The Mathematics Department offers a sequence of courses by which students can gain an understanding of the style and content of mathematics, become adept in its fundamental skills, develop an understanding of the analytic power of mathematics through problem solving, and begin to explore the subject for the beauty of its abstractions and the variety of its applications. Confidence building and minimization of fears are conscious goals. While technology is used in many situations, students are also asked to do work by hand to ensure a deep understanding; our emphasis is usually on “why,” instead of simply “how.”

Three years of math courses are required for graduation, although most students choose to take all four core courses (Algebra 2, Geometry, Precalculus and Calculus). Most students also explore other branches of mathematics through the range of one-term electives that are offered. A student may elect to do an independent study in an area of particular interest where a course is not offered.

Students have the opportunity to explore English, History, Mathematics, Science, Language, or Arts topics of interest under the supervision of a member of the appropriate department. After designing a project with a faculty member, the student presents a formal proposal to the Department Heads for approval. (An Independent Study may not duplicate the content of another course already being offered by the department because of schedule conflicts.) The student works in his or her own time and meets with the specified department member during one scheduled period per week for discussions and planning. Application forms are available from the Upper School Director. Proposals must have been submitted by the regular course selection dates.

This course covers all of the topics of an introductory Calculus course, exploring concepts in depth with a greater emphasis on both the abstract aspects of calculus and its various applications in the real world. Students will be expected to enter the class with a firm grasp of all concepts covered in previous math courses.

Prerequisite: Precalculus and departmental permission. Offered at the Honors level only.

Algebra II is a continuation of symbolic reasoning and understanding of mathematical models from Algebra I. The first term builds on topics such as polynomials and quadratic functions. In the second term, students will extend their algebraic reasoning to include topics such as nonlinear systems of equations, logarithmic functions, and exponential relationships.

Prerequisites: Algebra I or Intermediate Algebra. Offered at the Honors and Standard levels.

In this course, students will have the chance to learn a range of discrete math topics and grapple with a range of different problems that fall outside the spectrum of traditional high school mathematics. Topics covered may include finite sets and partitions, enumeration, probability, expectation, random variables, and elementary number theory, with an emphasis on applications of discrete mathematics, and fair division, voting systems, graph theory, chaos theory and non-Euclidean geometry. Students will be able to answer questions like: “how many Beaver students are involved in a theater production and in an athletic sport throughout the school year?”, “what is the probability of picking at least three red marbles out of a bag of seven white marbles and five red marbles?”, “find the value of 7 mod 4”, “if there is a car accident, what is the probability the person is between the ages of 16-21?” and “what states have both a pro basketball team and a pro hockey team?” Students will also be asked to think creatively and apply their knowledge to complex real-world problems.

Open to 11th and 12th graders or by departmental approval.

This course takes a discovery-based approach to the analysis of points, lines, planes, triangles, quadrilaterals, circles, parallelism, congruence, similarity, area, general polygons, and volume of solids. Students develop pattern-recognition, logic skills, and visual problem-solving skills through investigation, conjecture, argument, and proof. Additional topics may include statistics and coding.

Prerequisites: Algebra I, Algebra II. Offered at the Honors and Standard levels. Honors level requires departmental permission.

In this course, students will build a strong foundation for Algebra 2 by improving number sense, grappling with a variety of real-world applications, and working extensively with linear and quadratic equations, systems of equations, and polynomials. Students will also deepen their understanding of linear and quadratic functions while building their understanding of exponential and rational functions.

Game Theory is a branch of applied mathematics that is used to evaluate various social conditions. Students in this course will learn about the mathematics behind social and strategic situations. This course will focus on topics ranging from game strategy to problems of cooperation in everyday life. Case studies in resource depletion, global warming and conflict negotiation will be included. Student work will apply theory to real strategic environments.

Open to 11th and 12th graders or by departmental approval.

In this course, students will take a deeper look at various families of functions: rational, radical, exponential, logarithmic, parametric and polynomial. Students will learn about the ways in which domain, range, continuity, inverses, composition and transformation apply to those functions. Students will also have opportunities to analyze real-world data and generate predictive models. Topics from discrete math are often included in this course, as well.

Prerequisites: Algebra I, Algebra II, Geometry. Offered at the Honors and Standard levels. Honors level requires departmental permission.

Students in this course will learn about angle measurement, periodic behavior, and a range of applications related to both right triangle and circular trigonometry. Analytic geometry and polar coordinates are often included in this course, as well. Prerequisites: Algebra II and Geometry. Honors level requires departmental permission.

Prerequisites: Algebra I, Algebra II, Geometry. Offered at the Honors and Standard levels. Honors level requires departmental permission.

This course includes the gathering of data and a variety of sampling techniques, hypothesis testing, frequency distribution, normal distribution, correlation, linear regression, theoretical distributions, and inferential statistics. This course asks students to consider questions such as these: How is data summarized so that it is intelligible? How should statistical data be interpreted? How can we measure the inherent uncertainty built into statistical data? Students will be asked to collect, analyze and interpret real data to answer real questions in their areas of interest.

Open to 11th and 12th graders or by departmental approval.