Mathematics

Major year course. 3 credits. Form III.
Prerequisite: Math 3 or equivalent or departmental permission.

The goal of this course is to develop and strengthen algebraic skills, focusing on the second half of a traditional algebra sequence. The course emphasizes the relevance of algebra in the real world and our everyday lives. It begins with the study of functions and linear equations and continues through statistics, inequalities, exponential equations, quadratics, and factoring.

Major year course. 3 credits. Form III.
Prerequisite: Math 3 or equivalent or departmental permission.

This course covers material found in Intermediate Algebra at an accelerated pace, while also introducing the foundations of Geometry. The Intermediate Algebra topics focus on basic properties of functions and how they apply to linear, exponential, and quadratic functions. The Geometry topics introduce key definitions and theorems and how to apply them in formal deductive reasoning proofs. The next course in this sequence is Geometry and Advanced Algebra.

Major year course. 3 credits. Forms III-IV.
Prerequisite: Intermediate Algebra.

Geometry is a course in plane and solid geometry with an introduction to both logic and the methods of proof and an emphasis on algebraic application of geometric properties and theorems. Discovery is a central pillar of the course. Students are guided in an exploration of shapes and taught how to create conjectures about their properties and relationships. Upon developing a conjecture, students use gathered information to validate them with formal proof. These theorems are then used in a variety of problem solving scenarios, including the formation of new theorems. Although the discussion of formal postulates and the proof of various theorems are thoroughly explored, focus is on the construction of new proofs and application of theorems rather than memorization.

This course covers the traditional postulates and theorems discussed in Euclidean geometry. In addition, coordinate geometry is explored in depth. Considerable time will also be spent reviewing and applying skills developed in algebra.

Major year course. 3 credits. Forms III-IV.
Prerequisite: Intermediate Algebra or departmental permission.

Geometry Honors is a course in plane and solid geometry with considerable focus placed on logic and methods of proof. Discovery is a central pillar of the course. Students learn to independently explore the relationships between objects to develop conjectures about their properties and relationships. Upon developing a conjecture, students use gathered information to validate it with formal proof. These theorems are then used in a variety of problem solving scenarios, including the formation of new theorems. Although the discussion of formal postulates and the proof of various theorems are thoroughly explored, focus is on the construction of new proofs, not on the memorization of theorems.

This course covers the traditional postulates and theorems discussed in Euclidean geometry. In addition, coordinate geometry is explored in depth. Considerable skill in algebra is necessary for success.

Major year course. 3 credits. Form IV.
Prerequisite: Intermediate Algebra and Geometry or departmental permission.

This course is the second year of a three-year program leading to Calculus as a senior. This course covers the second half of the material covered in plane and solid geometry. It then covers the material in Advanced Algebra up to but not including trigonometry.

Major year course. 3 credits. Forms IV-V.
Prerequisites: Geometry.

The goal of the Advanced Algebra and Trigonometry course is to develop students’ ability to think about and apply algebraic models. The focus is on justification and support of mathematical reasoning. The learning environment emphasizes collaborative problem solving, through group inquiry and project-based explorations. Additionally, the use of various computer graphing programs allow students the opportunity to explore the work from different perspectives. Topics covered include a continuation of previously learned algebraic functions and a survey of trigonometric functions.

Major year course. 3 credits. Forms IV-V. Prerequisite: Geometry Honors or departmental permission.

The Honors course is designed to develop higher order thinking and problem-solving skills that are required to be successful in Advanced Placement courses and college mathematics. The course focuses on not only solving but justifying and supporting conclusions with mathematical reasoning. Students will work individually and collaboratively to expand their algebraic fluency, while incorporating technology as a tool for exploration.

Topics covered include a continuation of previous learned algebraic functions, an in-depth analysis of trigonometric functions, statistics and probability. Additional topics will be included to prepare students for the rigors of future Advanced Placement courses. This is a fast-paced course where students are expected to think outside the regular classroom material as well as to construct and defend valid mathematical arguments in support of their solutions.

Major semester course. 1.5 credits.  Form V-VI.
Prerequisite: Advanced Algebra & Trigonometry

Statistics is a one-semester introductory course to data analysis, with an emphasis on interpreting graphs, planning/executing statistical studies, and making inferences. The use of technology will be infused throughout the course. A hands-on approach will be taken to learning each concept, especially with regards to students collecting their own data.

Major year course. 3 credits. Form V.
Prerequisite: Geometry & Advanced Algebra or departmental permission.

Pre-Calculus is an integrated course in advanced algebra and trigonometry, whose unifying link is the concept of function. The work strengthens students’ conceptual understanding of problems and mathematical reasoning is emphasized throughout. To prepare students to continue their studies with calculus, the course emphasizes graphing and curve-sketching, with extensive use of technology. Students work through an advanced analysis of polynomial, rational, exponential and logarithmic functions. In addition, all trigonometric functions and properties are covered extensively, while elements of limits and differential calculus are introduced.

Major year course. 3 credits. Form V. Prerequisite: Advanced Algebra & Trigonometry Honors or departmental permission.

This course is designed for students who plan to study A.P. Calculus. The concepts of algebraic functions, exponential and logarithmic functions, numbers and number systems, trigonometric functions, analytic geometry, limits of functions, limits of series and sequences, and vectors are some of the topics covered. The concepts of differential calculus are covered in detail including applications such as optimization problems, related rate problems, and curve sketching.

Major year course. 3 credits. Form VI. Prerequisite: Advanced Algebra & Trigonometry.

This course prepares students for further study of mathematics in college. The concepts of function, numbers and number systems, trigonometric functions, analytic geometry, limits of functions, series and sequences, and combinatorics are some of the topics covered in Analysis. Early concepts of differential calculus are covered, including curve sketching of rational functions.

Major year course. 3 credits. Form VI.
Prerequisite: Pre-Calculus Honors or Pre-Calculus.

This course begins with a thorough exploration of functions and limits of functions before moving into topics in differential and integral calculus. The focus of the course is on the calculus of polynomial and rational functions with some exploration of exponential and trigonometric functions. Applications such as related rates of change, optimization problems, curve-sketching, and area under a curve will be included. This course does not prepare students for Advanced Placement.

Major year course. 3 credits. Form VI. Prerequisites: B+ or better in Pre-Calculus Honors, A- or better in Pre-Calculus, or departmental permission. This is a senior elective course; Form VI students will be given priority in placement. On rare occasions when spots are available, Form V students may be considered.

This course introduces students to the tools and concepts of exploring data, planning a statistical study, producing models using statistics and probability, normal distributions, sampling distributions, and statistical inference. A.P. Statistics is the equivalent of a one-semester college-level introductory statistics course and meets the requirements outlined by the College Board. Students enrolled in the course must take the Advanced Placement exam in May.

Major year course. 3 credits. Form VI. Prerequisite: Pre-Calculus Honors or Pre-Calculus and departmental permission. A minimum average of B+/A– is expected.

This is a rigorous college-level course that expects students to achieve conceptual understanding of the basics of calculus. This course is equivalent to a one-semester college freshman course in calculus. Course content follows the A.P. outline for AB Calculus. Students are required to sit for the AB Calculus A.P. exam in May.

Major year course. 3 credits. Form VI. Prerequisite: Pre-Calculus Honors and departmental permission. A minimum average of A/A+ is expected.

This course is equivalent to a full-year college freshman course in calculus. Course content follows the A.P. outline for BC Calculus. Students are required to sit for the BC Calculus A.P. exam in May. This course is very rigorous and suited for students who wish to pursue math or science in college.

Major semester course. Offered in fall. 1.5 credits. Honors. Open to students who have completed A.P. Calculus with a Calculus AB AP grade of 4 or higher or by departmental permission. Differential Equations may not be taken concurrently with Math 6.

In  this course, students will  explore methods for solving various types of differential equations. They will discover the theory that justifies the methods, as well as discuss real-world applications in relation to mathematical modeling.  Students will look at linear and nonlinear, first order and higher order differential equations. The course will introduce students to the nature of the solutions through the use of slope fields and explore approximating solutions through numerical methods. 

Major semester course. Offered in spring. 1.5 credits. Honors. Open to students who have completed A.P. Calculus with a Calculus AB AP grade of 4 or higher or by departmental permission. Linear Algebra may not be taken concurrently with Math 6.

This advanced mathematics course will explore systems of equations, linear transformations, and vector spaces. Linear algebra is foundational for advanced study in mathematics, but also an essential tool for many other disciplines including computer science, engineering, and economics. We will focus on both theory and application. Students can expect some formal tests, presentations, and group and individual projects. 

Major semester course. Offered in spring. 1.5 credits. Honors. Open to students who have completed A.P. Calculus with a Calculus AB AP grade of 4 or higher or by departmental permission. Number theory may not be taken concurrently with Math 6.

Number theory is the study of the set of natural numbers, from which all other numbers are based. A closer look at this seemingly simple set of numbers reveals that there is more to the natural numbers than meets the eye. Students will explore the rules of operations in this set of numbers and build higher levels of conceptual awareness through the exploration of algorithms and modular arithmetic. While exploring these concepts, students will develop an understanding of the various proof techniques in mathematics and build proofs of their own. Students will also explore applications of number theory, including applications of modern-day cryptography, and how they stem from the core concepts in number theory.

Major semester course. Offered in fall. 1.5 credits. Honors. Open to students who have completed A.P. Calculus with a Calculus AB AP grade of 4 or higher or by departmental permission. Discrete Mathematics may not be taken concurrently with Math 6. 

This course introduces discrete mathematical structures such as propositions, sets, graphs and trees. It uses a formal approach to discuss the language used in mathematical reasoning, and the basic concepts, properties and relationships among the discrete objects. Students will be introduced to the idea of mathematical thinking with different methods of proofs, and they will learn to recognize and express the mathematical ideas graphically, numerically, symbolically, and in writing. Real world applications of these discrete objects such as logic gates in computers, traffic routing and scheduling will also be covered in this course. No previous computer science experience is required.

Major year course. 3 credits. Honors. Form VI. Open to students who have successfully completed BC Calculus with an AP grade of 4 or higher and who have demonstrated a high level of ability in mathematics with departmental permission. This course is open only to Form VI students.

This course is designed for students who have completed the AP BC Calculus course and are interested in continuing their math education beyond high school. The course introduces students to various topics in advanced mathematics. While every year’s curriculum may be different, in the past such topics as advanced techniques of integration, partial derivatives, extremas and saddle points of 3-dimentional functions, linear, homogeneous and Bernoulli differential equations, hyperbolic functions and factorials of fractions had been covered. In addition, students research and present papers on various topics such as linear algebra, number theory, mathematics of economics and others.

Major semester course. 1.5 Credits. Forms V - VI. Prerequisite AAT or higher. 

This applied mathematics course introduces students to concepts fundamental to the mathematics of business and finance. Topics covered include:

• A refresher of key financial concepts and formulas: compound interest, annuities, net present values, internal rates of returns and inflation

• Financial analysis and accounting concepts including: gross, net and marginal revenues, expenses and profits, cash flows, assets and liabilities.

• Application of concepts to real world business and finance situations including: asset allocation, investment decisions, nominal vs. real returns, pre and post-tax returns, time value of money. yield curves and risk vs. return.

• Use of spreadsheets, specifically Microsoft Excel, to conduct financial analysis and make decisions.

• Decision making in the absence of perfect information.

While we will apply financial concepts to investment decisions, this is NOT a personal finance or investments course. This course will emphasize the application of mathematical formulae to real world situations. Although this course does not require the use of advanced mathematical concepts such as calculus or statistics, students should be very comfortable with the use and application of formulas to problem solving. Prior experience or at least comfort with spreadsheets and relative formulas would be an asset, but is not required.

This course is well suited for students planning to study business and finance at the post-secondary level. Classes will reflect the learning methods used at major undergraduate business programs and thus will rely on significant amounts of class discussion and small group work to drive student learning.

Major year course (3 credits). Forms V-VI.

This two-semester course is an introduction to basic economic concepts and principles. Students will learn to apply these concepts and principles to current economic issues and global events. Some of the major areas of focus are Federal Reserve policies in the past and present, current economic goals, externalities, globalization, and what makes an economy function to the best of its ability. Students are introduced to supply and demand analysis, fiscal and monetary policy, and trade. Students who complete this course may wish to further their study of economics through enrollment in A.P. Economics in their senior year; however, this course is not a prerequisite nor a guarantee for admission to the A.P. course.

Major year course. 3 credits. Form VI. Prerequisite is one of the following:

• Successful completion of the combination of Advanced Algebra and Trigonometry and Principles of Economics courses
• Successful completion of the Pre-Calculus course
• Departmental permission

Past performance in history, mathematics, and other disciplines is considered. This is a senior elective course; Form VI students will be given priority in placement. On rare occasions when spots are available, Form V students may be considered.

This course is the equivalent of two semesters of college-level economics. The course will cover macroeconomic principles such as supply and demand, inflation, unemployment, and fiscal and monetary policy, as well as microeconomic topics including the nature and function of product markets, price determination, perfect and imperfect competition, efficiency, equity, stability, growth, and the role of government. Assessments include final tests covering microeconomics and macroeconomics.