The Mathematics Department offers a sequence of courses by which students can gain an understanding of the style and content of mathematics, become adept in its fundamental skills, develop an understanding of the analytic power of mathematics through problem solving, and begin to explore the subject for the beauty of its abstractions and the variety of its applications. Confidence building and minimization of fears are conscious goals. While technology is used in many situations, students are also asked to do work by hand to ensure a deep understanding; our emphasis is usually on “why,” instead of simply “how.”

Requirements

Three years of math courses are required for graduation but students are encouraged to take Calculus before graduating. Most students also explore other branches of mathematics through the range of one-term electives that are offered. A student may elect to do an independent study in an area of particular interest where a course is not offered.

Honors

Honors placements by Departmental recommendation only.

Course Descriptions

Foundations for Algebraic Reasoning

This course, designed for students who have not completed Integrated Math 1, Algebra 1, or an equivalent, will build a strong foundation in algebraic reasoning. Students will grapple with real-world applications, work extensively with linear equations and systems, and gain additional exposure to exponential and quadratic relationships.

Not offered at the Honors level.

Integrated Math 2: Algebra, Geometry, and Data Science

Integrated Math 2 students expand their algebraic reasoning and understanding of mathematical models including quadratic equations and exponential functions. Students also explore probability and build upon their knowledge of transformations, congruence, and similarity while developing logic skills through conjecture, argument, and proof. Investigations in this course build connections between all topics covered. 

Prerequisites: Integrated Math 1, Algebra 1, or Foundations for Algebraic Reasoning. Offered at the Honors and Standard levels. Honors level requires departmental recommendation.

Integrated Math 3: Algebra, Geometry, and Data Science

Integrated Math 3 students continue to expand their algebraic reasoning and understanding of mathematical models including complex numbers, exponential equations, and polynomials. Students also explore sampling and build upon their knowledge of solid geometry and circle theorems while building connections between all topics covered. 

Prerequisites: Integrated Math 2. Offered at the Honors and Standard levels. Honors level requires departmental recommendation.

Precalculus - Functions

In this course, students will take a deeper look at various families of functions: rational, radical, exponential, logarithmic, and polynomial. Students will learn about the ways in which domain, range, continuity, inverses, composition and transformation apply to those functions. Students will also have opportunities to analyze real-world data and generate predictive models. Topics from data science are often included in this course, as well.

Prerequisites: Integrated Math 2 and Integrated Math 3. Offered at the Honors and Standard levels. Honors level requires departmental recommendation.

Precalculus - Trigonometry

Students in this course will learn about angle measurement, periodic behavior, and a range of applications related to both right triangle and circular trigonometry. Analytic geometry and polar coordinates are often included in this course, as well. Prerequisites: Algebra II and Geometry. Honors level requires departmental permission.

Prerequisites: Integrated Math 2 and Integrated Math 3. Offered at the Honors and Standard levels. Honors level requires departmental recommendation.

Calculus - Derivatives & Integrals

The Derivatives course includes all of the topics of an introductory Calculus course including limits, derivatives and their applications.
The Integrals course includes all of the topics of an introductory Calculus course including definite integrals, indefinite integrals and their applications.
Prerequisite: Precalculus. Offered at the Honors and Standard levels. Honors level requires departmental recommendation.

Advanced Calculus - Derivatives & Integrals (Honors)

This course covers all of the topics of an introductory Calculus course, exploring concepts in depth with a greater emphasis on both the abstract aspects of calculus and its various applications in the real world. Students will be expected to enter the class with a firm grasp of all concepts covered in previous math courses.

Prerequisite: Precalculus and departmental recommendation. Offered at the Honors level only.


Math Electives

Discrete Mathematics & Advanced Topics

In this course, students will have the chance to learn a range of discrete math topics and grapple with a range of different problems that fall outside the spectrum of traditional high school mathematics. Topics covered may include finite sets and partitions, enumeration, probability, expectation, random variables, and elementary number theory, with an emphasis on applications of discrete mathematics, and fair division, voting systems, graph theory, chaos theory and non-Euclidean geometry. Students will be able to answer questions like: “how many Beaver students are involved in a theater production and in an athletic sport throughout the school year?”, “what is the probability of picking at least three red marbles out of a bag of seven white marbles and five red marbles?”, “find the value of 7 mod 4”, “if there is a car accident, what is the probability the person is between the ages of 16-21?” and “what states have both a pro basketball team and a pro hockey team?” Students will also be asked to think creatively and apply their knowledge to complex real-world problems.

Open to Grade Levels: 11, 12, or by departmental approval.

Game Theory (BVR-X)

Game Theory is a branch of applied mathematics that is used to evaluate various social conditions. Students in this course will learn about the mathematics behind social and strategic situations. This course will focus on topics ranging from game strategy to problems of cooperation in everyday life. Case studies in resource depletion, global warming and conflict negotiation will be included. Student work will apply theory to real strategic environments.

Open to Grade Levels: 10, 11, 12

Statistics/Data Science (BVR-X)

This course includes the gathering of data and a variety of sampling techniques, hypothesis testing, frequency distribution, normal distribution, correlation, linear regression, theoretical distributions, and inferential statistics. This course asks students to consider questions such as these: How is data summarized so that it is intelligible? How should statistical data be interpreted? How can we measure the inherent uncertainty built into statistical data? Students will be asked to collect, analyze and interpret real data to answer real questions in their areas of interest.

Open to Grade Levels: 11, 12, or by departmental approval.