# Mathematics

Many of our students are destined to be leaders in fields where analytical and problem-solving skills are invaluable, and specific applications of mathematics are often indispensable. In the Mathematics Department, we give each student the necessary tools to understand theories and appreciate applications.

True problem-solving strength calls for a wide repertoire of knowledge. Students acquire a strong knowledge of mathematics through the study of algebra, geometry, trigonometry, and calculus. This ability to solve problems is further strengthened by learning to discern relationships between particular skills and concepts and the fundamental principles that unify them. Students learn to formulate key questions, analyze data, and apply learned strategies to new situations. In doing so, they are equipped not only to solve mathematics problems but also to use an analytical, well thought-out approach in seeking solutions in other areas of life.

- Algebra 1
- Algebra 2
- Algebra 2 Honors
- Geometry
- Geometry Honors
- Math 4: The Nature of Math / The Nature of Personal Finance
- Pre-calculus
- Pre-calculus Honors
- AP Calculus AB
- AP Calculus BC
- Multivariable Calculus
- Statistics
- Introduction to Programming
- Computer Science and Technology

## Algebra 1

This class introduces the basic principles of future mathematics courses. Students transition from the concrete to the abstract through a wide range of problem-solving situations. The class emphasizes the concept of functions and covers the real number system, operations with positive and negative numbers, simplifying algebraic expressions, solving and graphing linear equations and inequalities, applying rules of exponents, understanding operations involving polynomials, simplifying rational expressions and square roots, solving systems of linear equations, and solving both rational and quadratic equations.

## Algebra 2

This course aims for a mastery of the manipulative skills in real-number algebra as well as further developed problem-solving skills. Students review and extend their ability to manipulate polynomial and rational expressions and to solve linear, quadratic, fractional, and radical equations and inequalities. The course includes the study of irrational and complex numbers, matrices, conic sections, nonlinear systems of equations, sequences, series, right triangle trigonometry, and concludes with an introduction to exponential and logarithmic functions.

## Algebra 2 Honors

This course emphasizes step-by-step solutions. The pace is set to challenge students with high mathematical abilities. This second year of algebra begins with a review of the principles learned in Algebra 2 and proceeds into greater complexities, with subsequent introduction of the elements of exponents, functions, logarithms, trigonometry, sequences, and series.

## Geometry

This course introduces students to concepts in geometry and teaches how to write two-column and paragraph proofs. Basic algebraic skills are reinforced throughout this course with special emphasis on applications of congruence and similarity of triangles, properties of circles, areas of plane figures, and volumes of solids.

## Geometry Honors

This course is for students who have a genuine interest and high aptitude in math. In the class, students gain a greater appreciation of the nature of a mathematical system through the study of challenging mathematical proofs. Other topics emphasized are applications of congruence and similarity of triangles, properties of circles, areas of plane figures, and volumes of solids. Also, inductive and deductive reasoning are discussed, and algebraic concepts are reinforced through the study of coordinate geometry.

## Math 4: The Nature of Math / The Nature of Personal Finance

During the first semester, this course gives students the opportunity to explore the concept of infinity; to study mathematical patterns in nature, art, and music; to create various geometric solids; and to discover how patterns can be used to solve problems involving geometry, numeration systems, networks, topology, exponential growth and decay, and fractals. As students build skills in problem-solving and estimation, they also gain a better understanding of the historical development of mathematical ideas.

The content of the second semester gives students the opportunity to learn about essential elements of personal finance that they are likely to encounter as young adults both during and after college. Students learn about interest, the present and future value of money, debt, basic banking, investing, loans, retirement savings, insurance, and taxes. Throughout this course, students explore the nature of growth and decay, and compound interest. Overall, the course focuses on solving real-world problems and providing students with the basic knowledge and tools they will need to apply their problem-solving abilities to their financial life.

## Pre-calculus

This course is an introduction to analysis. The intent is to utilize all the mathematical concepts developed in previous math courses and to sum up the basic concepts of mathematics. In preparation for college-level calculus, pre-calculus integrates a number of topics including functions, inverse functions, theory of logarithms, functional trigonometry, polynomial equations, probability, and statistics.

## Pre-calculus Honors

This course offers a challenging introduction to the study of analysis after a brief review of basic mathematical concepts. This course integrates a number of topics, including an in-depth study of functions, theory of logarithms, trigonometry, polynomial equations, and statistics. Students are also introduced to limits and the interpretation of computation of derivatives.

## AP Calculus AB

## AP Calculus BC

## Multivariable Calculus

Multivariable Calculus covers a number of other topics beyond the AP Calculus BC curriculum, including calculating volumes by using shells, surfaces of revolution, and centers of mass and centroids. The course explores topics that are studied in a typical college-level third semester calculus course, including vectors and vector valued functions, differentiation and optimization in several variables, multiple integration, and line and surface integrals.

## Statistics

This course introduces students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. Students are exposed to four broad conceptual themes:

- Exploring data: describing patterns and departures from patterns.
- Sampling and experimentation: planning and conducting a study.
- Anticipating patterns: exploring random phenomena using probability and simulation.
- Statistical inference: estimating population parameters and testing hypotheses.

## Introduction to Programming

The purpose of this one-semester class is to introduce students to the concept of programming; no prior experience with computers and computer programming in particular is assumed. Students learn through short lectures, individual and group work during class, and by completing programming assignments and projects of varied complexity. Assignments are tailored to challenge interested, highly motivated students, and yet be accessible and interesting to students requiring more individual guidance. The course is based on the Processing programming language, a Java-derived language. Processing allows students who wish to continue their adventure with programming a relatively simple transfer to Java and JavaScript. At the same time, Processing, which is often referred to as the programming language for artists, makes the first steps in programming particularly rewarding since it allows for the creation of visually appealing graphical projects with very limited programming background needed.

## Computer Science and Technology

This full-year, rigorous course introduces students to the foundations of modern computing. The course covers a broad range of topics such as programming, algorithms, the Internet, big data, digital privacy and security, and the societal impacts of computing design. The course seeks to provide students with a foundation in computing principles so that they are adequately prepared with knowledge and skills to meaningfully participate in our increasingly digital society, economy, and culture. There are no prerequisites for this course. However, the majority of students will have taken the Introduction to Programming course at Santa Catalina. Thus, the class continues to build on programming skills using the Processing language.