Mathematics

List of 4 items.

• Integrated Math II/Accelerated Integrated Math II

  In Integrated Math II, students develop a mastery of the core topics in plane Euclidean geometry. Students learn to formulate mathematical arguments and to justify their claims about the geometric objects they study. To maintain and strengthen the algebra skills developed in Math I, students apply algebra to their study of geometry. Students are also introduced to ideas of vectors and parametric equations. In the accelerated level, students study geometric transformations and begin their study of trigonometric functions.

• Integrated Math III/Accelerated Integrated Math III

  In Integrated Math III, students continue to expand their understanding of functions by learning how to mathematically describe motion in a circle. Through this study, they learn about trigonometric functions and their applications to periodic motion. They learn how to use transformations of these functions to create models of real-world situations. Students also study matrices and exponential and logarithmic functions through real-world problems. Students are introduced to approximating instantaneous rates of change and working with different kinds of sequences. In the accelerated level, students also study ellipses, planes, and additional applications of matrices.

• Integrated Math IV/Accelerated Integrated Math IV

  This course is an in-depth study of functions, their graphs and their use in modeling real-world phenomena. Polynomial, rational, exponential, logarithmic, and trigonometric functions are studied from numerical, graphical, and analytical perspectives. Students graph functions  by hand and with the aid of graphing calculators. Other topics include combinatorics, probability, series and sequences, and limits. In the accelerated level, students also study conic sections and differential calculus.

• Semester and Yearlong Electives

  Statistics

  Statistics is the science of data, and data are numbers with a context. In contemporary society, collecting, summarizing, representing, and analyzing data are activities of major importance. Statistics serve to enhance social and scientific awareness and help us evaluate the numerous statistical claims we encounter. The study of statistics makes us better consumers of information. In this course, students will explore four big questions in statistics: What do we do with data? How do we get data? What do the data tell us and how do we interpret it? How do we communicate the results?

  
  Economics
  Economics is a social science that studies how societies allocate scarce resources to fill unlimited wants and needs. Through active laboratory simulations, students examine how their behaviors and interactions can be used to understand how prices, supply, and demand are determined. The course also delves into the study of broader economic phenomena, including GDP, employment, inflation, and fiscal and monetary policies. With a focus on critical thinking and analytical skills, this economics course equips students with a deep understanding of real-world economic issues and their implications, fostering the ability to evaluate policy decisions and make informed choices in an ever-evolving global economic landscape.

   

  Calculus/Accelerated Calculus
  Calculus is the study of change and accumulation. In this course, students study the fundamental ideas of differential and integral calculus. Topics include the definition and applications of the derivative, the definition and applications of the definite integral and the Fundamental Theorem of Calculus, and differential equations. The accelerated level begins with applications of derivatives and includes additional topics such as advanced integration techniques, Taylor series, the calculus of parametric and polar curves, hyperbolic trigonometry, and curvature.

   

  Multivariable Calculus

  Students explore calculus concepts such as the derivative, the integral, and their applications in higher dimensions. Using a problem-based approach, students analyze functions in several variables using tools including partial derivatives, multiple integrals, line intervals, vector calculus and Lagrange multipliers. This course is open to students who have completed Accelerated Calculus.

   

  Linear Algebra
  Linear Algebra is a college-level course designed to give students their first taste of abstract algebra, one of the major strands of mathematics. Topics include vector spaces, linear transformations, and matrix algebra. The course takes a highly theoretical approach, emphasizing learning to read and write formal proofs, and also includes applications in the natural and social sciences. 

  
  Chaos Theory and Fractals (Interschool Course)
  Chaos theory, a cutting-edge field of math that took off with the advent of modern computing, has applications in such diverse fields as meteorology and the stock market. In this course, students investigate fundamental ideas in chaos theory and the mathematical discipline of dynamical systems, an area of math focused on systems that change over time. Starting with the idea of iteration, students will explore how small changes in initial conditions can produce big differences in outcomes. They come to understand a hallmark of chaos theory and dynamics: even the most simple and deterministic systems can produce unpredictable behavior and even the most complex systems can reveal some kind of order. Finally, students see how these ideas apply to the beautiful world of fractals, including the Julia sets and the Mandelbrot set. Prerequisite: students must have completed Integrated Math III Accelerated.

   

  Collaborative Problem Solving (Interschool Course)
  In Collaborative Problem Solving students work together in an informal atmosphere to solve challenging math problems. Problems are taken from a variety of topics, including algebra, geometry, combinatorics, probability, and number theory. Problems are chosen for their interest, they are sometimes discussed for fairly long periods of time, and they are tackled collaboratively. The class should be of interest both to students who love math and want to learn more and to students who want to become better problem solvers.