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Mathematics Department Philosophy |  | Full-Year Course Offerings
The Mathematics Department seeks to contribute to students’ education through the study of abstract concepts and by developing problem-solving skills. By encouraging an intellectual progression from working concretely to handling abstractions, the Department’s offerings parallel and promote students’ cognitive development. Problem solving methods and analytical skills are developed with an eye towards the requirements of college level work and within the context of other aspects of our curriculum, chiefly our science offerings. To this end, we incorporate technology, in the form of graphing calculators and interactive software, into our work. But Mathematics remains a human endeavor and we encourage cooperative work, as part of a program of appealing to multiple modes of learning. Mathematics also constitutes a search for pattern, beyond its problem-solving aspect. With that in mind, we strive to instill in students an appreciation for mathematics as more than a tool, as a means of appreciating the regularity and beauty of the universe.
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Algebra I
Algebra I serves as an introduction to abstraction and to the tools of higher mathematics. Students are first taught to work with abstract quantities in solving linear equations and inequalities. This leads to representing equations graphically and then to quadratic equations. Student work is evaluated through nightly homework, quizzes, tests and occasional projects.
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Geometry
Geometry promotes deductive reasoning, through the study of proofs, along with a more concrete understanding of the mathematics of working with shapes in two and three dimensions. The course begins with an introduction to the terminology and concepts of geometry, which are developed through proofs, largely in two dimensions. As the year progresses, a third dimension is introduced and the concepts of surface area and volume are fleshed out. Student work is evaluated through nightly homework, quizzes and tests.
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Algebra II/Trigonometry
Algebra II/Trigonometry further promotes students’ abstract skills and seeks to give them a substantial mathematical toolbox that will serve them in higher level math and science courses. Topics progress from a review of Algebra I through quadratics and on to higher order equations, logarithms and finally an introduction to trigonometry. Student work is evaluated through nightly homework, quizzes, tests and cooperative work.
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Precalculus
Precalculus completes the study of algebraic technique and is designed for students with substantial ambition in mathematics, science, engineering and related areas. Logarithms, exponentials and trigonometry, introduced in Algebra II, are studied in more depth and with particular regard to applications. The course culminates with an introduction to the conceptual aspects of limits and both differential and integral calculus. Student work is evaluated through nightly homework, quizzes and tests.
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Advanced Placement Calculus (AB)
Advanced Placement Calculus is designed to offer a thorough introduction to the differential and integral calculus of a single variable. The course uses a variety of methods, numerical, graphical and analytical, to explore elementary functions. This is a demanding course, offering the possibility of college credit through the College Board’s AP program, and as such requires considerable commitment from students. It is expected that students enrolling in the course will have a thorough mathematical background, such as is offered in our Precalculus course. Student work is regularly evaluated through homework, quizzes and tests, culminating in the AP exam.
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Statistics
Statistics is designed to give the student a basic working understanding of the topic, appropriate for future work in such fields as economics, sociology and biology. This course is very much a practical, ‘hands on’ course, featuring projects in related areas of physical, biological and social sciences. Topics covered include probability, various types of distributions, sampling, hypothesis testing, correlations and regressions. Student work is evaluated through nightly homework, quizzes, projects and tests.
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Advanced Topics in Mathematics
Advanced Topics in Mathematics is a course intended for those students who have surpassed the normal high school mathematics curriculum and are invested in advancing in their studies of mathematics. In the spirit of a 'Topics' course, this course will offer a view into interesting and useful mathematics techniques, problem solving, and applications that is outside the mainstream high school curriculum. The course is driven mainly by student interest, and thus the topics may vary from year to year. The course introduces topics of formal logic and structures of logical argument, introduction to Set Theory, Number Theory, and Abstract Mappings during the first trimester. For the second and third trimesters, we will explore more advanced topics of Calculus of One Variable, as well as Infinite Sequence and Series, and an introduction to Vector Space Geometry and Calculus of Several Variables.
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