Mathematics

The Algebra course, designed by the faculty, has no textbook, and the sequence of content is similar to that in The Art of Problem Solving: Introduction to Algebra. Hundreds of problems are curated online through Google Docs and accessed by students via the School’s Schoology system. In working through these problem sets, students learn to see structure in algebraic expressions, perform arithmetic on polynomial and rational functions, generate and solve equations that describe numerical and geometrical relationships, and create and analyze graphs of these equations. Students use both the online graphing calculator Desmos and the mathematical computation program Mathematica to enhance and inform their exploration of these topics.

In Geometry, students receive a problem-based introduction to Euclidean plane geometry. By working through teacher-curated problem sets, they learn about congruent and similar polygons, circles and their relationship to trigonometry, and the importance of scale factor when dealing with problems of area and volume. In addition to solving problems, students prove theorems about the invariant properties of shapes in two and three dimensions. Classical straightedge and compass construction is introduced, along with the dynamic geometry software Geometer’s Sketchpad. An emphasis on deductive reasoning and creative problem-solving is present throughout the course. 

In Algebra II, the concept of functions and linear equations is explored, with an emphasis on creating mathematical models for more complex numerical and geometric patterns. Students continue their study of polynomials, working with higher-degree polynomial equations and graphs. They solve problems involving arithmetic and geometric sequences and series and are introduced to the basic concepts of combinatorics and probability. Students also use the online graphing calculator Desmos, the mathematical computation program Mathematica and the TI-84 graphing calculator.

In Precalculus, students explore trigonometry from a functional perspective and are introduced to rational, exponential and logarithmic functions. Emphasis is placed on algebraic invariants over entire classes of functions, and the course concludes with an introduction to limits. Students also use the online graphing calculator Desmos, the mathematical computation program Mathematica and the TI-84 graphing calculator.

A hallmark of the Prep School is its emphasis on individual students and their interests. Starting in ninth grade, students have access to a wide range of electives in art, music, theater, technology and physical education. As they advance through high school, they gain more autonomy in selecting their courses. By their junior and senior years, they create their entire academic programs in all subjects, including English, history, math, science, world languages and other elective courses. This approach fosters engaged, successful and independent graduates prepared for the next educational step in their lives. The flexible elective system ensures that no two academic years are the same.

Mathematics elective classes reflect the department’s commitment to teaching for understanding through problem-based instruction. Some previous mathematics electives offered are:

• Number Theory
• Advanced Geometry
• Computer Mathematics
• Discrete Mathematics
• Advanced Senior Seminar: Mathematics

This course is designed to teach high school students the equivalent of a one-semester college statistics course. Students learn to collect, explore and draw conclusions from data. The main purpose of course projects is to provide students with substantial experience in developing statistical studies and making sound connections and judgments between the design and the results of the experiment.

In either Calculus AB or BC, students are introduced to fundamental concepts such as limits, continuity, differentiation and integration. They also take the AP Calculus AB or BC exam. Each exam covers challenging applications of the derivative and a more sophisticated approach to infinite series. The courses use the online graphing calculator Desmos, the mathematical computation program Mathematica and the TI-84 graphing calculator.

This course is designed for students who are concurrently enrolled in BC Calculus and interested in continuing their mathematics studies in college. It covers two major topics: linear algebra (matrices, vector spaces, dot and cross products, eigenvalues and eigenvectors) and abstract algebra (symmetry, fields and groups). The course also explores additional higher-level topics such as probability, game theory and complex analysis, which are common gateways to developing the mathematical sophistication expected at the university level. Emphasis is placed on proof, mathematical rigor and elegant problem-solving approaches. This course is aimed at mature and self-motivated young mathematicians.