Course Descriptions
The Fundamentals
This course provides the foundation for subsequent math courses. It presents arithmetic from scratch, covering material traditionally met in grades five, six and seven, but based on the underlying axioms. This approach allows all that follows to make sense. The focus is on the number system--it historys and some of its manifestations: integers, fractions, decimals and percents. The goal is three-fold: to understand what these numbers are and that they are interchangeable, to acquire an ease with and facility at manipulating them, and to be confident about using them to solve problems. Units will be discussed--what they are and how to easily (and logically) change them from one system to another. The student will learn how to use a calculator, and, more important, how to estimate the answer before ever picking up the calculator (so you'll know whether to be startled by what the calculator tells you...).
Algebra 1
This course is a continuation of The Fundamentals course, above. The algebra is built up from the axioms. The work will alternately focus on conceptual understanding, the skills of manipulation, and the art of problem solving. Content includes formal solution of first order equations, linear graphing theory and practice, the care and feeding of irrational numbers, and methods of solving second order equations and inequalities.
Algebra 2
Algebra 2 begins with a fast paced review of Algebra 1, which leads naturally to an exploration of the properties of functions and relations. Linear programming provides a rich application. From there to analytic geometry; conics are studied geometrically, algebraically and graphically. And finally the study of logarithms and exponentials, their uses to model growth and decay, and their applications in the worlds of science and commerce. Time permitting, we'll study combinatorics, probability, and elementary statistics.
Geometry
This is a fabulous course with its formal, axiomatic approach the student learns the art of logical thinking while learning the usual geometric facts. Proof is emphasized throughout the course. This is a basis for the development of facility at problem solving. As this kind of learning needs time to gel, the course meets for a longer time than the other courses.
Trigonometry
At last: tangible, real world problems. It is here that problem solving skills are sharpened and algebra skills are solidified. This is a classical, in depth trig course. Material will include a visual presentation of what the trig functions are and where they and their names came from, their graphs and why those are useful, and the identities (which are indispensable for the study of physics and calculus). Other material includes complex functions, an introduction to vector algebra, polar graphing and, time permitting, the conic sections in polar form.
Pre-calculus
The solution of higher order equations is explored; function theory is elaborated. We extend the concepts used in linear programming to include methods of solution of large systems of equations, particularly matrix methods. We study sequences and series and their many applications, especially in the mathematics of finance. We learn proof by induction and the general form of the binomial theorem.
AP Calculus AB
The content is traditional, the approach is not. In addition to the traditional analytic approach, we give a visual demonstration of the connection between the "rate of change" problem and the "area" problem, as well as the "change in area" problem--the ideas embodied in the two Fundamental Theorems of calculus. Our objective is to see that the student has a visual as well as intellectual grasp of the basic ideas of the calculus, because this is what allows the student to "own" the material--to be able to use it at will to address and solve problems which require calculus. There is an emphasis on solving problems of all sorts: business, medicine, physics, astronomy, horse racing. This course will prepare the student to pass the national AP Exam in Calculus AB given in early May.