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Advanced Math Seminar

Teacher: Mr Poggioli

Period 2

Room R-306

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

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

Much of the inspiration for the course derived from a careful study of the Cambridge STEP (Sixth term Examination Paper). This is a test used by Cambridge to determine a student’s potential to undertake a difficult program in mathematics. The questions are similar in style to those found in an undergraduate course and require proficiency in a variety of topics as well as advanced problem-solving skills.

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.

Prerequisites

All students enrolled in the course are assumed to have had a thorough training in precalculus concepts, geometry, and trigonometry as well a reasonable command of the techniques and concepts of differential calculus.

Although many of the ideas we will discuss are based on concepts already familiar to the student, we will expand these ideas further, go into greater depth, and use them to solve sophisticated and challenging problems.

Extra Help

My free periods are 1, 3, 6, and 8. I am available for help by appointment. You can always set up a time through email but don’t wait until the last minute because, occasionally, I have other commitments during these periods.

I am also available for help during the Conference period every day except when there is a scheduled school activity. Although I will try to be available without appointment, it’s always good to let me know you’re coming.

Assessment

All tests and quizzes are announced well in advance.

Your tests will consist of a take-home and an in-class part. The in-class part will be straightforward and simply check that you have mastered the techniques we have discussed. The take-home questions will be more challenging. All test questions are pledged. You may ask me for guidance but receive no help from anyone in the class.

Homework assignments will consist of some short technical exercises as well as more advanced problems requiring considerable thought. Please start them on the night they are assigned so you can come by for help if required.