The Mathematics Department develops in each student knowledge, understanding, and curiosity about mathematics both as a discipline in itself and as a means of describing and understanding the outside world. Students learn problem-solving and analytical skills and logical thinking as they practice organizing data and tackling a variety of mathematical problems.

Independent Studies in Mathematics

Each registrant for an individual, independent term project must submit a written proposal to the chairman of the department. The proposal must be submitted at the time of registration for classes for the succeeding semester. The proposal must be written in essay form and contain a description of the project, the student’s purpose, and the scope of the project. Once a student’s proposal has been approved by the department and an advisor has been selected, the student will be expected to consult with his advisor at least once a week. The advisor will use his or her own judgment regarding the length of such meetings. The advisor may require written or oral interim reports at least once a week. The entire project must be completed and in the hands of the advisor on the last day of the semester’s classes. Interdepartmental projects will also be considered. The same procedure should be followed as above, but it would be advisable for the student to discuss his project with the respective department chairs before submitting his proposal.

Advanced Geometry

This course provides a modern approach to the study of geometry in the plane and in space as a deductive, axiomatic system. From the outset, students focus on writing rigorous proofs using both synthetic and coordinate methods. Coordinate geometry and transformations are integrated into the course throughout the year. Congruence, similarity, area, volume, and geometric inequalities are major topics of study.  Geometer’s Sketchpad is used as a tool for investigation and discovery.

Prerequisite: Algebra II. This course must be taken throughout the year.

Advanced Statistics

This full-year college-level elective course introduces students to statistical methods for collecting, analyzing and making inferences about data.  Major topics of study include techniques for analyzing single variable data, linear regression, sampling methods, survey and experimental design, probabilistic behavior of random variables, confidence intervals and statistical significance tests for means, proportions and regression, and chi-squared methods.  Students will complete three to four major projects throughout the year, collecting and analyzing variables of their own choosing, and writing about and presenting their findings.  Students will practice and develop their technical writing skills throughout the year.  Students should be comfortable working collaboratively as projects and most in class learning activities are group based.  Students who complete this course will be prepared for and expected to take the Advanced Placement Examination in Statistics in May.  This course is open to sophomores, juniors and seniors who have completed Algebra II.  Students may not drop this course to pursue a Senior Project.

Algebra II

This course is a study of linear, quadratic, polynomial, exponential, logarithmic, and trigonometric functions. Problems will point to real world relationships and data. Students will learn to describe linear, nonlinear, and periodic data. Graphing calculators and dynamic algebra software will be used extensively. Prerequisite: Algebra I and Geometry. This course must be taken throughout the year.

Boolean Algebra

This course is a one semester introduction to Boolean Algebra. The focus of the first half of the course will be circuitry using base 2 counting and logic and an overview of sets and the operations.  The focus of the second half of the semester is a survey of Number Theory, and Graph Theory, including Egyptian Fractions and Euler Circuits.  This elective meets five times during a two week cycle during the first semester.  Prerequisites:  Pre-Calculus and departmental approval.

Calculus

This is a college-level course in differential and integral calculus. Emphasis will be placed both on a conceptual understanding of the material as well as calculus applications. The course is less proof-based than Calculus AB and students will use calculus to understand and model real-world situations. Computers and graphing calculators are used where appropriate. The course is open to seniors who are not taking an advanced calculus course.

Calculus (AB)

This is a college-level course in differential and integral calculus; students are prepared to take the Calculus AB Advanced Placement Examination. Emphasis will be placed both on a conceptual understanding of the material as well as calculus applications. Computers and graphing calculators are used where appropriate.

Prerequisite: Pre-calculus Mathematics and departmental approval. This course must be taken throughout the year and may not be dropped to pursue a senior project.  Students taking this course will sit for the Advanced Placement Exam in May.

Calculus (BC) 12

This college-level course is intended for students who have a strong interest in mathematics. The syllabus of this course includes a full discussion of the formulas, techniques, and applications of integral calculus as well as polar and parametric functions. It also includes additional topics such as motion on a plane curve, sequences and series, and differential equations. Students who successfully complete Calculus BC will be prepared to take the Calculus BC Advanced Placement Examination. Computers and graphing calculators will be used when appropriate. Prerequisites: Calculus AB and permission of the department. This course must be taken throughout the year. Students may not drop this course in order to pursue a senior project.

Geometry

This course provides a modern approach to the study of geometry as a deductive, axiomatic system. Students learn both synthetic and coordinate methods for proving theorems. The emphasis of the course is on the geometry of the plane, but geometry of three dimensions is also taught where appropriate by extending two-dimensional concepts. Congruence, similarity, area, and volume are major topics of study.  Real-world applications of geometric concepts are introduced wherever appropriate.  Geometer’s Sketchpad is used as a tool for investigation and to deepen understanding.

Prerequisite: Algebra I.  This course must be taken throughout the year.

Linear Algebra 

This course is a one semester introduction to Linear Algebra, a branch of mathematics analyzing matrices, vectors, vector spaces, linear transformations, systems of linear equations in finite dimensions, and mathematical and physical applications.  This elective meets five times during a two week cycle during the first semester.
 

Prerequisites:  AB Calculus and departmental approval.

Math in Business, Finance, and Econ

This one-semester elective course introduces students to some applications of mathematics in business, finance and economics.  Topics of study may include, depending on time and student interest, basic financial models (interest, annuities, sinking funds, amortization, and bonds), Leontief models for relative income and production forecast, linear programming business optimization models using the simplex method, marginal analysis and profit optimization models, income and related inequality models, and a brief introduction to game theory.  While previous study of calculus is not required, students will learn about and apply some basic calculus concepts and techniques.  This course will meet five times per two-week cycle and is open to sophomores, juniors and seniors who have completed Algebra II.

Mathematical Modeling

Mathematical modeling is the application of mathematical concepts, structures, and techniques to describe and predict the behavior of real-world systems.  This course focuses on crafting models by reducing complex systems from the world around us into mathematical language, using mathematical techniques to analyze these models, and then interpreting those results in the context of our original real-world problems.  The mathematical structures and techniques employed include recursive and iterative functions, Euler’s method and nonlinear differential equations, and probability and agent-based modeling.  Topics covered include populations growth, finance, epidemiology, predator-prey scenarios, and error approximation.  Advanced feature of Excel, basic computer programming with Python, and agent-based modeling with NetLogo are introduce.  No programming experience is necessary. 

Prerequisite:  Algebra II and departmental recommendation.

Multivariable in Mathematics

This full year course investigates linear algebra and multivariable calculus, and makes heavy use of linear algebra in understanding vector functions. The course introduces the student to the study of vector spaces over the real numbers, linear mappings between vector spaces, and their matrix representations. Topics include an investigation of ways to represent and analyze lines and planes in space, with frequent use of the scalar product and cross product, the study of subspaces, bases, and dimension, the kernel and image of a linear mapping, and determinants. Eigenvalue problems arise occasionally throughout the course. The student is also exposed to examples of more general vector spaces (function spaces). The theory is applied to the solution of systems of linear equations, difference equations, and differential equations. Students continue with the study of the calculus of vector functions, with emphasis on functions defining curves in the plane, as well as curves and surfaces in space. The course treats explicit, parametric, and implicit representations of curves and surfaces, along with their tangent lines and planes. The uses of partial derivatives, directional derivatives, and the gradient are explored. The study of integration includes iterated integrals and multiple integrals, with Fubini’s Theorem tying them together, along with line and surface integrals, culminating with the important theorems of Green and Stokes. Applications include extrema problems (with Lagrange multipliers), volume and surface area, and physical interpretations of the vector field theory. 

Precalculus (11)

This course builds on the functions learned in Algebra II.  Trigonometric functions in particular, are explored in great depth. Throughout the year the students model real-world data with mathematical functions.  They also study matrices, sequences and series and statistical analysis.  The last unit of the year, limits, provides a transition to the study of the Calculus.

Prerequisite: Algebra II.  This course must be taken throughout the year.

Precalculus BC Mathematics

This course covers the same topics as does Pre-Calculus, but in the greater depth. 

Prerequisite: Algebra II.  This course must be taken throughout the year.