This is a course of independent study aimed at preparing very motivated students for a university program in pure mathematics. The basic component consists of the academic stream of high-school math, including AP Calculus AB. The enrichment components are mainly based on Paul Zeitz’s The Art and Craft of Problem-Solving. Gilbert Strang’s Introduction to Linear Algebra provides a capstone in Grade 12.
- September 2016 – January 2016: Complete Precalculus 11 and Zeitz chapters 3 and 6. I’ve added enrichment problem sets to chapters 1 and 2 of the Precalculus book. If there is time left over at the end of the semester, do Zeitz chapter 7.
Tentative Five-Year Plan
- Grade 8: Mathématiques 9 and Math 10, enriched with Problem-Of-The-Week, Pascal contest, and Zeitz ch. 1-2.
- Grade 9: Precalculus 11, enriched with Combinatorics & Number Theory (Zeitz ch.6-7)
- Grade 10: honours Algebra and Geometry (Zeitz ch. 5&8), and other enrichment topics of your choice (perhaps Stilwell’s The Four Pillars of Geometry)?
- Grade 11: Pre-calculus 12 & AP Calculus 12 with Mme Daniels, enriched with Zeitz ch. 9 (note: this chapter is really hard!) or better: Michael Spivak’s Calculus.
- Grade 12: Zeitz ch. 4; Linear Algebra (Strang, ch. 1-6) or another honours topic of your choice