Diploma Program Credit: Students can consult with their Diploma Program Director to consider program credit for a course. Beyond courses that explicitly participate in a diploma program, in many core courses, students can design their major projects to meet diploma program credit guidelines.

Algebra I

Algebra I is the first course of a two-year sequence in high school Algebra. It is for students who have not had a full year of Algebra. The course develops algebraic skills through multiple perspectives: analytically, graphically and numerically. There is a focus on analyzing functions, particularly linear and quadratic functions, in a variety of contexts. Core skills are built for later math classes, including work with exponents, polynomials and basic right triangle trigonometry. An emphasis is placed on algebraic problem-solving skills, conceptual understanding, and graphical analysis of functions. Students will gain facility with various technologies including graphing calculator software and spreadsheets. Wherever possible, students work with data drawn from real world situations within the cross-curricular, thematic grade-level setting.

Successful completion of Algebra I positions the student for the study of Integrated Geometry or Honors Geometry with Data Analysis.

Prerequisite: None Credit: MATH Semester: Full Year

Geometry and Algebra Concepts

Geometry and Algebra Concepts is for students who have had exposure to Algebra but will benefit from hands-on, applied engagement with both algebra and geometry in a concrete setting. By allowing students to explore abstract topics in greater depth, it secures the foundational skills needed to succeed in later math classes. The course solidifies algebraic and spatial skills through multiple perspectives: analytically, graphically and numerically. An emphasis is placed on conceptual understanding. Students work with data drawn from real world situations, including student generated data, and routinely use manipulatives. Wherever possible, our investigations draw on cross curricular grade-level themes. Topics include expressions, equations, and inequalities; ratio, proportion and similarity; linear equations and lines of best fit, linear systems; area and volume, coordinate graphing and distance, congruence and similarity, right triangle trigonometry, and circles. Geometry and Algebra Concepts is complemented by Nonlinear Methods, a spring semester elective, for the study of quadratics, polynomials and exponents.

Successful completion of Geometry and Algebra Concepts and Nonlinear Methods positions the student for the study of Algebra II.

Prerequisite: Algebra I Co-requisite: Nonlinear Methods (Spring) Credit: MATH Semester: Full Year

Nonlinear Methods

This semester elective course is designed for students who have had Algebra I and seek to solidify the concepts typically taught in the second semester of an algebra course: polynomials and factoring, exponents and radicals, quadratic equations, graphs of linear systems and quadratic functions. These topics often require more exploration time than a typical Algebra I course can offer. Students will benefit from targeted practice with exponents and quadratics in particular.

Nonlinear Methods is taken concurrently with 2nd semester Geometry and Algebra Concepts. Successful completion of Nonlinear Methods readies the student for the study of Algebra II.

Prerequisite: Algebra I Credit: MATH Semester: Spring

Integrated Geometry

Integrated Geometry seeks to build sterling algebra and spatial skills for later math classes. In a series of fast-paced units, we solidify Algebra I through study of linear systems, polynomials and factoring, exponents and radicals, and quadratic equations. Integrated Geometry covers a minimum of one semester of accelerated Geometry. Geometry topics include points, lines and planes, triangles & similarity, right-angle trigonometry, circles, area and volume. An introduction to proof will be offered as time and class progress permits. Students will gain facility with various technologies such as graphing calculators, graphing software and spreadsheets. This is a non-honors course interspersed with opportunity to engage with higher order conceptual thinking and problem solving. Students demonstrating aptitude and a distinguished work record will be considered for Honors Algebra II in their sophomore year.

Successful completion of Integrated Geometry readies the student for the study of Algebra II or Honors Algebra II.

Prerequisite: Algebra I Credit: MATH Semester: Full Year

Honors Geometry with Data Analysis

Honors Geometry with Data Analysis explores concepts at both a deeper and more theoretical level. It is intended for the student with a deep interest in mathematics who enjoys discovering connections. In addition to the study of core geometric concepts and relationships, the course centers on a rigorous examination of logic, conjecture and proof. Logical inference is a key skill across disciplines. By extending students’ primarily computational exposure to mathematics, the study of logic and proof in Geometry lays the foundation for a more theoretical approach to high school mathematics. The class will further cover basic data analysis, plane and solid geometry, transformations and coordinate geometry, congruence and similarity, right triangle trigonometry and an introduction to the unit circle. Emphasis is placed on developing students’ critical thinking and collaborative skills. A solid foundation in Algebra I is a prerequisite in this accelerated class.

Successful completion of Honors Geometry with Data Analysis readies the student for the study of Honors Algebra II.

Prerequisite: Algebra I and Faculty Recommendation Credit: MATH Semester: Full Year

Honors Algebra II

Honors Algebra II explores concepts at both a deeper and more theoretical level. It is intended for the student capable of handling a faster pace who enjoys discovering connections. The course centers on a rigorous examination of the theory of polynomial algebra through the study of functions: (i) linear, quadratic, polynomial, inverse functions and their transformations; (ii) a variety of equations and inequalities, (iii) polynomials, rational roots, root finding algorithms, and graphing techniques, (iv) exponential and logarithmic functions, and (v) introductory trigonometry (vi) probability and combinatorics. We introduce practical applications and modeling. A major theme of this course is patterns in reasoning, including visual analysis, formal proof, and problem-solving. Oral and written communication concerning the logic of procedures and interpretation of results is central to our work. In the spring semester, students choose a capstone investigation: an exploration in which to dedicate themselves to their own learning and to that of the class at large. Examples of past deep-dives include algebraic topology, Pascal’s triangle, and projectile motion.

Prerequisite: Integrated Geometry or Honors Geometry with Data Analysis, Faculty Recommendation

Credit: MATH Semester: Full Year

College Algebra and Trigonometry

This year-long course is designed to strengthen a student’s Algebra skills and introduce foundational trigonometry topics. Content includes a comprehensive study of quadratic, polynomial and exponential functions, exponential and logarithmic equations in applied contexts, an introduction to right triangle and circular trigonometry, and an exploration of data distributions and introductory statistical concepts. Throughout, students apply their conceptual skills to solve problems in real-world situations within a cross-curricular, grade-level context. The focus is on securing algebraic fluency and deepening understanding.

Successful completion of College Algebra & Trigonometry opens the pathway to Statistics, Precalculus, or a math elective.

Prerequisite: Algebra II Credit: MATH Semester: Full Year

Introduction to Precalculus with Modeling

In this class, students use functions studied in their previous course in contexts arising in Precalculus. Polynomial, exponential and trigonometric functions will serve to model phenomena such as projectile motion, a vibrating string, and bacterial growth. Conic sections are explored in applied contexts involving ellipses and parabolas. Integrated into the curriculum is the study of linear, exponential, and polynomial regressions, so that students may evaluate the effectiveness of various mathematical models by evaluating r-squared and plotting residuals. Students are introduced to sampling and surveying techniques. Data and research is collected from the physical sciences and social sciences, so there is a significant interdisciplinary component to the course. Intermediate Algebra skills (solving quadratic, radical, exponential and logarithmic equations) are reviewed and secured in the process.

Successful course completion ensures the student is ready for Precalculus or Statistics.

Prerequisite: Algebra II Credit: MATH Semester: Full Year

Precalculus

The focus of Precalculus is on the concept of function and the use of functions as mathematical models. Precalculus prepares the student for the study of change, which is calculus. We work with functions that represent change – polynomial, rational, exponential and trigonometric functions. The course is taught from the point of view of the general theory of functions, so algebraic facility with, and an in-depth understanding of polynomial, rational and inverse functions is indispensable. The first semester explores exponential and logarithmic growth. We investigate growth processes and fit curves to data, culminating in a project on exponential growth and epidemics. This lays the foundation for cross-curricular investigations involving biological processes and sustainability. In the spring semester, our focus shifts to trigonometry: trigonometric equations and the modeling of periodic phenomena. Topics necessary for success in either a calculus or statistics course (including conic sections, regression techniques, and sequences & series) will be studied. Students should anticipate some review of material from previous courses as a bridge towards more advanced understanding.

Prerequisite: Algebra II Credit: MATH Semester: Full Year

Honors Precalculus

This problem based inquiry course focuses on the advanced study of a wide range of mathematical topics, including polynomial, exponential, logarithmic, power and trigonometric functions; conic sections and analytic trigonometry; complex arithmetic and polar equations; sequences and series. Additional topics such as parametric representation of functions, matrices and vectors may be introduced as time permits. Honors Precalculus is intended for the student with a strong interest in mathematics who enjoys discovering connections. The course assignments are designed to promote and emphasize communication of mathematical ideas, persistence in solving challenging problems, self-reliance, resourcefulness, and collaboration. In the spring semester, Honors Precalculus students choose a capstone investigation: an exploration in which to dedicate themselves to their own learning and to that of the class at large. Examples of past deep dives are: the Golden Ratio in art and music, recursive functions in computer science, conic sections and planetary motion, Euler’s constant “e.” Deep dives encourage the student to reach beyond curricular boundaries. The pace is swift, and the student will need to have secured a solid foundation in intermediate algebra prior to this course.

Prerequisite: Honors Algebra II and Faculty Recommendation Credit: MATH Semester: Full Year

Honors Statistics

Honors Statistics is intended for the student with a solid mathematics background and an interest in exploring statistical inference. Statistical inference is the art of making valid generalizations from samples. Topics include estimation, measurement error, and tests of statistical significance such as chi-square and P-tests. In addition to planning and conducting a study, students will estimate population parameters and critically evaluate conclusions obtained from data. The course requires creativity, logical thinking and organization. Its objective is to provide students with pragmatic tools for assessing statistical claims and conducting their own statistical research. Successful completion of Honors Statistics confers a conceptual foundation equivalent to an introductory college statistics course.

Prerequisite: Algebra II and Faculty Recommendation Credit: MATH Semester: Full Year

Calculus

Calculus was developed some three-hundred years ago to solve problems of change and motion. Two thousand years earlier, Greek minds puzzled the paradox of instantaneous motion: can an arrow flying through the air be captured at any instant, as a still object suspended in mid-air? The course emphasizes an intuitive, geometric understanding of calculus concepts. We will focus on the big ideas underpinning calculus: derivatives, integrals and their connection in the Fundamental Theorem of Calculus. Working within contexts whenever possible, we will explore the meaning, use, and interpretation of the derivative; apply techniques of differentiation to solve optimization problems; use the definite integral in applications involving accumulation. Differential equations with slope fields are introduced as time permits. Physics students will relish solving problems involving distance, velocity, and acceleration.

Prerequisite: Precalculus (B+ or above) and Faculty Recommendation Credit: MATH Semester: Full Year

Honors Calculus

Honors Calculus explores concepts at both a deeper and more theoretical level. Topics include limits and continuity, the derivative and its applications, the integral and its applications, the Fundamental Theorem of Calculus, differential equations with slope fields, and Taylor approximations. Our study will culminate in a modeling project involving logistic growth and epidemics, which will bring the graphical, numerical, and analytic methods developed throughout the course into multiple cross-curricular connections. Time and student interest permitting, we will explore infinite sequences and series, definition and tests for convergence, Taylor series, and parametric equations. This course is equivalent to a robust semester of college-level calculus and a foundation for the aspiring engineer and any student looking to take or earn credit for Calculus in college.

Prerequisite: Honors Precalculus (B+ or above) and Faculty Recommendation Credit: MATH Semester: Full Year

Multivariable Calculus and Linear Algebra

This course forms a bridge between calculus and theoretical, proof-based courses typically encountered in college. A brief introduction to proof aims at mastery of increased levels of rigor, dealing with mathematical notation, and learning how to write, present, and analyze proofs. We then extend the ideas of calculus to functions in more than one variable: lines and curves in 3D space, partial derivatives, level curves and gradients, line and surface integrals, and Lagrange multipliers. In the spring semester, we introduce Linear Algebra: the study of linear systems of equations, vector spaces, and linear transformations. Students come to understand a matrix as a linear transformation relative to a basis of a vector space. Eigenvalues, eigenvectors, and their applications in discrete dynamical systems will enable students to undertake projects in population dynamics and networking. Aspiring computer scientists will learn the underpinnings of graphics, image processing, cryptography, machine learning, and optimization.

Prerequisite: Honors Calculus (B+ or above) and Faculty Recommendation Credit: MATH Semester: Full Year

Applied Math & Physics with Computer Science (CSX)

This course is an interdisciplinary offering from the computer science, physics, and math faculty. Student assignments will reflect concepts from all three disciplines including: projectile motion; orbitals; strings; particles; matrices and area below a curve (Riemann). Simple graphics will be included as part of the course. Significant time outside of the classroom is expected. This course includes competitions in the American Computer Science League as well university led competitions.

Prerequisite: Computer Science I and II, Precalculus, Physics, Faculty Recommendation Credit: SCI, CSCI, MATH

Semester: Full Year Diploma Credit: Engineering

*Mathematics electives are designed to supplement and not to replace a student's study of the above core mathematics curriculum.

Mathematics of Public Policy

This is a project-based class in which students will engage in analysis of institutions, policies, and systemic issues in American society and internationally. Using a case study approach, topics such as income inequality, inequities in housing, education, and health care will be examined from a mathematical perspective. There is a strong statistical component, and students will be expected to represent data sets, find correlation between variables, and do hypothesis testing to investigate topics of their choosing.

Prerequisite: Algebra II Credit: MATH Semester: Fall

Mathematics of Personal Finance

How do you create the life you want to live and avoid common financial pitfalls? In developing substantial technological skills to model and track financial growth and management, this project based class will cultivate the crucial tools of budgeting, investing, taxes, time value of money, and the use of technology to forecast expected returns. This is a semester-long dive into personal finance.

Prerequisite: Algebra II Credit: MATH Semester: Fall

Mathematics of Entrepreneurship

The second part of the financial mathematics elective track expands into entrepreneurship and markets. How do you create the company you want? You will need a business plan: budgeting, breakeven analysis, market positioning, branding and competition analysis. We will leverage the technology tools acquired in Personal Finance. Projects will be student driven and culminate in an investment pitch.

Prerequisite: Algebra II, Mathematics of Personal Finance Credit: MATH Semester: Spring

Mathematics of Sustainability

This is a project-based class which will examine the mathematics of the three aspects of sustainability: economic, social, and environmental. For the first three quarters, students will use a case study analysis approach (topics such as recycling, composting, packaging of food, energy production and conservation, water use, deforestation, and the food industry) that will provide insight into each of the types of sustainability. In the fourth quarter, students will develop and pitch a proposal for a product, program, or policy that is sustainable in all three areas.

Prerequisite: Algebra II Credit: MATH Semester: Spring Diploma Credit: Sustainability