Mathematics

Algebra IB

Algebra IB provides the opportunity for students to finish mastering fundamental algebraic topics and techniques including evaluation and simplification of algebraic expressions, solving and graphing linear equations, solving linear systems, operations with polynomials, simplifying radical and rational expressions, graphing and solving quadratic equations, and introduction to exponential equations and functions. Throughout the course, students will have opportunities to develop their problem-solving strategies and number sense by using multiple methods to understand abstract concepts, engaging in mathematical modeling, and communicating using graphical, numeric, and algebraic representations. Prerequisite Algebra IA, the equivalent, or placement. (Full year course)

Geometry

Geometry focuses on concepts of Euclidean Geometry with opportunities for students to apply and practice their Algebra I skills. Geometric topics examined include parallel and perpendicular lines, transformations, triangle congruence and similarity, quadrilaterals, right triangle trigonometry, and area and volume. The dynamic geometry software GeoGebra is used to develop students’ inductive and deductive reasoning, to explore fundamental geometric and algebraic relationships, and to aid in geometric problem-solving. In addition, students will be expected to develop patience and resilience as they solve more lengthy application tasks (projects) and communicate their results through write-ups and oral presentations. Prerequisite: Algebra I, Algebra IB,  the equivalent, or placement. (Full year course)

Algebra II

In Algebra II, students apply new elementary functions (e.g., polynomial and logarithmic) and algebraic techniques to model and solve problems that extend their work in Algebra and Geometry. Topics examined include transforming and modeling with linear functions, complex numbers, applications using quadratic, polynomial, radical, exponential, and logarithmic functions, and an introduction to rational functions. In addition, students continue to refine their problem-solving abilities by engaging with application tasks (projects) that require independently making mathematical conjectures about patterns and relationships, sometimes using technology. They are expected to communicate their results through oral presentations and written reports that integrate prose, presentation of collected data using tables and graphical representations, and mathematical justification. Prerequisite: Geometry, the equivalent, or placement. (Full year course)

Honors Algebra II

Honors Algebra II covers all of the topics of Algebra II at a faster pace with greater depth. Additional topics may be presented as times allows. Honors classes are designed for enthusiastic, curious, and resilient mathematicians that are developmentally ready to dive deeply into math. Not only is the pace faster in these courses, but students are challenged every day to apply their knowledge to unfamiliar and novel situations. Students are expected to think flexibly across different areas of math and solutions are not always immediately clear from the prompts given. Teachers of these courses usually serve as coaches, guiding students and offering advice as needed (as opposed to telling students exactly how to solve a problem), while students work collaboratively during class to solve challenging problems. Prerequisite: Geometry and recommendation of the math department (components include: Excellent or Outstanding performance in Geometry, recommendation of your Geometry teacher, and strong performance on the Honors Algebra II placement test). (Full year course)

Math Teaching Assistants

Teaching assistants are vital contributors to our classes. TAs attend class each day, help students with practice problems and resolve homework difficulties, answer questions, and grade homework. They run review and extra-help sessions and volunteer at math cafe once per week. As the year progresses, TAs plan and teach full lessons. This course is graded Pass / No Pass. Prerequisite: Consent of department. (Fall- or Spring-semester course)

Precalculus

Teaching assistants are vital contributors to our classes. TAs attend class each day, help students with practice problems and resolve homework difficulties, answer questions, and grade homework. They run review and extra-help sessions and volunteer at math cafe once per week. As the year progresses, TAs plan and teach full lessons. This course is graded Pass / No Pass. Prerequisite: Consent of department. (Full-year course)

Honors Precalculus

Honors Precalculus covers all of the topics of Precalculus at a faster pace with greater depth. Additional topics may be presented as time allows. Honors classes are designed for enthusiastic, curious, and resilient mathematicians that are developmentally ready to dive deeply into math. Not only is the pace faster in these courses, but students are challenged every day to apply their knowledge to unfamiliar and novel situations. Students are expected to think flexibly across different areas of math and solutions are not always immediately clear from the prompts given. Teachers of these courses usually serve as coaches, guiding students and offering advice as needed (as opposed to telling students exactly how to solve a problem), while students work collaboratively during class to solve challenging problems. Prerequisite: Hon Algebra II, the equivalent, or Algebra II with teacher recommendation; consent of the teacher and the department chair. (Full-year course; Honors)

Statistics

Statistics covers both descriptive and inferential statistics connecting current events and students’ backgrounds and interests. In descriptive statistics, students obtain the tools to assess the validity of data that they are confronted with in the media and their everyday lives. Students will learn how to describe and analyze professional data sets or those that they gather (e.g., through conducting censuses, surveys, and other experiments) and communicate the results of their analyses. Statistical topics examined include central tendency and variation, data displays (e.g., bar charts, histograms, box plots, line plots, scatter plots, and dot plots), the normal model, and bivariate linear regression. In Inferential Statistics, students learn to analyze variation in data by using confidence intervals and apply inferential statistical tests. Statistical methods examined include hypothesis tests for regression, proportions, and means. Both the computer and the calculator are integral to the course. Prerequisite: Algebra II, or the equivalent. (Full-year course)

Honors Statistics

Honors classes are designed for enthusiastic, curious, and resilient mathematicians that are developmentally ready to dive deeply into math. Not only is the pace faster in these courses (Honors Statistics is taught at the pace and rigor of a college-level course), but students are challenged every day to apply their knowledge to unfamiliar and novel situations. Students are expected to think flexibly across different areas of math and solutions are not always immediately clear from the prompts given. Teachers of these courses usually serve as coaches, guiding students and offering advice as needed (as opposed to telling students exactly how to solve a problem), while students work collaboratively during class to solve challenging problems. In Honors Statistics we begin by examining the topics of central tendency and variation, data displays, and probability. This leads to the study of inferential statistical topics that include the concepts of statistical models and use of samples, variation, statistical measures, sampling distributions, probability theory, and tests of significance. Students will be expected to critically analyze quantitative research, evaluate the evidence on which generalizations are made, and communicate the results of their analyses orally and in writing. The format and stylistic tendencies of professional research papers are also explored and understood to retain and question extant work and as a model for our own work. Prerequisite: Algebra II, Hon Algebra II, or the equivalent, and the consent of the teacher and the department chair. (Full-year course)

Calculus

Calculus will introduce students to the basics of differential and integral calculus. Concepts of the derivative as a slope and the integral as area will be explored using real-world examples as well as from a graphical, numerical, algebraic, and verbal perspective. Activities using technology will be utilized to help students understand concepts. Introductory rules for finding derivatives and integrals will be mastered and applied. Prerequisite: Precalculus or placement.  (Full-year course )

Honors Calculus I

Honors classes are designed for enthusiastic, curious, and resilient mathematicians that are developmentally ready to dive deeply into math. Not only is the pace faster in these courses (Honors Calculus I is taught at the pace and rigor of a college-level course), but students are challenged every da y to apply their knowledge to unfamiliar and novel situations. Students are expected to think flexibly across different areas of math and solutions are not always immediately clear from the prompts given. Teachers of these courses usually serve as coaches, guiding students and offering advice as needed (as opposed to telling students exactly how to solve a problem), while students work collaboratively during class to solve challenging problems. Honors Calculus I integrates key topics such as slope and area from earlier courses with new concepts such as infinity and limits, to develop a strong understanding of the key parts of a beginning calculus course. In addition to the above, students will study continuity, derivatives, and integrals, as well as their applications, slope fields, and differential equations. Concepts are approached through a four-step process: Graphically, numerically, analytically, and verbally. The use of technology to visualize concepts is prevalent. Prerequisite: Hon Precalculus, placement, or Precalculus with teacher recommendation, consent of the teacher and department chair. (Full-year course)

Honors Calculus II

Honors classes are designed for enthusiastic, curious, and resilient mathematicians that are developmentally ready to dive deeply into math. Not only is the pace faster in these courses (Honors Calculus II is taught at the pace and rigor of a college-level course), but students are challenged every day to apply their knowledge to unfamiliar and novel situations. Students are expected to think flexibly across different areas of math and solutions are not always immediately clear from the prompts given. Teachers of these courses usually serve as coaches, guiding students and offering advice as needed (as opposed to telling students exactly how to solve a problem), while students work collaboratively during class to solve challenging problems. Honors Calculus II is recommended for students with strong backgrounds in the problem-solving aspects of one-variable calculus. Students will prove the key theorems and results from first year calculus and make connections between calculus and other disciplines through projects. Topics examined include limits and continuous mappings, the interval theorems (Intermediate Value, Extreme Value, and Mean Value Theorems), significance of the derivative, integrability, modeling with differential equations, improper integrals, techniques of integration (integration by parts, trigonometric substitution, and partial fractions), sequences and series, Taylor polynomials, and parametric curves and polar coordinates. Prerequisite: Hon Calculus I, placement, or Calculus with teacher recommendation, consent of the teacher and department chair. (Full-year course)

Game Theory

Do you play games? Do you ever wonder if you’re using “the right” strategy? What makes one strategy better than another? In this course, we explore a branch of mathematics known as game theory, which answers these questions and many more. Game theory has many applications as we face dilemmas and conflicts every day, most of which we can treat as mathematical games. We consider significant global events from fields like diplomacy, political science, anthropology, philosophy, economics, and popular culture. Specific topics include two-person zero-sum games, two person non-zero-sum games, sequential games, multiplayer games, linear optimization, and voting and power theory. (Fall- or spring- semester course)

Linear Algebra

In this course students learn about the algebra of vector spaces and matrices by looking at how images of objects in the plane and space are transformed in computer graphics. We do some paper-and-pencil calculations early in the course, but the computer software package Geogebra (free) will be used to do most calculations after the opening weeks. No prior experience with this software or linear algebra is necessary. Following the introduction to core concepts and skills, students analyze social networks using linear algebraic techniques. Students will learn how to model social networks using matrices and to discover things about the network with linear algebra as your tool. We will consider applications like Facebook and Google. Prerequisite: completion of Geometry and Algebra 2 or the equivalents. (Fall-or spring- semester course)

Multivariable Calculus

In this course students learn to differentiate and integrate functions of several variables. We extend the Fundamental Theorem of Calculus to multiple dimensions, and the course will culminate in Green’s, Stokes’ and Gauss’ Theorems. The course opens with a unit on vectors, which introduces students to this critical component of advanced calculus. We then move on to study partial derivatives, double and triple integrals, and vector calculus in both two and three dimensions. Students are expected to develop fluency with vector and matrix operations. Understanding of a parametric curve as a trajectory described by a position vector is an essential concept, and this allows us to break free from 1-dimensional calculus and investigate paths, velocities, and other applications of science that exist in three-dimensional space. We study derivatives in multiple dimensions, we use the ideas of the gradient and partial derivatives to explore optimization problems with multiple variables, and we consider constrained optimization problems using Lagrangians. After our study of differentials in multiple dimensions, we move to integral calculus. We use line and surface integrals to calculate physical quantities especially relevant to mechanics and electricity and magnetism, such as work and flux, and we employ volume integrals for calculations of mass and moments of inertia. We conclude with the major theorems (Green’s, Stokes’, Gauss’) of the course applying each to some physical applications that commonly appear in calculus-based physics. Prerequisite: The equivalent of a college year of single-variable calculus, including integration techniques, such as trigonometric substitution, integration by parts, and partial fractions. Completion of the AP Calculus BC curriculum with a score of 4 or 5 on the AP Exam would be considered adequate preparation. (Full-year course)

Number Theory

Once thought of as the purest but least applicable part of mathematics, number theory is now by far the most commonly applied: every one of the millions of secure internet transmissions occurring each second is encrypted using ideas from number theory. This online high school Number Theory class covers the fundamentals of this classical, elegant, yet supremely relevant subject. This course provides a foundation for further study of number theory, but even more, it develops the skills of mathematical reasoning and proof in a concrete and intuitive way, great preparation for any future course in upper-level college mathematics or theoretical computer science. (Fall-  semester course)

Problem Solving w/ Engineering & Design

This course investigates various topics in science, technology, computer programing , engineering, and mathematics using a series of projects and problems that are both meaningful and relevant to the students’ lives. (Fall-semester course)