Mathematics

Algebra I is a formal introduction to the notation, skills, and conceptual framework of the foundational principles of algebra. Students review simplifying algebraic expressions before becoming fluent in solving one-variable equations and inequalities. The course then progresses to the study of linear equations and inequalities in two variables. Emphasis is placed on the multiple representations of a linear equation, including a table of values, graph on a coordinate plane, and symbolic notation. Systems of linear equations are solved via graphical and algebraic methods. The course also includes properties of exponents, polynomial expressions, factoring, and an introduction to simplifying radical expressions. Students will develop fluency with abstract algebraic reasoning through the use of concrete and pictorial models (e.g, bar models, algebra tiles, and other manipulatives).

This course explores topics in Euclidean geometry with an emphasis on problem solving and proof. Beginning with an introduction to logical principles, the deductive organization of geometry is developed through a combination of intuitive and rigorous investigations. The course is designed to give students a range of skills associated with this branch of mathematics and to continue their preparation for the study of precalculus mathematics. The course includes logic, isometries, congruence proofs, properties of geometric figures, coordinate geometry, a study of similarity, areas of polygons, and volumes of polyhedra.

Focused on exploring functions both algebraically and graphically, this course builds upon students’ previous understanding of linear and quadratic functions while introducing absolute value, radical, exponential and logarithmic functions. Students will use TI-84 graphing calculators to enhance their understanding of the relationship between the graphs of functions and their equations. Students finish the year with an introductory study of probability and statistics.

This course is a preparation for advanced mathematic courses including calculus. In this course, students expand on their previous knowledge of functions. Students delve deeper into the analysis of polynomial, rational, exponential, and logarithmic functions; and they are introduced to trigonometric functions. Additionally, students explore sequences and series, complex numbers, analytical trigonometry, and probability and statistics. Students utilize a graphing calculator to visualize graphs and support them in problem-solving.

This course may be taken either independently of or in sequence with Probability and Statistics II. This course may be taken simultaneously with another math course after students have completed the Geometry and Algebra II-level courses. Topics covered include sampling and data, descriptive statistics, probability, and the Normal Distribution. Probability and Statistics I and II may complete the Upper School's math requirement, along with the Precalculus-level courses.

This course extends the concepts studied in Probability and Statistics I. It may be taken simultaneously with another math course. Topics covered include inference tests for proportions and means, two proportions or two means, and linear regression. Completion of this course after Geometry and Algebra II satisfy the Upper School's three-year math requirement.

This course involves a study of geometric concepts using a variety of methods, formalizing the geometric ideas first learned in lower and middle school. Concepts are explored using constructions, algebraic models, and theorems. Euclidean proof strategies are used during the study of congruence, polygons, angles related to polygons and circles, similarity, and applications of the Pythagorean Theorem. Proofs are rigorous and multi-step, preparing students to prove more complex problems. Understanding the concepts of area in two-dimensional objects and surface area and volume of three-dimensional objects finishes the year. In Honors Geometry, the focus is on rigor and precision, allowing students to begin to see the importance of notation and the universal language of mathematics.

The focus of this course is the study of mathematical functions algebraically and graphically. Throughout the course, students build upon their previous understanding of linear and quadratic functions while introducing absolute value, radical, exponential, logarithmic, and rational functions. The concept of a function is introduced through the study of properties of functions, operations on functions, and function notation. Students will use a variety of graphing utilities to enhance their understanding of the transformations of functions graphically and algebraically. In addition, there will be a strong emphasis on modeling real-world data using different types of functions and understanding which function to use. Students finish the year with an introductory study of probability and statistics.

This course is a preparation for advanced mathematics courses including calculus. Polynomials, polynomial functions, rational functions, polar and parametric equations are studied using analytical techniques and a graphing calculator. The study of complex numbers includes polar forms and roots of complex numbers. Other topics include order in the real number system, principles of exponents and radicals, operations on functions, exponential and logarithmic functions, curve fitting, and the analytic geometry of the conic sections.

This course may be taken either independently of or in sequence with Advanced Probability and Statistics II. The course is designed for students who have completed a precalculus course and wish to investigate a wide variety of applications of statistical concepts. This course may be taken simultaneously with a calculus course.

Topics covered include descriptive statistics, probability, the basics of combinatorial mathematics, random variables, and experimental design.

This course extends the concepts studied in Advanced Probability and Statistics I. It may be taken simultaneously with a calculus course.

Topics covered include confidence intervals and significance tests for proportions and means, two proportions or two means, regression, chi-squared tests, and T-tests. Students continue to use R, a statistics software program that was introduced in the first semester of the sequence. Students who take both semesters of Advanced Probability and Statistics will be prepared to take the Advanced Placement exam in Statistics.

This is a one-semester course designed to be a preparation for the Topics in Data Science course which is taught in the Spring semester. We will spend the semester learning basic packages and techniques in Python to perform statistical analysis. Along the way we will use Python to perform basic probability computations that include descriptive statistics, statistical visualization, and modeling.

Topics in Data Science is an interdisciplinary course which combines ideas and concepts of Statistics and Computer Science. In this course, the students will learn how to source data, how to organize the data, and how to understand various aspects of the re-organized data. Students will learn detailed information about data science libraries in Python including pandas, scikitlearn, and library. Most of the first half of the course will be spent teaching aspects of Python which will be used in the rest of the course. An introductory knowledge of Python gained through the prerequisite course options is expected of students entering the course. All students will complete a project using a real-world data set.

This course will introduce students to the three core topics of calculus: limits, differentiation, and integration. Students will study these topics as well as their applications to gain a foundational understanding of the main ideas of calculus. This course is a high-school level calculus course and would not prepare students to take the AP Calculus AB exam.

This course offers an accelerated study of a rigorous undergraduate calculus curriculum. It includes a comprehensive investigation of the three core topics of calculus: limits, differentiation, and integration, including several applications. This course is designed as a college-level calculus course that will prepare students to take the AP Calculus AB exam.

This course continues the study of single-variable calculus started in Calculus A/B. It includes further integration techniques and applies the core topics of calculus to polar and parametric equations, sequences and series, differential equations, and vector valued functions. This course is designed as a college-level calculus course that will prepare students to take the AP Calculus BC exam.

Multi-variable is a one-semester course using a college-level textbook. The topics covered will include: parametric and polar curves and parametric surfaces; equations and representations of lines, planes and surfaces in three-dimensions; differentiability of multivariable functions and partial derivatives; optimization of multivariable functions, including Lagrange multipliers for constrained problems; and multiple integrals. We will use graphing calculators for some basic computations, but we will extensively use computer algebra systems for numerical computations and visualization.

Discrete Dynamical Systems is a one-semester course using a college-level textbook. Discrete dynamical systems are studied with an emphasis on the dynamics of the quadratic map. Included in the topics covered are formal and informal approaches to periodicity and chaos; fractals; and dynamical systems including the computer code to produce Julia Sets.

Linear Algebra is a one-semester course using a college-level textbook. The topics covered will include: solving linear equations using matrices, an introduction to linear transformations, general matrix algebra, the theory and applications of determinants, general vector spaces, Möbius transformations, and eigenvalues and eigenvectors. If there is time we will discuss orthogonality and least-squares problems. We will use graphing calculators for some basic computations, but we will extensively use computer algebra systems for numerical computations.

Combinatorics and Graph Theory is a one-semester course using a college-level textbook. The topics covered will include: introductory counting principles including permutations and combinations, general principles of graphs and trees, Eulerian and Hamiltonian graphs, graph coloring, and matrix applications to graphs. If we have time we will discuss other applications of graph algorithms. We will use graphing calculators for some basic computations, but we will extensively use computer algebra systems for numerical computations.