131–134 of 134 posts
Is there a version or a similar book that deals with Calculus?
[Author here] We hear you! Here's a similar book for Calculus: https://github.com/the-little-book-of/calculus In this book, I cover Functions, Derivatives, Integrals, Multivariable Calculus, and Infinite Processes. In addition, I've included appendices with sketch proofs and applications to Physics, Probability and Statistics, and Computer Science.
Tried to pick a book to get into linear algebra recently, the experience was fairly hellish. First course this, second course that, done right, done wrong... I'd to the LADR4e route, but I don't have the proof-it chops yet...
I like Serge Lang's books for clarity of explanations. He has an Introduction to Linear Algebra which concisely covers the basics (265 pages in the main text), and grounds the matrix computations in the geometric interpretation. Be aware that Lang has another book, called just "Linear Algebra", which is more theoretical.
Tried to pick a book to get into linear algebra recently, the experience was fairly hellish. First course this, second course that, done right, done wrong... I'd to the LADR4e route, but I don't have the proof-it chops yet...
You might want to checkout the book Practical Linear Algebra: A Geometry Toolbox by Dianne Hansford and Gerald Farin (its 1st edition was simply named The Geometry Toolbox: For Graphics and Modeling ) to get an intuitive and visual introduction to Linear Algebra. Pair it with Edgar Goodaire's Linear Algebra: Pure & Applied and you can transition nicely from intuitive geometric to pure mathematical approach. The autho…
Earlier quoted context omitted.
Where's the circularity? What you're saying is fine as an abstract presentation, but I was talking about how students might initially come to learn about matrices, so just introducing column vectors as representing points in 2 and 3 dimensional space and how matrices transform them is fine. Beginning with the field and vector space axioms might be fine for sophisticated students, but I don't think it would make for a…
But the question was about deriving the multiplication rule. I said you could derive it from systems of equations directly and gave a proof. > and how matrices transform them is fine this is circular. You are introducing/assuming the multiplication rule right here. You can't then derive it
I realise though that I was answering more "How does it work?" (application) rather than "Why does it work?" (derivation)
For the latter, something involving sets of linear equations is probably best, as you initially said