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Immersive Linear Algebra – A free interactive online book

immersivemath.com

21–30 of 80 posts

Re: Immersive Linear Algebra – A free interactive online book

#21

I'm sure that this a wonderful book, but please note the error right off the bat in equation 1.3 The tangent of the angle in question is b/a NOT a/b as stated. Probably a good idea to keep an sharp eye on the math as you go along in this thing.

Thanks for the catch! The site has now been updated.

Re: Immersive Linear Algebra – A free interactive online book

#22

This looks awesome. The popup-help's are a little jarring though since there's no indication as to which words will trigger a popup. Also: "Oh come on, you should know what a vector, v, is by now. Check out Chapter 2, for crying out loud." seems kind of harsh to say to the reader while they're reading the first sentence of Chapter 2..

"Kind of harsh" is an understatement. Insulting the reader like this is not acceptable. Mathematics is already difficult enough to learn by its very nature. Authors, you don't need to help make it more difficult. We already have a hard enough time convincing people that they can learn something this difficult.

Thanks for the feedback. We have removed the popup for "vector".

Re: Immersive Linear Algebra – A free interactive online book

#23

I'm sure that this a wonderful book, but please note the error right off the bat in equation 1.3 The tangent of the angle in question is b/a NOT a/b as stated. Probably a good idea to keep an sharp eye on the math as you go along in this thing.

Send me your name to immersivemath@gmail.com and we will add you to the acknowledgements section!

Re: Immersive Linear Algebra – A free interactive online book

#24
I always see linear algebra on HN and many people comment on how they never understood the subject. This makes me ask: what exactly is it that people don't get about linear algebra? What makes it appear to be a difficult subject?

As someone who has used linear algebra almost every day in some form over the last decade, it's hard to get a perspective of what aspects are challenging to the beginner. And since I TA courses that involve linear algebra, it is good to know where the problems are.

Re: Immersive Linear Algebra – A free interactive online book

#25

I always see linear algebra on HN and many people comment on how they never understood the subject. This makes me ask: what exactly is it that people don't get about linear algebra? What makes it appear to be a difficult subject? As someone who has used linear algebra almost every day in some form over the last decade, it's hard to get a perspective of what aspects are challenging to the beginner. And since I TA cour…

What it is, I think was my major problem.

Matrix multiplication, ranks etc. are some of the most random seeming operations you can tell a student to memories.

Re: Immersive Linear Algebra – A free interactive online book

#26

I'm sure that this a wonderful book, but please note the error right off the bat in equation 1.3 The tangent of the angle in question is b/a NOT a/b as stated. Probably a good idea to keep an sharp eye on the math as you go along in this thing.

Send me your name to immersivemath@gmail.com and we will add you to the acknowledgements section!

That's o.k. I'm usually the one making boo-boos like that. Glad we caught it.

Re: Immersive Linear Algebra – A free interactive online book

#27

I always see linear algebra on HN and many people comment on how they never understood the subject. This makes me ask: what exactly is it that people don't get about linear algebra? What makes it appear to be a difficult subject? As someone who has used linear algebra almost every day in some form over the last decade, it's hard to get a perspective of what aspects are challenging to the beginner. And since I TA cour…

I think it's mostly because mathematics is taught as is with little or no attention to practical applications of the theory. For instance, till date, I could not see how eigen values/vectors are useful.

Re: Immersive Linear Algebra – A free interactive online book

#28

I'm sure that this a wonderful book, but please note the error right off the bat in equation 1.3 The tangent of the angle in question is b/a NOT a/b as stated. Probably a good idea to keep an sharp eye on the math as you go along in this thing.

Thanks for the catch! The site has now been updated.

[deleted]

Re: Immersive Linear Algebra – A free interactive online book

#29

I always see linear algebra on HN and many people comment on how they never understood the subject. This makes me ask: what exactly is it that people don't get about linear algebra? What makes it appear to be a difficult subject? As someone who has used linear algebra almost every day in some form over the last decade, it's hard to get a perspective of what aspects are challenging to the beginner. And since I TA cour…

I found that the level of abstraction that linear algebra is taught at is really weird. On the one hand it was never really taught in connection with algebra in general, or put into a wider mathematical context. On the other hand we were never really shown any real world used of linear algebra or how the concepts maps onto practical applications.

It wasn't before years later when A) I'd taken more abstract algebra courses that introduced concepts like tensors and fields and B) I'd taken more practical computational courses where I had to do things like use linear algebra in 3D graphics and use eigenvectors to do dimensionality reduction and PCA, that I really understood the subject and its place in the world.

Just saying here's a random object (that we'll call a "matrix"), here's some random steps (that we'll call "taking a determinant"), now memorize how to apply the steps to the object and see if the result is zero, didn't lead to much deeper understanding.

Re: Immersive Linear Algebra – A free interactive online book

#30

I always see linear algebra on HN and many people comment on how they never understood the subject. This makes me ask: what exactly is it that people don't get about linear algebra? What makes it appear to be a difficult subject? As someone who has used linear algebra almost every day in some form over the last decade, it's hard to get a perspective of what aspects are challenging to the beginner. And since I TA cour…

I think it's mostly because mathematics is taught as is with little or no attention to practical applications of the theory. For instance, till date, I could not see how eigen values/vectors are useful.

One nice application is that the eigenvectors of a stochastic matrix correspond to stationary states of the Markov chain. That leads naturally to a conversation about PageRank, which is super useful because it made billions of dollars for some people. Then you could talk about the use of eigenvectors for principal component analysis in data science, which is making a lot of money for other people right now. If these examples are not useful, then I don't know what is.
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