Mathematics

Mathematics and the mathematical patterns found throughout our surroundings offer us a powerful and beautiful way of viewing the world. The St. Stephen’s mathematics department seeks to enable students to recognize and assimilate mathematical relationships and to use them to make predictions and draw conclusions.

The department’s objectives are to:

Stimulate curiosity about the application of mathematics in the world around us;
Foster independent, creative and critical thinking in a cooperative learning environment;
Develop students’ ability to persevere in the face of difficulty;
Encourage articulate communication of ideas in oral and written form;
Promote the use of technology in the learning of mathematics; and
Cultivate solid foundational skills necessary for complex mathematical analysis.

The curriculum serves students with varying abilities, enabling them to gain confidence in and expand their mathematical skills and to become effective problem solvers and communicators of mathematical ideas. Students develop logical reasoning and critical analysis skills and an appreciation for the beauty and unified structure of mathematics.

Advanced sections cover the subject in greater depth and breadth and are so designated on students’ transcripts. Admission to and retention in an advanced course is by departmental approval and may require confirmation of ability by a placement examination.

Upper School students are required to complete three mathematics credits and take math through their 11th-grade year.

Algebra I

Algebra I integrates knowledge of variables and their use with concepts and operations of arithmetic in a formal, logical development of elementary algebra. Accuracy and precision are essential components of instruction, as is the development of problem-solving strategies. The content of the course includes an in-depth study of linear equations and inequalities, graphing, operations with polynomials, factoring, rational expressions and equations, introduction to functions, radical expressions and equations, and the quadratic formula. Word problems and applications of increasing complexity are addressed throughout the course.

1 credit
Geometry

Students are introduced to traditional plane and solid Euclidean geometry, as well as coordinate geometry, constructions and transformational geometry. Both independent problem-solving and cooperative group work are elements used in the investigation of geometric truths. Students learn theory and application, formal and informal proofs, and symbolic and visual approaches to problems. The course provides a firm foundation in understanding the relationships between and within geometric figures, and it develops the skills to reason effectively. Computer-assisted explorations, as well as compass and straightedge constructions, are part of the course throughout the year as they relate to the topics covered. The course helps to prepare students for the challenges of higher-level mathematics.

Prerequisite: Algebra I.

1 credit
Adv Geometry

Advanced Geometry is intended for those students who have well-developed spatial and abstract reasoning skills. In addition to the topics presented in Geometry, this course includes a more formal emphasis on deductive logic and proof. Proofs using deductive or indirect reasoning, paragraph or two-column form, and construction are utilized to enhance logical thinking and creative problem-solving. Inductive discovery of principles is facilitated by the use of the computer, models and experimentation. Special projects heighten the student’s appreciation for the application of geometry to the real world, the historical significance of the subject, and recent discoveries in mathematics.

Prerequisite: V- or higher in Advanced Algebra I or departmental approval.
1 credit
Algebra II

Algebra II builds on the concepts and skills mastered in Algebra I and expands these ideas with further applications and more challenging problem-solving. It also utilizes technology, primarily in the form of graphing calculators and graphing software, as a tool for opening doors to new approaches. In addition to the topics introduced in Algebra I, Algebra II includes the study of irrational and complex numbers, polynomial equations, exponential and logarithmic functions, analytic geometry, trigonometry, data analysis, and probability. The course provides a firm foundation in the language and application of algebra and in the skills and knowledge necessary to succeed in higher levels of mathematics.

Prerequisite: Geometry.

1 credit
Adv Algebra II

A rigorous course that prepares students for successful transition into Advanced Precalculus, Advanced Algebra II enables them to master advanced algebraic concepts and skills, to think independently, and to utilize appropriate methods of problem-solving. The content of the course includes topics covered in Algebra II, as well as data analysis, combinatorics, probability and a more in-depth study of trigonometry. Those topics that are covered in Algebra II are studied in greater depth and scope, with special emphasis on critical thinking and application of concepts.

Prerequisite: V- or higher in Advanced Geometry or departmental approval.

1 credit
Precalculus

Precalculus provides students with a firm foundation in the theory and use of functions and their graphs. Each type of function addressed — including polynomial, rational, exponential, logarithmic and trigonometric — is explored algebraically, graphically and geometrically. Other topics include analytic geometry, complex numbers, data analysis, probability, and sequences and series. Graphing calculators and graphing software are used extensively to enable students to make subtle connections between topics within the course.

Prerequisite: G- or higher in Algebra II or departmental approval.

1 credit
Adv Precalculus

Advanced Precalculus is a more rigorous examination of those topics essential to the study of calculus. Major topics include the study of advanced graphing, functional analysis, exponential and logarithmic functions, trigonometric functions and their applications, analytic geometry, sequences and series, data analysis, combinatorics and probability, matrices, polar and parametric functions, and polar representation of complex numbers. An introduction to calculus at the end of the course includes limits, continuity and the development of instantaneous rates of change. Emphasis is on conceptual understanding and real-world applications.

Prerequisite: V- or higher in Advanced Algebra II or departmental approval.

1 credit
Calculus

Calculus is designed to prepare students for a college-level calculus course, with an emphasis on process and applications rather than on theory. The topics include a Precalculus review, functions and their graphs, limits, derivatives and applications, integration, and the calculus of exponential, logarithmic and trigonometric functions.

Prerequisite: G- or higher in Precalculus or departmental approval.
1 credit
Adv Calculus AB

Advanced Calculus AB is a standard college-level course in the calculus of one variable. Emphasis is not only on a clear understanding of the concepts but also on their applicability in real-world situations. Major topics include limits, continuity, derivatives and applications, integrals and applications, transcendental functions, and first-order differential equations. Mastery and retention of Advanced Precalculus topics are assumed.

Prerequisite: V- or higher in Advanced Precalculus or departmental approval.

1 credit
Adv Calculus BC

Advanced Calculus BC is a rigorous, in-depth study of the calculus of one variable. In addition to the topics presented in the Advanced Calculus AB course, this course includes topics such as infinite series, Taylor polynomials, parametrically defined functions, and polar coordinates. Mastery and retention of Advanced Precalculus topics are assumed.

Prerequisite: departmental approval.
1 credit
Multivariable Analysis

Students are introduced to further mathematical applications of calculus, as well as other topics in advanced mathematics. Topics include advanced techniques of integration; three-dimensional analytic geometry; vectors and vector-valued functions; multivariable and vector calculus, including multiple and line integrals; and the theorems of Green and Stokes.

Prerequisite: departmental approval.
1 credit
Stats and Selected Topics

This course offers students an alternative in the mathematics they choose to pursue beyond the level of second-year algebra. Approximately half the year is spent introducing students to the core concepts of statistics, while the remainder of the year is spent exploring the applications of mathematics in diverse contexts, including career and daily life. Throughout the course, students focus on the mathematical techniques of problem-solving and analysis that foster habits of effective thinking in life outside the classroom. Topics may include some or all of the following: networks, graphs and critical paths; fractal geometry; non-Euclidean geometry; topology; logic, binary arithmetic, digital logic, encoding and the mathematics of computers; number theory; and personal finance and avenues of investment.

Prerequisites: Algebra II and 12th-grade students only.
1 credit
Adv Statistics

This activity-based course provides students with a rigorous, in-depth study of the fundamental concepts and techniques employed when working with data. The course exposes students to four broad conceptual themes: exploratory analysis, planning a study, modeling using probability and simulation, and testing hypotheses using statistical inference. Technology plays a major role in the course. Statistical computer software is used, and students learn to use the internet as part of the statistical research process. Motivated students who have completed Algebra II should consider taking Advanced Statistics as an alternative or supplement to Precalculus and/or Calculus.

Prerequisite: Algebra II. Preference will be given to 12th-grade students.
1 credit
Linear Algebra

Linear algebra is the study of vector spaces and the structure of linear mappings between such spaces with a strong emphasis on the theory underlying them. Topics include vector spaces, the structure of linear transformations and matrices, determinants, matrix calculations, and eigenvalues and eigenvectors of matrices.

Prerequisite: Departmental approval
Ind Study Adv Math

Students who have completed Multivariable Analysis before the 12th-grade year may work with a faculty member to complete a course of study in advanced topics, such as differential equations, linear algebra, abstract algebra or topology.

Prerequisite: departmental approval.
1 credit