Mathematics Course Offerings
Mathematics Course Offerings
Yearlong Courses
ALGEBRA AND GEOMETRY
Algebra
In this class, students move beyond the straightforward application of algorithms and are pushed to use abstract reasoning and creativity to solve problems they have not explicitly seen before. Students adopt the view that math is thinking . When thinkers do not see the answer to a problem, they want to make sense of the situation then consider as many possible solution strategies. Students enter the course with a variety of backgrounds in algebra and are equally challenged in applying and synthesizing their knowledge as they collaborate with peers in class and puzzle through solutions. Students will study a wide-range of topics, including modeling linear and quadratic equations, graphing and solving problems with absolute value and radical expressions, solving systems of equations, using inequalities to model scenarios, simplifying algebraic expressions, solving shared-work problems. Students will also expand their resilience and communication skills, while solidifying their skills in algebra and making connections to geometry applications.
Geometry
This course develops the skills required for more advanced mathematics, with an emphasis on the in-depth study of traditional topics of geometric proof, as well as the study of the Pythagorean Theorem, triangles, circles, quadrilaterals, coordinate geometry, polygons, optimization, parabolas and transformations. Students are expected to have a mastery of algebra and a facility with investigative and collaborative problem-solving approaches.
Honors Geometry
This course develops the skills required for more advanced mathematics, with an emphasis on the in-depth study of traditional topics of geometric proof, as well as the study of the Pythagorean Theorem, triangles, circles, coordinate geometry, polygons, optimization, parabolas, transformations, parametric equations and vectors. Students are expected to have a mastery of algebra and a facility with investigative and collaborative problem-solving approaches.
Algebra 2
Algebra II is designed to help students prepare for more advanced mathematics courses by strengthening their skills and conceptual understanding beyond basic algebra. Students will approach problems using a discovery-based method and will learn to investigate the problems, communicate their findings, and validate their results. Whenever
appropriate problems will be designed that model real-world situations and students’ life experiences. Students will study a wide range of topics including function review, quadratics, polynomial functions, exponential growth and decay, and systems of equations.
PRE-CALCULUS AND CALCULUS
Precalculus
This course expands upon the skills and themes introduced in Geometry. While students consider the properties and applications of each of the major trigonometric function families in isolation, significant time is also dedicated to the study of function composition and transformations. Special emphasis is placed on using functions to model real-world phenomena.
Honors Precalculus
This course expands upon the skills and themes introduced in Honors Geometry. A major theme of the course is to uncover laws of trigonometry by deploying the skills developed in geometry to study the properties of triangles. Students also study circles, three-dimensional vectors, matrices, circular motion, quadrilaterals, exponential functions and parametric descriptions of curves.
Calculus
This course is a study of the concepts and skills of calculus. An emphasis on the applications of calculus allows students the opportunity to investigate and collaborate on projects. While this course provides students with a sound understanding of calculus, it is not intended to prepare students for the Advanced Placement Calculus AB examination.
Advanced Study Differential Calculus
AS Differential Calculus begins with a review of topics in trigonometry, progresses to a study of a variety of topics drawn from discrete mathematics and analysis, and culminates in a comprehensive treatment of differential calculus and its applications. Students study the continuity and differentiability of functions, derivative rules, curvature, optimization, related rates, and the three-dimensional position, velocity and acceleration of particles.
Advanced Study Calculus AB
This course covers differential and integral calculus, with an emphasis on applications drawn from the physical, biological and social sciences. After completing this course, students may elect to review independently for and take the Advanced Placement Calculus AB examination.
Advanced Study Calculus BC
This course continues the study of calculus begun in AS Differential Calculus. Students study integral calculus and its applications, as well as polynomial series approximations. After completing this course, students may elect to review independently for and take the Advanced Placement Calculus BC examination.
Advanced Study Multivariable Calculus
This course extends the foundational concepts of single-variable calculus to functions of multiple variables, focusing on spatial visualization and higher-dimensional analysis. Students will investigate partial derivatives, gradients, and optimization techniques to understand how complex systems change across multiple inputs. The curriculum covers the evaluation of multiple integrals and explores vector calculus, including line and surface integrals.
ADVANCED TOPICS
Advanced Topics Tutorial in Mathematics
Advanced Topics Tutorial in Mathematics is a course designed for students who have completed Advanced Study in Multivariable Calculus. Recent topics have included cryptography, linear algebra, differential equations, discrete logic, and proving Euclidean geometry from scratch. Topics can vary each year based on student and faculty interest.
Semester-long Electives
COMPUTER SCIENCE
Intro to Computer Science
An introductory course aimed at presenting the mechanisms that power the digital world by initiating students in the problem-solving skills associated with designing computer code. This course is suitable for students with no programming background as well as those with familiarity and experience. Discussion and writing topics include history and functionality of the internet, ethics of digital citizenship, and current concepts pulled from recent headlines. Classroom activities balance between collaborative coding projects and discussions and debates on current events in the digital world.
Object Oriented Programming in Java
This course refines the student’s programming ability while introducing the concept of object-oriented programming. Increasingly, larger and more complex projects bolster the student’s ability to craft working components while simultaneously promote project and time management skills as well as instill confidence in the student’s developing ability. This course roughly follows the AP Computer Science A syllabus with tangents to allow for further exploration in project-based learning. Students completing this course will have basic preparation to take the AP test.
Data Structures and Design in Java
This course continues and advances the study of the Java programming language as well as the concepts of object- oriented programming covered in Object Oriented Programming in Java (JAVA1). Students refine their understanding of inheritance, interfaces, and additional Java structures utilizing project work to apply those techniques and problem- solving skills towards programming challenges. While not an AP prep course, students are thoroughly exposed to the type of questions asked on Computer Science A tests and should be well prepared to take the spring exam. Students should have completed either the Java 1 course or demonstrated, through testing, a capability and experience with programming. It is strongly advised that students with casual, self- taught programming skills not skip the Java 1 course.
Microcontroller Programming and Robotics
This course develops a student’s ability to program microcontrollers and other embedded devices. This specific type of programming is essential for developing products and devices that physically interact with the environment through sensors, actuators, and information display. Students will engage in electronic development skills including circuit design, implementation via breadboarding and soldering, and product deployment. As a final project, students will design and contribute a collaborative project build to aid the school community.
STATISTICS AND ECONOMICS
Advanced Study Statistics
This course is a non-calculus-based introduction to statistics that focuses on four major themes: exploring and analyzing data, planning studies and collecting data, mathematical modeling, and testing hypotheses through statistical inference. After completing this course, students may elect to review independently for and take the Advanced Placement Statistics examination.
Applied Mathematics I: Fair Distribution
Math can often be seen as incredibly important and somewhat useless. This course will focus on the real-world applications of the mathematics you have been learning all of your life, focusing on the question of “what is fair?” A basic definition of fairness might be that “everyone gets what they need”, but how do we test this definition mathematically? What role does mathematics play in the needs of the individual, the community, and the world? What are the social justice implications of living in a world that is not mathematically fair? These are some of the many questions we will discuss in this course. Topics include:
- Combinations and Permutations
- Probability
- Expected Value
- Casino Gaming
- Distribution of Wealth (inheritance)
- Voting Techniques
- Gerrymandering
Applied Mathematics II: Efficiency
Math can often be seen as incredibly important and somewhat useless. This course will focus on the real-world applications of the mathematics you have been learning all of your life, focusing around making our world a more efficient place. A basic definition of efficiency might be to “achieve a goal with the least amount of effort or wasted resources.” How should a company schedule meeting times when multiple people have to be in multiple meetings? What is the optimal route for a school bus to take when picking up students for school? Where should cell phone companies build their towers so that everyone gets a signal? These are some of the many questions we will discuss in this course. Completion of Applied Mathematics I: Fair Distribution is not required to take this course.
Advanced Study Mathematical Economics
A basic understanding of economics is fast becoming a requirement for effective citizenship in a modern democracy. This course aims to provide students the necessary tools to understand and participate in discussions of economic policy. In any authentic economics curriculum students study decision-making: they learn to recognize the myriad
constraints in life—not only those of budget and how to spend one’s money, but also those of time and how to spend one’s life—and then study how to maximize various goods in the face of those constraints. This is not a course in finance. Stocks and bonds are largely just an example of a particular marketplace. Their role in macroeconomic policy is important to understand, but the real focus of the course will be the study of scarcity in general. Heavy emphasis will be placed on the application of mathematical techniques drawn from algebra, calculus and statistics. Some new techniques will be introduced, but much of the focus will be on the application of previously studied concepts.