Objectives
We will be studying a variety of mathematical topics for the purposes of improving knowledge of the subject material and improving problem-solving skills.
Syllabus
The syllabus will vary from year to year, but we will choose topics from among the following categories:
Number reasoning and induction
Algebraic manipulation
Polynomials and roots
Advanced factoring techniques
Complex numbers
Vectors and 3-D geometry
Matrices
Trigonometry
Derivatives and graphs
Sequences and series
Parametric functions
Hyperbolic functions
Integration techniques
Differential equations
Inspiration
Much of the inspiration for the course derived from a careful study of the Oxford-Cambridge STEP problems. It my goal that any student who finishes the course would be well-equiped to take the STEP exam. Although this may not be a personal goal of any student in the class, it does provide a reasonable set of achievable outcomes for any student wishing to pursue higher mathematics, physics, or other quantitative fields at the university level.
Some classroom time will be spent learning new concepts. However, the majority of our time will be student-directed problem solving. The expectation is that students will find their skills most effectively improved by confronting challenging problems under the guidance of the teacher and their peers. The material we will look at is difficult and demanding but also accessible to anyone who has patience and perseverance.
Assessments
I will assign homework frequently. These can be short practice problems or more extended problems requiring thought and organization. Try to start on them assignment early so that if you have problems you can come see me for a discussion. I will often collect your homework and read through it. I may even return it and require it to be rewritten. Please keep in mind that this can be a very fruitful exchange between us, helping you learn from your mistakes and clarify your thinking.
Occasionally I will give short quizzes. These will focus on specific technical skills and will be worth from 25 to 50 points.
Tests will occur at the end of major sections. These are always announced. The test will (almost always) consist of a few extended questions that you will take home and work on. You will be given from one to two weeks to complete them. You may not receive any help except from a teacher. You will be expected to model correct mathematical presentation, organization, language, terminology, and depth of rigor. These will be worth 100 points.
Occasionally I will schedule in-class tests.
Extra help
My free periods are 2 and 5 and (usually) 4. I’m happy to help you whenever I’m available. I’m also free before and after school on Mondays, Thursdays and Fridays as well as lunchtimes.