# Mathematics

The Mathematics Department at Columbus School for Girls is committed to a core college preparatory curriculum that reflects the mandates set forth by the National Council of Teachers of Mathematics in “Curriculum and Evaluation Standards for Teaching Mathematics.” Mathematics must be ever-developing so that students continually expand their understanding of mathematical concepts in both breadth and depth as they progress through middle school and upper school. We strive to maintain a balance between skills and concepts, the concrete and the abstract, intuition and formalism, structure and problem solving, and induction and deduction. At CSG, both the teaching and the study of mathematics remain responsive to our understanding of the quickly growing area of advanced computing technology.

The goals of the Mathematics Department are that all students learn to value mathematics, apply mathematical techniques confidently, skillfully, and accurately, reason mathematically, use mathematical reasoning as a problem solving tool when appropriate, communicate mathematically, and become efficient users of modern technology. Students are encouraged to seek and to accept appropriate challenges as they pursue their mathematics education.

- Algebra I
- Geometry
- Honors Geometry
- Algebra II
- Honors Algebra II
- Advanced Placement Statistics
- Introduction to Pre-Calculus
- Pre-Calculus
- Pre-Calculus/Calculus A
- Advanced Placement Calculus AB
- Advanced Placement Calculus BC
- Multivariable Calculus
- Linear Algebra

## Algebra I

Algebra I is an in-depth course in the study of algebra that provides the essential foundation for all further study of mathematics at the Upper School level. Students study operations with polynomial, rational, and radical expressions, factoring; solving linear, quadratic, absolute value, rational, and radical equations, inequalities and systems, and linear and quadratic functions and their graphs. The class emphasizes the development of algebraic computational and problem-solving skills. Students are introduced to graphing technology.

## Geometry

The content of Geometry includes a strong emphasis on the basic concepts of Euclidean Geometry and the development of logical reasoning, including the formal method of proof. The class integrates concepts of coordinate and three-dimensional geometry with plane geometry. Students learn a drawing/construction software program that they use throughout this course*.*

## Honors Geometry

The content of Honors Geometry is similar to Geometry but emphasizes formal proofs. Geometry includes a strong emphasis on the basic concepts of Euclidean Geometry and the development of logical reasoning, including the formal method of proof. The class integrates concepts of coordinate and three-dimensional geometry with plane geometry. Students learn a drawing/construction software program that they use throughout this course.

## Algebra II

Algebra II is a continuation of the study of algebra. Topics covered include a review of Algebra I, linear equations, quadratic equations, factoring, graphing using transformations, irrational and complex numbers, and exponential and logarithmic functions. Students enrolled in this level of Algebra II take Introduction to Pre-Calculus the following year.

## Honors Algebra II

In Honors Algebra II, students engage the formative concepts of mathematics and gain computational competence in order to prepare them for the demands of Pre-Calculus the following year. Algebra II is an in-depth course in which the student continues the study of algebra. The course content commences with a review of Algebra I topics and progresses to include a study of the irrational and complex numbers, quadratic equations and functions, equations and numerical methods, exponential and logarithmic functions, sequences and series, probability, and trigonometry. Graphing technology plays an integral role in the mathematics of this course.

## Advanced Placement Statistics

Advanced Placement (AP) Statistics is a year-long course that is the equivalent of a semester of introductory college statistics. The course provides students with a strong foundation in basic statistics and prepares the students for the AP Statistics Examination. The four main concepts of the course are data exploration, sampling and experimentation, probability and simulation, and statistical inference. In addition to thinking critically about the concepts, students are also expected to write clear and concise explanations. Students learn to think logically and critically in order to solve and explain interesting and complex problems. Statistics emphasizes an interdisciplinary application of mathematics to other academic fields.

## Introduction to Pre-Calculus

Introduction to Pre-Calculus is a bridge course between Algebra II and Pre-Calculus. It provides students with an opportunity to strengthen their algebra and problem-solving skills as well as to gain some experience with elementary pre-calculus concepts prior to undertaking the more theoretical course in Pre-Calculus. This course is a skill-level introduction to these topics. Graphing technology plays an integral role in this course.

## Pre-Calculus

This course focuses on the concepts and methods essential to the study of college-level calculus. It enables students to model a written description of a physical situation with a function, use technology to help solve problems, experiment, interpret results, and verify conclusions, and determine the reasonableness of solutions, including size, relative accuracy, and units of measurement. Students will be encouraged to communicate mathematics orally as well as in written form. The class emphasizes the study of linear, polynomial, rational, exponential, logarithmic, trigonometric, inverse trigonometric, absolute value, and piecewise functions, each of which will be represented graphically, numerically, analytically, and verbally. Additional topics studied include conic sections, complex numbers, vectors, and the polar coordinate system. The year ends with a chapter on limits, continuity, and derivatives.

## Pre-Calculus/Calculus A

This course covers all topics in both the traditional pre-calculus course and some of the beginning topics of calculus. This class prepares our highest-level mathematics students for our most advanced course offerings (AP Calculus BC, Multivariable Calculus, and Linear Algebra). Students who complete this course successfully will enroll in AP Calculus BC the following year.The course teaches students to model a written description of a physical situation with a function; to use technology to help solve problems, experiment, interpret results, and verify conclusions; and to determine the reasonableness of solutions, including size, relative accuracy, and units of measurement. Students communicate mathematics both orally and in written form. First semester topics include logarithmic functions, exponential functions, and trigonometry. Second semester topics include sequences, series, probability, analytic geometry, limits, and basic derivatives.

## Advanced Placement Calculus AB

This course consists of a full academic year of work in calculus that is comparable to courses in colleges and universities and prepares students for the AP Calculus AB examination. Centered on the themes of derivatives, integrals, limits, approximation, and applications and modeling, this course is primarily concerned with developing the students’ understanding of the concepts of calculus and providing experience with its methods and various interdisciplinary applications. It emphasizes a multi-representational approach to calculus with concepts, results, and problems expressed geometrically, numerically, analytically, and verbally. This course focuses on broad concepts and widely applicable methods rather than on manipulation and memorization and, although computational competence is an important outcome, it is not at the core of this course. Students use technology regularly to reinforce relationships among the multiple representations of functions, to confirm written work, to implement experimentation, and to assist in interpreting results.

## Advanced Placement Calculus BC

Through a multi-representational approach to calculus with concepts, results, and problems expressed in geometric, tabular, numerical, analytic and verbal form, this course prepares students for the AP Calculus BC examination. Students are expected to work both together and independently to apply, synthesize, and articulate their understanding of the interconnectedness of the various mathematical topics to which they have been introduced over the years. The course begins with a review of material related to the themes of limits and continuity and quickly builds to explore the concepts of derivatives and their applications, definite and indefinite integrals (including improper integrals) with applications, differential equations and mathematical modeling, sequences and series, and concludes with a study of parametric, vector-defined, and polar functions.

## Multivariable Calculus

This semester course follows AP Calculus BC and is an introduction to multivariable calculus. It is designed to be a college-level course in terms of both its content and rigor. The class links applications to science and computer technology in order to help students visualize the three-dimensional problems. The course content includes vector-valued functions, functions of several variables, partial derivatives, directional derivatives, gradients, extrema, multiple integrals, line integrals, Green’s Theorem, parametric surfaces, Divergence Theorem, and Stokes Theorem.

## Linear Algebra

This rigorous semester course follows Multivariable Calculus and provides the sophisticated mathematical content necessary for application to college-level science and engineering classes. The course content includes systems of linear equations, matrices, determinants, vector space, coordinate systems and bases, linear transformations, eigenvalues, eigenvectors, inner product and orthogonality, orthogonal matrices, geometric, and real-world applications.