Mathematics

The core mathematics courses take students through a four-year, integrated program which replaces traditional courses in Algebra 1, Geometry, Algebra 2, and Precalculus. These courses contain three major content strands: Algebra and Functions, Geometry and Trigonometry, and Statistics and Data Analysis—culminating with a capstone project. Upon completion of Analysis of Functions, students will be prepared for Calculus. Juniors or seniors may choose, however, to take other math electives in addition to, or instead of, Calculus.

Core Mathematics Courses

Math 1
This course explores topics including: organizing and interpreting data, data distribution, measures of variation, coordinate graphs, algebraic formulas, linear and nonlinear functions, linear equations, properties, modeling data, algorithmic problem-solving, critical path analysis, properties of space shapes, geometric theorems, exponential functions and modeling, and simulation models.

Math 2
This course explores topics including: matrix models and operations, coordinate planes, designing and programming algorithms, solving systems of equations, isometric transformations, correlation, linear least squares models, variability, direct and inverse power variation, fractional powers, radical expressions, vertex-edge graph models, optimization, geometric form and function (triangular linkages; sine, cosine, and tangent ratios; linear velocity, periodic change; radian measure), and probability distributions and their graphs.

Math 3
This course explores topics including: Law of Sines and Cosines, solution of systems of equations and inequalities, linear programming, formalization of the function concept, nonlinear models (polynomial, exponential, and rational), field properties of real numbers and their application to re-expressing algebraic expressions and solving equations and inequalities symbolically, algebraic proof, deductive and inductive reasoning, proof by counterexample, theorems involving angle measure, proving similarity and congruence of triangles, arithmetic and geometric sequences and series, finite differences, linear and nonlinear recurrence relations, and function iteration.

Analysis of Functions
Analysis of Functions is designed to serve as the bridge between the Bay School’s core courses and a college-level calculus course. As such, Analysis of Functions focuses on deepening students’ understanding of advanced functional characteristics (including location and multiplicity of zeros, end behavior, and continuity), algebraic manipulation of complex expressions and equations, basic function families and transformations thereof, the behavior and usage of trigonometric functions, and proof by algebraic identity. Students also extensively study functional inverses and logarithms, including the number e, the natural logarithm, and the use of logarithms in solving exponential equations. The course introduces complex numbers, the complex plane, and properties of this number system. Graphing calculators are used extensively throughout the course.

Elective Courses—2007-2008

Calculus
This is a course in single-variable calculus. It covers differentiation and integration and their applications, including differential equations. Key units include: the derivative; differentiation formulas and techniques; applications of differentiation; the definite integral; constructing anti-derivatives; techniques of symbolic integration; applications of integration; building Riemann sums; and modeling with differential equations.

Game Theory
This course is designed as an advanced mathematics elective, to be taken after students have finished at least the first two of their core sequence mathematics courses. Students in this course will examine the theoretical aspects of Game Theory, and will then, through case-studies and a project, examine the ways in which Game Theory can be applied to areas such as biology, foreign affairs, military strategy, anthropology, and other situations that involve competition for resources.

Probability and Simulation
In this course, students explore the major mathematical ideas of probability. Probability and Simulation is taught in an investigation-based manner similar to that used in Math 1, Math 2, and Math 3. It makes heavy use of technology (TI’s and software) as well as traditional mathematical techniques. Major topics include: simulation models, waiting time distributions, binomial distributions, and Monte Carlo methods and Markov processes.

Statistics
This course models the research skills necessary for many college majors. Students learn how to design experiments, organize data into tables and graphs, model sampling distributions, and test hypotheses. Students will apply their skills in a multitude of contexts that draw from existing data and data generated from student experiments and surveys. For example, students will investigate sports statistics, medical data, and social phenomenon. In doing so, they learn to evaluate evidence, debate, and critique studies. The course goal is for students to understand the many connections between mathematics and their own lives, and ultimately to become informed consumers. The statistical methods taught in this course are ideal for students interested in pursuing studies in the social sciences, sciences, business, and communication fields.