I am having trouble writing this morning, so I hope that blogging here will loosen my brain and thoughts will start to spill out properly.

I am working on my linear algebra books. “What’s that?”, you say, “You are writing books, plural, for a course?” Yes. I have taught linear algebra many times in the last few years, and I finally felt dissatisfied enough with my old materials and prepared enough with my ideas about the course to write everything from scratch. So, I am writing these:

- A primer, or reader, which discusses the basics of linear algebra but sticks entirely to the plane and 3-space.
- A workbook, which has a sequence of tasks I can use to run an IBL course.

My basic model for this is how I run my Euclidean Geometry course. I have the students read Euclid’s *The Elements* Books I-IV, and I have designed a sequence of tasks to go with that. The idea is to treat *The Elements* as the existing research literature, and then pose ‘research questions’ which drive the students to understand the material and learn to do math on their own. In geometry, we are working on proof-writing, definition-making, and conjecturing. This works great.

I want to copy the model for linear algebra, so I need something to replace *The Elements*. So I am writing it. I am trying to use the old-fashioned, discursive style that you would find in math texts pre-WWII, too. The text is much more a narrative, and avoids the now-standard “Defn-Thm-Proof” setup. Definitions and results pop up as we find them.

So, now I am about 75% of the way through writing chapter one, and I am past deadline for getting this to my students. They have the first half of the chapter, which got us through yesterday. I had hoped to give them the second half to read last night… and I failed.

My current sticking point is making a transition from talking about norms, angles, and the dot product in the plane, to talking about the equation of a line through the origin. I have written the start of three different versions today, and been happy with none of them. So, I am going to take a break and start again in about an hour.

Maybe I’ll read the copy of Math Horizons that just arrived.

ps. If you want to follow along with my crazy experiment, I use github. The files are here.

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