trying to be a mile wide AND a mile deep
I include this because it wasn’t in any of the books in which I looked for it when I last taught linear algebra. Exercise: show that if a vector space (over the real numbers) has at least two vectors, it has infinitely many. Simple proof: If V has two vectors, one of them is nonzero. […]
Here are a few handouts I’ve used in the past to teach parts of calculus. Relating latitude and longitude to spherical coordinates. Bonus appendix about great circles. Trigonometry review for calculus students. A guide to curve sketching. Painfully detailed examples of surface integration.
If the Pythagorean theorem is mysterious to you, try this activity. I can’t guarantee it will make everything clear, but I hope it will at least help. You need paper, pencil, scissors, and a ruler; probably it wouldn’t hurt to have an L-shaped ruler to get right angles, or you could use graph paper. First, […]
When I was an undergraduate, we had an entire class dedicated to making the transition from calculus-type mathematics to abstract upperclass-level mathematics. We learned basic logic and set notation and manipulation, proof structures, and induction, proving simple number theory results that didn’t require additional new concepts beyond induction. I got to teach such a course […]
In February of 2011, I gave a talk to the Dartmouth Math Club about linear algebra. This post replicates the page of resources I made for the club members related to that talk, and adds one new one. Slides from the talk. Pdf about uses of linear algebra. From Oliver Knill, Harvard Math, near the […]