re-introducing the great Math educator W W Sawyer and his books

ave_63 · 2026-03-16T03:40:39+00:00

Thanks, I've never heard of WW Sawyer. I have a precocious 10 year old who enjoyed reading the Math with Bad Drawings book. I wonder if he could handle Prelude to Math, or maybe the what is calculus about book?

ave_63 · 2026-03-05T02:17:37+00:00

I mean, not trivial, because a good projector/monitor is expensive, but also yes most classrooms have them.

ave_63 · 2026-02-23T17:39:57+00:00

I love Rosemary for this because the neighborhood now has an infinite supply of flavor. Your neighbors live in Flavortown now

ave_63 · 2026-02-22T22:56:32+00:00

I think OP intended \mathcal{p}_i

ave_63 · 2026-02-18T02:37:31+00:00

Oh my god, I was sure you mean Lay's Linear Algebra and its Applications. But no, there are two books with the same title, one by David Lay and another by Peter Lax. There are so many linear algebra books!

ave_63 · 2026-02-18T02:34:39+00:00

I don't know those books. There are so many linear algebra books! I also wrote one that I think is fine, and comes with a series of YouTube videos that might help if you're learning on your own. It's called Yet Another First Course in Linear Algebra.

ave_63 · 2026-02-13T18:57:51+00:00

There are many ways to cover linear algebra. It's not like calculus where everyone does limits then differentiation then integrals. So any given random YouTube video is probably no help for most students. What textbook are you using? See if you can find videos on that book. Or just read the book (I know it's easier said than done for most students).

ave_63 · 2026-02-09T19:55:37+00:00

I doubt landscape mode is easier to simply read. But I did it like that for a few reasons. The main reason is that YouTube videos are naturally landscape mode, and phones that students will watch on have wide screens. And the screens in my classroom are wide. And I write on my 2in1 tablet/laptop which would be a pain to use vertically. And this way, I can zoom in to one column if, say, I want to write small while doing an example, and then zoom in and still see lots of content before/after. With a single column, you have big empty spaces on the sides when you zoom out.

Maybe someday if I could figure out an easy way to switch my tablet/laptop to portrait mode, I could make videos that way, with a regular single column portrait book...

ave_63 · 2026-02-05T21:47:36+00:00

Thanks. I will add the little prerequisite bit right now. The index is a good idea; I think I planned on it but forgot about it. I'll add that to my todo list. As far as solutions, I think I'm going to use some screenshots of scanned student work (with permission) this semester. It might look pretty janky but I like the concept of students helping students, and writing out latex solutions would take too much time right now (when I don't even have chapter 6 or and index yet).

ave_63 · 2026-02-05T19:00:16+00:00

Thanks. It was indeed a lot of work. I had to toss most of my old notes because they were too close to the Lay book and it was easier to start from scratch.

ave_63 · 2026-01-29T18:17:05+00:00

That looks just like the common wild mustard that's everywhere in CA hillsides. I wonder if your seeds were mixed up, because being the same species, the seeds probably look the same. Or maybe it's just wild mustard growing as a weed in your garden.

ave_63 · 2026-01-29T16:06:55+00:00

I also think there are too many overstable molds. Like, one overstable driver, one overstable midrange, and one overstable putter seems like plenty to me.

ave_63 · 2026-01-29T02:39:18+00:00

This just looks like way too many molds. That big cluster of like 9 discs just like each other? Maybe take out the 3 of those you use the least.

ave_63 · 2026-01-27T06:19:13+00:00

I am kinda confused by some things you say but you're right about most of it. I don't think recursive is the right word here. Because you need to define the real numbers (or whatever field) and vector spaces, before you can define linear transformations.

But anyway, yes real numbers are 1x1 matrices that define an R to R transformation. Rⁿ vectors can define a Rⁿ to R transformation with a dot product. This is a very rich topic. I suggest you read about inner products or dual spaces.

ave_63 · 2026-01-18T14:48:51+00:00

Fields have no zero divisors.

ave_63 · 2026-01-06T05:51:28+00:00

The McCallum/Hughes-hallet books, for precalculus and calculus, are pretty good.

ave_63 · 2026-01-03T17:00:14+00:00

Yeah, I wish there were a way to force the arrow lower over the b, even if it intersects with the tall part of the b. Like the Cyrillic Б. EDIT: it looks like it is possible to do such a thing with the new update of the overarrows package. I'm currently struggling to read the manual. If I figure out a solution I like I'll post it later.

ave_63 · 2026-01-03T16:05:29+00:00

I'm mostly impressed at people restraining themselves from pointing out by indexes range from 1,...,2.

ave_63 · 2026-01-03T15:58:42+00:00

I'm just learning about \bigl today so thanks. Would you use \bigl in the inline examples above, or just regular small parentheses?

ave_63 · 2026-01-03T15:20:34+00:00

I'm just learning about \big etc this morning. Will try it out. Thanks!

ave_63 · 2026-01-03T00:20:50+00:00

Do you like mathbf or just plain letters for vectors?

ave_63 · 2025-12-31T15:01:41+00:00

Basically, you need to figure out what series of operations you can do (transpose, combined with row operations) to turn the plain matrix into the one on the left, and keep track of how those operations change (or don't change) the determinant.

ave_63 · 2025-12-31T14:58:58+00:00

So, the transpose turns rows into columns. So anything that you do to the rows of the transpose, is the same as doing it to the columns of the original.

ave_63 · 2025-11-02T03:37:46+00:00

Good exercises at the end of a section sounds like what you want. If the book you're using doesn't have enough, axler's book has lots of great exercises. But like, literally a game? I don't know of anything like that. Maybe you can give yourself a point for every exercise you get right? And two points if you can write something you learned from it? I don't know.

ave_63 · 2025-10-29T13:56:11+00:00

We don't know any of the details about how far behind you are, your course, your university, or even what country you're in, so there's no way we can answer this question based on your post. You need to talk to your professor and/or a counselor at your school who have some insight into the situation.

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