Departmental Offerings

The following course descriptions detail the likely offerings during any school year, though specifics will vary from term to term and course lineups are always changing. Click on the course titles below for full descriptions.

  • Advanced Calculus Topics - BC and Introduction to Multivariable Calculus

    This second year calculus course begins with the analytic study of vectors, lines, planes and surfaces in space, partial differentiation and multiple integration. Other topics included are advanced methods of integration, sequences, infinite series, series of functions and their derivatives and integrals, and the calculus of parametrically defined functions and polar functions. Students will be prepared to take the BC level AP exam in the spring. Prerequisite: satisfactory completion of AP Calculus AB.
  • Advanced Placement Calculus AB

    This course follows the Advanced Placement syllabus for first-level calculus. The topics covered are the elementary functions, limits, the derivative and its applications, and the integral and its applications. Prerequisite: permission of the department.
  • Advanced Placement Computer Science

    This course is for mathematically talented students who can manage its quantitative and technical challenges on top of their regular mathematics program. The course covers the mathematical foundations and language fluency necessary to produce logically correct, efficient, and readable computer-based solutions to a wide range of problems. Students complete two or three major programing projects, with special attention paid to programming methodology: design, coding, testing and documentation; development and analysis of sorting, searching, numerical algorithms, recursive algorithms and string processing; and programming in Java, including an exploration of its important features, class hierarchies, control structures and use of built-in Libraries. Prerequisite: permission of the department. Open to sophomores, juniors, and seniors.
  • Advanced Placement Statistics

    This is a mathematical treatment of the subject that demands of the student greater algebraic skills—but no less appreciation for the worldly nature of the subject—than is demanded by a conceptual statistics course. A careful treatment of experimental design, correlation, least squares regression, confidence intervals, and statistical inference makes up the backbone of this course, with student projects and investigations used liberally to engage the learner in these ideas. Prerequisite: permission of the department. Open to seniors.
  • Applied Functions

    This trimester course is intended for students who have completed the usual study of polynomial, exponential, logarithmic, and trigonometric functions. The emphasis is on using these functions to make mathematical models of real data. The graphing calculator and Fathom are used extensively. There are no in-class tests in this course. Students are assessed primarily on written lab assignments explaining how their equations, graphical representations of data, and situations are connected.
  • Computer Applications

    Big data are all around us. How can computer applications help us sift through and provide meaningful knowledge from the heaps of data that comprise our information world? Students develop some coding skills as a basis of their work, but also rely on pre-written modules to facilitate their investigation. Students bring an area of interest they would like to pursue in taking this course. Open to juniors and seniors.
  • Data Structures and Robots

    Using Java, students extend their understanding of data structures and algorithms by completing projects involving hashing, sets, lists, trees, and maps. Algorithms associated with these ideas involve more advanced approaches, including recursion, simulated annealing, q-learning, and backtracking. Over the course of the year, increasing emphasis is given to these ideas in the control of autonomous robots. Beginning with a study of basic engineering elements, students go on to use both Mindstorms vehicles and NAO humanoid robots to tackle typical problems of coordination, localization, navigation, and communication in robotics settings. Sensor-actuator design and implementation are at the core of this experience so that the robots created are autonomous. Taught in a seminar style, this course carries the expectation that students are able to work under their own initiative to complete a variety of major projects during the year. Prerequisite: permission of the department. Open to seniors.
  • Introduction to Calculus

    This trimester course examines the two central concepts of calculus, the derivative and the integral, in an applied, problem-solving setting. Students acquire a sense of the usefulness of calculus in business, economics, and science. They use algebraic, geometric, and trigonometric fundamentals covered earlier in their mathematics education as they learn to execute the mechanics of calculus. This course is appropriate for both those who will go on to study calculus at the university level and for those who are completing their mathematics education.
  • Java and Engineering

    This course provides an introduction to advanced programming algorithms in Java as well as principles of robotics and the programming of autonomous machines. Also studied: exhaustive search backtracking simulated annealing genetic algorithms, and exotic data structures that can be combined to solve a variety of important problems in computer science. In robotics we look at biological systems as “existence proofs” of sensory and control solutions and search for creative ways to simulate these in our own vehicles.
  • Math II

    This course builds on the foundation of Algebra I with an increased emphasis on problems requiring multi-step solutions and on reading and writing about mathematics. Some geometric topics are introduced, as well as aspects of deductive reasoning. Students receive their first exposure to complex numbers, rational expressions, functions, rational and real exponents. 
  • Math III/ Math III Honors

    The first of a two-course sequence to prepare students for the study of calculus, an understanding of conjectural and deductive thought (including proofs), and a sense of the variety of mathematical fields and the distinctions and connections among them. Also covered: the basics of the Euclidean geometry of triangles, parallels and circles using synthetic and analytic perspectives; the use of a programmable graphing calculator, the analytic geometry of translations and scale changes; the fundamental mathematics of real numbers and functions; and a study of polynomial, rational, algebraic, exponential, and logarithmic functions.
  • Math IV/ Math IV Honors

    A continuation of Math III, covering subtler methods, results, and proofs in geometry; including triangle trigonometry, circular functions, and analytic trigonometry; conic sections; and topics from discrete mathematics, analysis, and other fields. There is some emphasis on modeling, and one honors section spends the last third of the year starting the Calculus AB Advanced Placement syllabus.
  • Multi-Variable Calculus

    This third-year course in calculus extends the ideas of two dimensions to 3-space and beyond. Notions of slope, tangency, concavity, arc length, and volume are re-crafted to fit the broader possibilities that arise in this new context. Vector, parametric, and polar representations are also treated thoroughly.  Several “landmark” results are derived, including. The course, which features regular presentations by students to their classmates, culminates in the treatment of line integrals and Green’s Theorem.
  • Number Theory & Cryptography

    In an “information revolution,” the protection and communication of data is of considerable value. Methods for keeping computer systems, military data, manufacturing secrets, and other sensitive data out of the hands of those to whom it doesn’t belong require interesting—and surprisingly beautiful—mathematical ideas. Not just for the computer-oriented, this course is designed for any students with curiosity about numbers. The class also examines the twists and turns that make up the colorful history of coding and code breaking.
  • Statistics

    A descriptive approach to the standard methods of collecting, organizing, and interpreting data. Methods of sampling, experimentation, and measurement are covered, as are the frequency tables, distributions, and graphs used to present data collected in such ways.  Correlation, prediction, causation versus association, and confidence intervals are presented.  Designed to train students to have a critical eye, and to give them the language with which to express this understanding and criticism.

Faculty

  • Kurt Meyer

    Chair of Mathematics Department; Environmental Action Committee Advisor
    Bowdoin College - BA
    Smith College - MAT
    Bio
  • Peter Fagan

    Mathematics; Athletic Director
    Plymouth State University - BS
    Plymouth State University - MEd
    Bio
  • Sabina McMahon

    Dean of Students; Mathematics
    Colgate University - BA
    Columbia University - MA
    Bio
  • William Okin

    Mathematics; Horse Program
    Middlebury - BA
    UC Santa Barbara - MA
    Bio
  • Tyler Popa

    Admission Associate
    Gonzaga University - BBA
    University of Notre Dame - M Ed
    Bio
  • Kamala Qalandar

    Mathematics
    University of California, Santa Barbara - PhD
    Bio
  • Theana Snyder

    Mathematics
    Colorado College - BA
    Colorado College - MA
    Bio
  • Jonathan Swift

    Director of the Thacher Observatory; Mathematics; Science
    University of California, Berkeley - PhD
    Bio
  • Gallia Vickery

    Mathematics; Dance Program Director
    Princeton University - AB
    Bio