Mathematics

List of 24 items.

• Geometry

  Geometry
  (1 credit, prerequisite: Algebra I)
  
  This course is designed to expose students to the structure of geometry while enhancing and strengthening algebraic skills in a geometric context. Areas of study include points, lines, planes, inductive and deductive reasoning, an introduction to proofs, and all properties of geometric figures. Algebra I topics are  reintroduced and used with every geometry topic studied in order for students to gain a firmer algebra foundation heading into Algebra II. This course is followed by Algebra II; students who wish to enroll in Algebra II (Adv.) must independently complete summer enrichment and take a placement test. (Formerly known as  Geometry-Functions, the course name changed in 2023-2024.)
  
  

• Geometry (Adv)

  Geometry (Adv)
  (1 credit; prerequisite: Algebra I)
  
  This Euclidean geometry course is designed to develop an understanding of a mathematical system, develop powers of spatial visualization, facilitate understanding of coordinate geometry, and enable students to present clearly written, logical proofs. Students will study properties, theorems, and applications relating to lines, triangles, quadrilaterals, polygons, and circles. Deductive reasoning and the role of proof in mathematics are emphasized in this course. This course is followed by Algebra II or Algebra II (Adv). (Formerly known as Geometry-Euclidean, the course name changed in 2023-2024.)

• Geometry-Trigonometry (H)

  Geometry-Trigonometry (H)
  (1 credit; prerequisite: Algebra I)
  
  This honors course begins with all topics covered in the Geometry course. These topics are extended to cover vectors in a plane and their application, laws of sines and cosines, coordinate geometry with conic sections, principles of logic, and advanced topics in trigonometry. This is a demanding course that requires time and
  effort, and the most successful students in this course will be those who enjoy guided, independent learning. This course is followed by Algebra II-Precalculus (H) or Algebra II (Adv).

• Algebra II

  Algebra II
  (1 credit; prerequisite: Geometry)
  
  This course develops and extends the topics presented in Algebra I. New topics introduced include the theory of polynomial  functions, logarithmic and exponential functions, linear programming, matrices and determinants, regression, and  sequences and series. This course is followed by Precalculus. It is not recommended for students who wish to take Precalculus (Adv). Students who do try to move into Precalculus (Adv) the following year will be required to complete specified work in trigonometry in the summer and pass a placement test over that material before being allowed to enroll in Precalculus (Adv).

• Algebra II (Adv)

  Algebra II (Adv)
  (1 credit; prerequisite: Geometry)
  
  This advanced course will cover all material in the Algebra II course and extend those topics to include advanced topics in the areas of trigonometry and probability. The pace of this class and the depth at which concepts are studied distinguishes this course from Algebra II. This course is less rigorous than the Algebra II-Precalculus (H) course, but it is a demanding course in which more
  responsibility is given to the students for their individual learning. This course is followed by Precalculus (Adv).

• Algebra II-Precalculus (H)

  Algebra II-Precalculus (H)
  (1 credit; prerequisite: Geometry-Trigonometry (H))
  
  This course is a continuation of the Geometry (H) course and it covers all material in the Algebra II courses. Topics are extended to include probability and statistics, mathematical induction, functional analysis, trigonometric functions, equations and identities, limits, and derivatives. Mathematical modeling and concepts from plane, solid, and analytical geometry are included
  throughout the course. As with Geometry (H), this is a demanding course and the most successful students in this course will be those who enjoy guided, independent learning. This course is followed by AP Calculus AB or AP Calculus BC and Lab* (*with recommendation of teacher and Math Department Chair).
  
  

• Precalculus

  Precalculus
  (1 credit; prerequisite: Algebra II)
  
  This course offers a study in the development of three basic ideas: analysis of functions, including trigonometric functions; mathematical modeling; and the use and analysis of data (including regression and probability). Topics include a study of trigonometry and an introduction to calculus. This course is generally followed by Calculus. It is not recommended for students who wish to take an AP Calculus course the following year.
  
  

• Precalculus (Adv)

  Precalculus (Adv)
  (1 credit; prerequisite: Algebra II (Adv))
  
  This course includes an in-depth review of algebraic and trigonometric functions with emphasis on graphing as well as Upper School Curriculum 3 an introduction to Calculus including limits and the definition of the derivative. The pace of this class and the depth at which concepts are studied significantly distinguish this course from Precalculus. This course is normally followed by AP Calculus AB (though a few students take AP Calculus BC and Lab). Students from Algebra II who wish to take this course must complete specified summer work in trigonometry and pass a placement test over that work before being allowed to enroll. 
  
  

• Data Analytics I

  Data Analytics I
  (1/2 credit; fall semester; open to class 11-12*;
  prerequisite: Algebra II)
  
  This semester-long course offers an introduction to the most essential skills for data science. Using the R programming language, students will learn how to import data, transform it into the most useful structure, create visualizations, and construct linear models to make predictions. The course is project-based and interdisciplinary, involving elements of math, science, and coding. Assessments include four major projects as well as smaller, in-class assignments throughout the semester. (*Priority enrollment for Class 12 students.) (This course not available in 2025-2026.)

• Data Analytics II

  Data Analytics II
  (1/2 credit; spring semester; open to class 11-12*; prerequisite: Data Analytics I)
  
  This course provides students with a hands-on introduction to the more advanced principles of data visualization, using and refining the skills learned in Data Analytics I. The course bridges the gap between creative storytelling and technical analysis, preparing students to use data to inform, inspire, and persuade. The course will be project-based and interdisciplinary. Students will draw data from the physical and social sciences, analyze it using mathematical techniques, and transform it into a visualization to persuade or tell a story. (*Priority enrollment for Class 12 students.) (This course not available in 2025-2026.)

• Data Analytics (H)

  Data Analytics (H)

  (1 credit, yearlong, open to class 10-12; prior or con-
  current enrollment in any of the following: Algebra

  II-Precalculus (H), Precalculus (Adv), AP Computer
  Science A, or Computer Science I & II)
  
  This year-long course offers a thorough investigation of data analytics with the R programming language. In the first semester, students will acquire skills in data analysis, including data visualization, transformation, exploration, and modeling, along with fundamental programming concepts to automate processes. The second semester will focus on the application of these skills to advanced topics such as statistical inference, hypothesis testing, and machine learning. By the end of the course, students will be proficient in using R for data analytics and applying advanced statistical methods and machine learning techniques to real-world data. Successful completion of this course will equip students with the necessary skills to pursue further studies in data science or related fields. No previous programming experience is required. (*Priority enrollment for Class 12 students.)
  
  

• Introduction to Calculus

  Introduction to Calculus
  (1 credit; prerequisite: Precalculus)
  
  The course will begin with a review of necessary algebraic concepts from Algebra 2 and Precalculus. Students will complete an in-depth study of functions and operations on functions, primarily ideas and skills that will be used extensively throughout the remainder of the year. What will follow is a treatment of limits, both algebraically and graphically. This will lead to the definition of derivative as a limit. This idea will be explored in the context of the algebraic functions. Topics will include the basic rules of differentiation, along with some applications of the derivative (science, finance, theoretical, etc). The integral will be introduced as the antiderivative, and students will then use the integral to ‘undo’ differentiation. The focus will be on the algebraic functions first, and some applications of integration will be addressed. With time permitting, students will review their Analytic Trigonometry from Precalculus, and the previous concepts of differentiation and integration will be revisited through the lens of Trigonometry. (This course not available in 2025-2026.)
  
  

• Calculus

  Calculus
  (1 credit; prerequisite: Precalculus)
  
  This course offers a study of calculus at the non-AP level, with a focus on the applications of calculus to business, management, economics, medicine, and the social sciences. The topics covered include limits, continuity, derivatives, and integrals of algebraic and
  trigonometric functions with greater emphasis on the algebraic functions. This course prepares students for success in a college calculus course. 

• AP Calculus AB

  AP Calculus AB
  (1 credit; prerequisite: Precalculus (Adv) or Algebra II-Precalculus (H))
  
  This course follows the syllabus of the AP Calculus AB exam: topics include functions, graphs, limits, derivatives, and integrals. It is roughly equivalent to the first semester of calculus at most universities. Juniors who take this course may take AP Calculus
  BC (3D), though some take AP Calculus BC (Lab), or AP Statistics as seniors.

• AP Calculus BC

  AP Calculus BC
  (1 credit; prerequisite: Algebra II-Precalculus (H) or Precalculus (Adv))
  
  This accelerated mathematics course follows the syllabus of AP Calculus BC using a combination of guided instruction and laboratory exploration. Students will continue to use Desmos graphing software and graphing calculators but will also be introduced to Mathematica software, often used in college mathematics courses. Labs will be used to enhance and refine previously discussed ideas. Students considering this level should
  love math, be skillful using algebra and precalculus concepts, and come prepared to master a full year of college calculus. For non-seniors, this course is traditionally followed by Differential equations (H) and/or Linear Algebra I (H).

• AP Calculus BC Plus

  AP Calculus BC Plus
  (1 credit; prerequisite: AP Calculus AB)
  
  In the first semester this course extends the topics from AP Calculus AB to finish the syllabus for the AP Calculus BC exam. The second semester moves into three-dimensional calculus, concluding with Green’s Theorem. It also includes review of first-semester material for the AP exam in May.
  
  

• AP Statistics

  AP Statistics
  (1 credit; open to class 10-12*; pre- or co-requisite: Precalculus)
  
  This elective course may be taken at any time after Precalculus or concurrently with Precalculus, though it does not serve as part of the three-course Upper School required math sequence. This course is equivalent to an introductory college-level course in Statistics; it introduces students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. Important components of the course include the use of technology
  for interactive and investigative aspects of data analysis, projects, laboratories, cooperative group problem solving, and writing as a part of concept-oriented instruction. (*Priority enrollment for Class 12 students.)
  
  

• Differential Equations (H)

  Differential Equations (H)
  (1⁄2 credit; fall semester; prerequisite: AP Calculus BC)
  
  This fall course applies the independent-but-guided method of AP Calculus BC (Lab) to the syllabus of typical university-level differential equations courses. There is a three-fold emphasis: solving basic classes and systems of differential equations by hand; use of Mathematica to produce solutions to “real-world” problems; learning how to develop and solve mathematical models of natural and economic phenomena. It requires facility with Mathematica. Students who have completed only an AB Calculus course may be considered for enrollment with the permission of the instructor. This course is traditionally followed by Multivariable Calculus (H).

• Multivariable Calculus (H)

  Multivariable Calculus (H)
  (1⁄2 credit; spring semester; prerequisite: AP Calculus BC)
  
  This course applies the independent-but-guided method of AP Calculus BC (Lab) to the syllabus of typical university-level multivariable courses. It includes partial differentiation and integration with respect to multiple variables; it culminates with the vector calculus theorems (Green’s, Stokes’, Gauss’s) and the theory of Lagrange multipliers for multi-variable optimization. This course
  traditionally follows Differential Equations (H), although that course is not a pre-requisite.

• Linear Algebra I (H)

  Linear Algebra I (H)
  (1/2 credit; fall semester; corequisite: BC Calculus with permission of department)
  
  This course examines linear algebra from a theoretical perspective, with an emphasis on developing proof-writing skills. Over the course of the semester, students will study linear algebra  preliminaries, finite-dimensional vector spaces, and linear maps. While this course does not require calculus, it does require a high level of mathematical maturity, and enrollment concurrent with BC Calculus will be with permission of the department. Use of Mathematica is not necessary, but may enhance a student’s experience in the class. A high level of comfort with independent learning is very helpful, and we will work on developing that skill over the course of the semester. Assessments will consist of concept checks, quizzes, tests, and projects.

• Linear Algebra II (H)

  Linear Algebra II (H)
  (1/2 credit; spring semester; prerequisite: Linear Algebra I (H); corequisite: BC Calculus with permission of department)
  
  This course is a follow-up to Linear Algebra I (H). In the second semester we will continue to develop mathematical industry and proof-writing skills as we study eigenvalues and eigenvectors, inner product spaces, and orthonormal bases. Use of Mathematica is not necessary, but may enhance a student’s experience in the class, especially in researching various applications. A high level of comfort with independent learning is essential. Assessments will consist of concept checks, quizzes, tests, and projects.

• Partial Differential Equations (H)

  Partial Differential Equations (H)
  (1/2 credit; spring semester; prerequisite: Differential Equations (H))
  
  This course is a survey of topics in Partial Differential Equations. Students will be introduced to the Fourier series, solving by separation of variables, the heat equation, Laplace’s equation, the wave equation, and other topics as the interests of the class determines. Use of Mathematica is not necessary, but may enhance a student’s experience in the class. A high level of comfort with independent learning is essential. Assessments will consist of concept checks, quizzes, tests, and projects. Students may enroll concurrently with Multivariable Calculus (H) or Linear Algebra II (H) with permission of the department. This course not available in 2025-2026.

• Complex Analysis I (H)

  Complex Analysis I (H)
  (1⁄2 credit; fall semester; Directed Study*; prerequisite: Multivariable Calculus (H))
  
  This course serves as an introduction to complex analysis. Topics include a review of complex algebra and a brief introduction to complex geometry, followed by an overview of the analysis of complex functions and the Mandelbrot set. The semester ends with a treatment of complex differentiation (including the Cauchy-Riemann equations and analycity).

• Complex Analysis II (H)

  Complex Analysis II (H)
  (1⁄2 credit; spring semester; Directed Study*; prerequisite: Complex Analysis I (H))
  
  This course is a continuation of Complex Analysis I and includes topics such as complex integration, Cauchy’s formula, residue calculus, and conformal mappings.