Tips for writing math solutions for others

Question

I am working a bit on a collection of Linear Algebra examples, as well as some examples on induction. This is what is taught freshman year at our university.

I intend to release this to the public, either by selling printed copies or releasing it online.

Since I do not have experience using such material myself, there are some questions I would like some opinions on:

• How much theory should I include? Is references to course litterature enough?
• Is there a format preference? Small text, so that the collection is more enviromental-friendly, or with big marginals for notes?
• Best way to deal with misprints?
• Should induction and Linear algeba be separate pieces?

Please share your experience if you have done something similar.

EDIT: An answer I seek is something along the lines of: "I am a "something" stident, and I prefer "something", and would like to see more of "something".

Answer 1

On previous web sites, I've seen many people asking for more examples on Singular Value Decomposition (SVD). Strang's LA book does this, but some folk want more. Another thing that some undergraduates do, but then forget, but then need to do again in other courses is QR factorization (Gram-Schmidt); so, you should have multiple examples.

Those are 2 things that are pretty straight-forward for most, but examples (after the theory) would be good.

Answer 2

I am an undergrad student, and I just finished taking Application of Linear Algebra. Here is what I want from a linear algebra text:

EXAMPLES WHICH ACTUALLY DEMONSTRATE THE POINT.

An example of what I don't ever want to see: the first example in my textbook was to show how to do matrix multiplication. Simple, right? No. They used a square symmetric matrix multiplied by itself to demonstrate this, and didn't walk through the individual steps. It just gave some matrix A and said look! A.A = B. See? And of course we didn't.

So please! Check that your examples can only be understood one way, and that this way is the way you intend.