{∅, {∅}, {∅, {∅}}} : Rage Against the Meat Grinder

A reminder of the SMSG (early 1960's experimental high school math texts) : some links

I am just finishing up my notes from going through all the exercises in Introduction to Matrix Algebra, circa 1960.  I am presently going through the APPENDIX, which contains "Research Exercises."   The first exercise covers the topic of quaternions in the guise of matrices.   It is so interesting that I feel like I have ingested some mild drug (no, it's not coffee!  It's well passed midnight).

I made it through the text in a few weeks, filling nearly two entire sketch pads.  Fortunately, awhile back I had tracked down the Teacher's Commentary (called "Unit 24") --- found it somewhere in Germany of all places off ebay for about only $12.   SMSG was based in the United States, so I was excited to find the movement had found its way all the way across the pond to that mysterious place I am forbidden to love.

Whoever sold it to me must have known what a blessing it was to me.  The solutions in the Teacher's Commentary were essential to fully appreciating the material.  (I had to highlight this in red to clarify that, for many of the exercises, I most likely would not have even known where to begin, as far as what kind of solution was expected, if I had not happened to be destined to be the receiver of such an odd gem/relic.)  I really feel blessed to have gone through hardbacks, and to have acquired them at such generously low prices.  It appears nearly impossible to even track down a digitized scanned version of the Teacher's Commentary for the Matrix Algebra module, and there is no site of another hard copy, at least not one that anyone is willing to part with.  It is for this very reason that I have basically recorded in my own writing in large sketch pads nearly the entire contents, altering some of the notation to suit my tastes, and adding explanations when I was able to do so.  So, in effect, I pulled a modern day monk project off in a few weeks, and I think my hand-written copy may take on a certain glow, as long as I don't make too many smudge marks.  It's all in pencil!   

I just can't bring myself to work with a pen doing math(s) of any kind.  I constantly need an eraser.  So be it.  That is my preference.  I know this will make the writing disappear much sooner, but, hell, we all fade away fairly quickly relative to "geological time," in a flash actually.

If you (Holden) ever go through the digital version (called Unit 23), do not hesitate to request detailed solutions to problems.  I would scan pages from my own notes as well as original Teacher's Commentary (unit 24), and upload to Dropbox (which is full), deleting several files from the voice diary of a drunken madman.

Note that the Analytic Geometry UNIT 64 module DOES have the Teacher's Commentary UNIT 65 module digitized.  It covers conic sections and even 3-space.

I think you will find the approach they took refreshing in comparison to our 21st century track.