Mathematics

The Bay School mathematics program has been designed with three key goals in mind. First, it presents challenging mathematical content to develop quantitative literacy. Second, it provides a solid mathematical foundation for students who may wish to study math- and science-related fields in college and beyond. And third, it places significant emphasis on training students to think like mathematicians. "Thinking like a mathematician" includes working collaboratively with one's peers; looking at the world through a mathematical lens to find interesting mathematics in a variety of situations; persevering on challenging problems; choosing mathematical representations that apply to a given problem; recognizing what mathematical tools might be appropriate for a given problem and using those tools in a meaningful way; and communicating mathematical ideas elegantly in a variety of forms and media.

The Bay School's integrated core mathematics courses replace sequential courses in Algebra 1, Geometry, and Algebra II. Students who complete Analysis of Functions will be prepared for Calculus. In addition to these two standard high school electives, Bay offers a range of advanced elective courses which expose students to a broad range of mathematical fields.

Core Mathematics Courses

Math I
Math I introduces students to tabular, graphical, recursive, and algebraic approaches to problem-solving. The course focuses on the use of these tools in dealing with linear models and scenarios. Math 1 also deals extensively with descriptive statistics, basic algebra, and qualitative examinations of two- and three-dimensional geometric figures.

Math II
In Math II, students extend their study of algebra and geometry. The course focuses on the study of exponential and power models, matrices and their applications in a variety of contexts, multiple approaches to solving systems of linear equations, and the study of two-dimensional shapes from a coordinate and transformational geometry perspective.

Math III
Math III covers topics drawn from advanced algebra, plane geometry, and triangle trigonometry. Within the context of these topics, students are also introduced to the idea of formal deductive proof, as opposed to the inductive reasoning emphasized in Math 1 and Math 2. Another major theme running throughout the course is using mathematics to create models of real-world phenomena and analyzing and interpreting the predictions made by those models.

Elective Courses

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 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.

Analytic Geometry
Analytic Geometry is a course in which algebra and geometry blend together in powerful and interesting ways. The course explores geometric ideas visually and intuitively, using, among other things, a geometric drawing and visualization application on our laptops. Algebra is then used to create rigorous formal proofs of theories derived from our observations. Proofs will be written in both traditional Euclidean style and in analytic style. Particular emphasis is placed on conic sections and their equations.

Calculus
This is a course in single-variable differential and integral calculus with an emphasis on applications to the physical, life, and social sciences. Major concepts are developed through the investigation of practical, real-world scenarios. Topics covered include applications of the derivative as a rate of change and a slope, symbolic formulas for computing derivatives, applications of the definite integral as an accumulation function and an area, creating mathematical models using Riemann sums, symbolic techniques of anti-differentiation, and creating mathematical models using differential equations.

This course has been designated as an honors course by the University of California).

Game Theory
Game theory is the study of quantitative strategic decision-making in which one person's success in making choices depends on the choices made by others. Students in this course examine the theoretical aspects of Game Theory, and 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.

History of Mathematics
Following the stories of number theory, calculus, and geometry, this one-trimester course asks students to draw parallels between the Arts, Philosophy, and Mathematics. Students study number systems from different civilizations; the philosophy of mathematics; the structure of numbers; the concept of the infinite; and the geometry of the plane, the earth, and beyond. While this course asks students to practice rigorous mathematical thinking, emphasis is placed on conceptualization and communication over computation.

Seminar in Independent Mathematical Study
This course differs significantly from other Bay School math courses in that students will not work collaboratively with their peers on a regular basis. Instead, they pursue individual study of a topic using materials available in print or online. Each student in this one-trimester course spends the term studying a mathematical topic of his or her choosing, with instructor approval and guidance. Students will present their work to the class periodically throughout the term, keep a written "work diary" of their progress, have regular one-on-one meetings with the teacher as progress checks, write and solve problem sets related to their topic of study, and produce a final paper and presentation for the class at the end of the term. Most students who enroll in the seminar will have completed either Analysis of Functions or Calculus; however, any student who is academically and intellectually independent, self-motivated, persistent, and flexible is encouraged to apply.

Statistics
This course explores how to collect reliable data about a population and how to interpret the data meaningfully. Students build significant hands-on experience in designing and implementing experiments, surveys, observational studies, and simulations, and learn how to use confidence intervals and hypothesis tests to quantitatively analyze their results. They develop tools to communicate their work effectively in a variety of forms. Through the use of examples and case studies drawn from a variety of disciplines, students explore how statistics is both used and misused in mainstream and scientific media. The course culminates with a capstone project in which students design and execute an original research project which draws on their experiences throughout the course.