Tentative Sequence
The following can be telescoped for students who demonstrate greater ability.
| Grades | Coursework | |
|---|---|---|
| 1–4 | Euclidean geometry | (Trachtenberg) arithmetic |
| 5–6 | Euclidean geometry | prealgebra |
| 7 | Euclidean geometry | elementary algebra |
| 8–9 | linear algebra | elem. alg. & analytic geometry |
| 10 | linear algebra | elem. alg. & trigonometry |
| 11 | linear algebra | calculus |
| 12 | lin. alg. & diff. eq. | calculus |
Possible Texts
The Trachtenberg Speed System of Basic Mathematics (Die Trachtenberg-Schnellrechenmethode), Jakow Trachtenberg, tr. Ann Cutler and Rudolph McShane.
Elements of Algebra (Vollständige Anleitung zur Algebra), Leonhard Euler, ed. Christopher James Sangwin.
Elements (Στοιχεῖα), Euclid, tr. T. L. Heath (vol. 1, vol. 2).
Geometry (La Géométrie), René Descartes, tr. David E. Smith and Marcia L. Latham. Note: preceded in the foundation of analytic geometry by Omar Khayyam’s Discussions of the Difficulties in Euclid.
Algebra, I. M. Gelfand and A. Shen?
Textbook to be written after Divine Proportions: Rational Trigonometry to Universal Geometry, N. J. Wildberger.
Cogito, Credo, Petam 
Bending and Stretching Classroom Lessons to Make Math Inspire. Thought you’d enjoy this article at nyt.com today as well as the related videos.
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That was a fun read. Thanks!
Now for the videos.
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