The Academic Program: Mathematics

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| Grade Nine | Grade Ten | Grade Eleven | Grade Twelve |

Our school expects all students to be firmly grounded in mathematics, and our main lessons in mathematics cover such topics as permutations and combinations, projective geometry, introduction to calculus, and higher mathematics. In addition to main lessons, four mathematics classes per week are required during the first three years, and provide a comprehensive survey of algebra, plane and solid geometry, trigonometry and pre-calculus. These year-long classes are enriched by geometrical and perspective drawing and by work in applied mathematics and computer programming. Year-long advanced courses in calculus and computer science are offered as electives.

Grade Nine

Math I: Algebra A/B

In these year-long courses students work on expressions and equations and their relationship to word problems, graphing expressions and equations, and inequalities and quadratic equations. Grades are based on weekly quizzes, a main lesson book and a final exam.

Permutations and Combinations Seminar—In this course students explore permutations, combinations, Pascal's Triangle, and the binomial theorem. Students develop the binomial theorem using their knowledge of the counting principle. Grades are based on weekly quizzes, a main lesson book, and a final exam.

Keyboarding Workshop—This course reviews computer system fundamentals, personal computer applications software, and computer communications. Students use personal computers to complete assignments in word processing, spreadsheet analysis, database management, and other applications.

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Grade Ten

Math II: Geometry A/B—In these year-long courses students cover a standard curriculum of area, volume, trigonometry, Euclidean proofs, loci, and the Cartesian plane. Throughout the year students will work to exercise their spatial imagination often using geometric constructions as a means to this end.

Proof and Calculations Seminar—The purpose of this course is to introduce students to the concept of establishing mathematical laws and constants to a certainty. To this end, the students learn how to do formal two-column proofs and work through Archimedes' method for calculating. Grades are based on a mid-block quiz, a main lesson book and a final exam.

Bits and Bytes Seminar with Lab—This seminar provides an overview of the development of computers and explains the major principles in hardware and in mathematics that underlie the modern computer. In class, students use circuit boards and logic chips to wire together their own binary half-adders.

Introduction to Computer Programming Seminar—This course is an introduction to the computer language Q-BASIC and to computer programming in general. Students begin by working out programs on paper, and then proceed to writing, running and debugging a few small programs, and finally writing a game program that involves turning pseudo-random numbers into draws from a deck of cards. Grades are based on class participation, the few small programs, and the final game program.

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Grade Eleven

Math II Algebra II & Trigonometry A/B—
These are courses in Elementary Functions. The courses begin with a review of linear and quadratic equations and functions, then treat the topics of complex numbers, exponential and logarithmic functions, conic sections, trigonometric functions, polar coordinates, complex numbers and vectors. The Algebra II and Pre-calculus course is a preparation for the senior year elective in Calculus.

Projective Geometry Seminar—Projective Geometry is one of a group of non-Euclidean geometries invented in the nineteenth century. At its foundation lies a change in Euclid's problematic fifth postulate. Instead of assuming that parallel lines never meet, parallel lines are postulated to meet exactly once, at the infinite point. The students in the course are confronted with the question, "What is my assumption about the world?" The main lesson book for this seminar consists of a series of plates. Clean, precise constructions are demanded, but no written text is required.

Introduction to Calculus Seminar—In projective geometry, students wrestled with the concept of the infinitely distant point; in calculus, students wrestle with the concept of the infinitely small interval. Through a practical example of searching for the instantaneous speed of a falling object, the students discover the process of taking a limit. Using limits, students calculate derivatives and apply them to examples of curve sketching. Grades are based on class participation, assignments, quizzes, a main lesson book, and a final exam.

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Grade Twelve

Calculus Elective—This is a demanding course, requiring strong skills from algebra and an interest and ability in math. In preparation for college, the students are required to work quite independently and exercise self-discipline. The in-class tests are timed, and require facility with the skills covered during class. In contrast, the assignments pose challenging questions, which require many days of thought and the ability to synthesize independently the ideas from the course and previous work in math. During the first half of the year, the topic is differential calculus; whereas during the second half students work with many applications of the integral. Towards the end of this course, the students solve differential equations and use solids of revolution to find the volumes contained by different curves. Grades are based on assignments, class participation, quizzes and a final exam.

Computer Programming Elective—This course is a yearlong introduction to computer programming that uses the computer language C++, a procedural language with object-oriented extensions that is regularly used by computer programmers. Students spend most of the year exploring the procedural aspects of this language, eventually turning to the more advanced object oriented side of C++. Grades are based on assignments, quizzes, and a final exam. This course is not offered every year.

Math Topics: Chaos Theory Seminar—The field of Chaos Theory is a young one, appearing only in the last twenty years, and finding its place at the boundaries between mathematics, computing, and the natural sciences. It is not a study of disorder, rather the recognition that within apparently disorganized systems lays enormous order, and out of apparently trivial equations enormous complexity springs. In this class, students apply features of chaos theory to the creation of computer-generated fractals. Outside of class, each student researches an application of chaos theory to a field of his or her own choice and submits a practical or artistic project showing how chaos manifests itself in our world. The course requirements include two tests and a final exam.

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