grade AI output). The inverted classroom approach works well for me. Students read the textbook on their own (and I encourage them to use office hours, collaborate, or use AI tools if they need more explanations), doing checkpoint exercises to make sure they understand the material, and class time is spent on working problems.