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.
This course is designed for students who have not completed Algebra 1 through quadratics in middle school. Students will build a strong foundation in algebraic reasoning and grapple with real-world applications. Work will focus on solving linear equations and systems and the exploration of exponential and quadratic relationships.
Not offered at the Honors level.
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 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.
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.
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.
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.
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.
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. Students can opt to take this class at the Honors level.
Open to Grade Levels: 11, 12, or by departmental approval.
Delve into the realms of Probability and Matrix Theory through the fascinating lens of Markov Chains and other applications. After learning the fundamentals of probability and matrix theory, you will work with models of possible event sequences. This course blends theory with applications to explore how matrices are used to understand and calculate probabilistic processes and systems.
Students can opt to take this class at the Honors level.
Prerequisites: Algebra 2 and Geometry
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.
Students can opt to take this class at the Honors level. Prerequisites: Integrated Math 3 or Algebra 2 and Geometry
