I am in the process of compiling a collection of exercises in Linear Algebra, (freshman course).

This is mainly just a series of examples, with a short theoretical introduction to each chapter with a few broad ideas of the concepts used in the problems.

My audience are students that prefers to learn from reading an example, and looking at previous tests/exams rather than reading the theory.

Are there any good tips about what a reader might prefer:

  • Should the solutions appear directly after the problem statement, or in the end of the book?
  • Would a reader like references to other literature, or is that just annoying?
  • Any other tips and suggestions?

I think you could combine both approaches (directly after and end of book): Directly under give the shorthand solution (just the bottom line of the answer) and at the end of the book give a more complete solution (the full solution).

This way, the studends can make sure they have come to the right solution immediately. If they didn't, they can refer to the end of the book to review the complete solution.

  • Solve the first 1 or 2 problems completely right in front of the question, so the student gets an idea of what to do. For the others, give a short answer (like final solution: x = 20) below the question, so students can check if they got the right answer, but put the complete solution at the end.
  • Put reference only if its useful- to an undergraduate. My whole Degree course was full of references to books that were written for Ph.D. students, and that the Professors loved, but were completely useless to me as they were too advanced. If you must, put in references to simple books in the Appendix, with a short note on why they were useful. But yeah, in most cases its just annoying: "Look at me, I read all these journals to write this book, Im so smart".
  • Get Feedback from actual students. Have them sitting in front of you trying to solve the problems. If they do them at home, they might just skim through them, or be polite and say they loved the book, when they didnt. So have them in front of you, and see how they progress. Are they actually getting better when working through the problems, so that they are finding the later problems easier?

I was always very good at math and I enjoyed it quite a bit (math competitions, state awards, etc.. etc..) but I always found Math textbooks to be almost completely useless. The problem was that aside from giving sample problems, they didn't help me understand the problem. The lecture did that and the book was just a massive homework assignment.

So, I'd say that the chapters should show explanations. Detailed walkthroughs of the lecture material. Problems with the steps explicated and answered. If I have a sheet of homework, I want to be able open the textbook and have it help me, not have it give me more homework.

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