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 a course designed to help students make the transition from the conceptually-oriented inductive reasoning approach used in much of Math 1, Math 2, and Math 3 to the more rigorous deductive approach often seen in higher-level mathematics and science courses. Students who think they may have any desire to study a math- or science-related field in college should take this class. Topics covered in this class include function transformations, the theory of inverse functions, logarithms, polynomial and rational functions, analytic trigonometry, and advanced algebraic manipulations. Prerequisite: Math 3.

Calculus. This is a two-trimester course in single-variable differential and integral calculus with an emphasis on applications to the physical, life, and social sciences. Major concepts will be developed through the investigation of practical, real-world scenarios. Topics covered will 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 antidifferentiation, and creating mathematical models using differential equations. Time permitting, students may also study Taylor series and their applications. (Note: This course has been designated as an honors course by the University of California). Prerequisite: Analysis of Functions.

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 two-trimester course has two guiding questions. First, how can you collect meaningful data about a population without examining every single member of the population? Second, how can you analyze this data quantitatively to reach statistically valid conclusions about your population? In both trimesters, students will look at a wide variety of examples and case studies drawn that illustrate how statistical concepts are applied in the life, social, and physical sciences. Students will also spend a significant amount of time designing their own statistical studies, collecting data, and analyzing the results. Prerequisite: Math lll, or instructor permission.

Topology.  What would you do if Acre started serving soup on plates? Hopefully, you’d eat your soup out of a tea mug instead. Topology is the mathematical study of shapes and spaces. Bowls and plates share the same topological categorization, but a coffee mug is different because of the hole made by the handle. In fact, in topology, squares, rectangles, parallelograms, trapezoids, and circles are all considered to be the same. Topology is the branch of mathematics we get when we ignore things like size and angle. But here’s the tricky question: if we ignore these ways of measuring, how can we tell when two shapes are different? When you take topology, you’ll figure this out. You’ll also explore shapes like the Mobius Strip, the Klein Bottle, the torus, and ideas about gluing, orientability, and dimension, including ways to represent the 4th dimension. Prerequisite: Math III.