# Mathematics

Through lectures, seminar-style classroom discussions, collaborative work and independent study, the St. Andrew's Mathematics Department aims to teach students to read, write and speak about mathematics with clarity and precision. Students learn to use and interpret mathematics graphically, numerically and algebraically in the context of skill development, practical problem-solving and formal proofs. Various technologies, including SMART Board, TI-SmartView software, graphing calculators, spreadsheets, The Geometer’s Sketchpad and other programs help students develop multiple perspectives by introducing them to mathematical modeling and research. In addition to traditional forms of assessment, the Department uses assignments such as papers, journals, individual and group projects, oral presentations and defenses, and peer evaluations to expose students to a wide variety of mathematical research and discourse. The ultimate goal of the mathematics faculty is to help students recognize and appreciate the utility of mathematics as well as its intrinsic beauty.

## Math Department News

## Mathematics Requirement

Students are required to earn four yearlong course credits in mathematics. One of those courses must be Precalculus or Honors Precalculus.

# Math Courses

## Yearlong Courses

- Algebra
- Geometry
- Honors Geometry
- Precalculus
- Honors Precalculus
- Calculus
- AS Differential Calculus
- Advanced Study in Calculus AB
- Advanced Study in Calculus BC
- Advanced Study in Mathematical Economics
- Advanced Topics Tutorial in Mathematics

## Algebra

### Open to III & IV Form students

In this class, students move beyond the straightforward application of algorithms and are pushed to use abstract reasoning and creativity to solve problems they have not explicitly seen before. Students adopt the view that *math is thinking*. When thinkers do not see the answer to a problem, they want to make sense of the situation then consider as many possible solution strategies. Students enter the course with a variety of backgrounds in algebra and are equally challenged in applying and synthesizing their knowledge as they collaborate with peers in class and puzzle through solutions. Students will study a wide-range of topics, including modeling linear and quadratic equations, graphing and solving problems with absolute value and radical expressions, solving systems of equations, using inequalities to model scenarios, simplifying algebraic expression, solving shared-work problems. Students will also expand their resilience and communication skills, while solidifying their skills in algebra and making connections to geometry applications.

## Geometry

### Open to IV Form Students

### Prerequisite: Algebra

This course develops the skills required for more advanced mathematics, with an emphasis on the in-depth study of traditional topics of geometric proof, as well as the study of the Pythagorean Theorem, triangles, circles, quadrilaterals, coordinate geometry, polygons, optimization, parabolas and transformations. Students are expected to have a mastery of algebra and a facility with investigative and collaborative problem-solving approaches.

## Honors Geometry

### Open to III & IV Form students

### Prerequisite: Algebra or Placement Test

This course develops the skills required for more advanced mathematics, with an emphasis on the in-depth study of traditional topics of geometric proof, as well as the study of the Pythagorean Theorem, triangles, circles, coordinate geometry, polygons, optimization, parabolas, transformations, parametric equations and vectors. Students are expected to have a mastery of algebra and a facility with investigative and collaborative problem-solving approaches.

## Precalculus

### Prerequisite: Geometry or placement test

This course expands upon the skills and themes introduced in Geometry. While students consider the properties and applications of each of the major trigonometric function families in isolation, significant time is also dedicated to the study of function composition and transformations. Special emphasis is placed on using functions to model real-world phenomena.

## Honors Precalculus

### Prerequisites: Honors Geometry or placement test

This course expands upon the skills and themes introduced in Honors Geometry. A major theme of the course is to uncover laws of trigonometry by deploying the skills developed in geometry to study the properties of triangles. Students also study circles, three dimensional vectors, matrices, circular motion, quadrilaterals, exponential functions and parametric descriptions of curves.

## Calculus

### Prerequisite: Precalculus

This course is a study of the concepts and skills of calculus. An emphasis on the applications of calculus allows students the opportunity to investigate and collaborate on projects. While this course provides students with a sound understanding of calculus, it is not intended to prepare students for the Advanced Placement Calculus AB examination. Text: Hughes-Hallett et al., *Calculus*.

## AS Differential Calculus

### Prerequisite: Honors Precalculus

AS Differential Calculus begins with a review of topics in trigonometry, progresses to a study of a variety of topics drawn from discrete mathematics and analysis, and culminates in a comprehensive treatment of differential calculus and its applications. Students study the continuity and differentiability of functions, derivative rules, curvature, optimization, related rates, and the three-dimensional position, velocity and acceleration of particles. Text: Hughes-Hallett et al., *Calculus* and supplementary material.

## Advanced Study in Calculus AB

### Prerequisite: Precalculus

This course covers differential and integral calculus, with an emphasis on applications drawn from the physical, biological and social sciences. After completing this course, students may elect to review independently for and take the Advanced Placement Calculus AB examination. Placement is determined by the department. Text: Hughes-Hallett et al., *Calculus*.

## Advanced Study in Calculus BC

### Prerequisites: As Differential calculus or calculus AB

This course continues the study of calculus begun in AS Differential Calculus. Students study integral calculus and its applications, as well as polynomial series approximations. After completing this course, students may elect to review independently for and take the Advanced Placement Calculus BC examination. Placement is determined by the department. Text: Hughes-Hallett et al., *Calculus*

## Advanced Study in Mathematical Economics

### Open to V & VI Form students

### Prerequisite: Precalculus or higher

### Yearlong elective

A basic understanding of economics is fast becoming a requirement for effective citizenship in a modern democracy. This course aims to provide students the necessary tools to understand and participate in discussions of economic policy. In any authentic economics curriculum students study decision-making: they learn to recognize the myriad constraints in life—not only those of budget and how to spend one’s money, but also those of time and how to spend one’s life—and then study how to maximize various goods in the face of those constraints. This is not a course in finance. Stocks and bonds are largely just an example of a particular marketplace. Their role in macroeconomic policy is important to understand, but the real focus of the course will be the study of scarcity in general. Heavy emphasis will be placed on the application of mathematical techniques drawn from algebra, calculus and statistics. Some new techniques will be introduced, but much of the focus will be on the application of previously studied concepts.

## Advanced Topics Tutorial in Mathematics

### Open to VI Form Students

### Prerequisites: AS Calculus BC

Advanced Topics Tutorial in Mathematics is a course designed for students who have completed Advanced Studies in Calculus BC. In alternating years, the course is (i) a year-long treatment of Multivariable Calculus or (ii) a tutorial that investigates different topics of advanced mathematics taught by a different teacher in the department. Recent topics have included cryptography, recreational mathematics, discrete logic, and proving Euclidean geometry from scratch. Topics can vary each year based on student and faculty interest.

## Semester-long Electives

- Advanced Study in Statistics
- Introduction to Computer Science
- Introduction to Data Science
- Object Oriented Programming in Java
- MicroController Programming and Robotics
- App Development in Swift

## Advanced Study in Statistics

### Semester-long half-credit course

### Open to v & VI Form students

### Prerequisites: Precalculus

This course is a non-calculus-based introduction to statistics that focuses on four major themes: exploring and analyzing data, planning studies and collecting data, mathematical modeling, and testing hypotheses through statistical inference. After completing this course, students may elect to review independently for and take the Advanced Placement Statistics examination. Text: Bock, Velleman, DeVeau,* Stats: Modeling the World.*

## Introduction to Computer Science

### Open to all Forms

An introductory course aimed at presenting the mechanisms that power the digital world by initiating students in the problem solving skills associated with designing computer code. This course is suitable for students with no programming background as well as those with familiarity and experience. Discussion and writing topics include history and functionality of the internet, ethics of digital citizenship, and current concepts pulled from recent headlines. Classroom activities balance between collaborative coding projects and discussions and debates on current events in the digital world.

## Introduction to Data Science

### Open to IV, V, VI Form students

Ninety percent of all the data in the world was created in the past two years, and the rate at which we are creating new data is only increasing. As the world adds more information of every possible variety at an ever-increasing rate, how can we possibly keep up? This course will teach you the tools of data science, a new and growing field that uses powerful computing tools to collect, manipulate, analyze and visualize data, grounded in mathematics. We will focus our efforts on using data to explore compelling and intriguing questions drawn from current political topics, current trends in economics and science, popular culture, and student interest. We will study statistical and mathematical modeling, and learn how we can analyze a dataset to make powerful predictions. This class will culminate in a project where students will use the tools they’ve learned to tell a story using data about a question of interest to the student (not unlike stories on The Upshot or FiveThirtyEight). This class will also spend a significant amount of time considering the ethics of “big data”—who owns all of the data you’re generating when you carry a smartphone around with you every day, and what exactly can a company do with that “anonymous” data? What are the promises and perils of being able to sequence your genome for less than the cost of a new pair of sneakers, and how will you be able to comprehend and safeguard that data?

## Object Oriented Programming in Java

### Open to IV, V, VI Form students

### Prerequisites: Intro to Computer Science or instructor permission

This course refines the student's programming ability while introducing the concept of object-oriented programming. Increasingly, larger and more complex projects bolster the student's ability to craft working components while simultaneously promote project and time management skills as well as instill confidence in the student's developing ability. This course roughly follows the AP Computer Science A syllabus with tangents to allow for further exploration in project based learning. Students completing this course will have basic preparation to take the AP test.

## MicroController Programming and Robotics

### Open to IV, V, VI Form students

### Prerequisite: Intro to Computer Science or instructor permission

This course develops a student's ability to program microcontrollers and other embedded devices. This specific type of programming is essential for developing products and devices that physically interact with the environment through sensors, actuators, and information display. Students will engage in electronic development skills including circuit design, implementation via breadboarding and soldering, and product deployment. As a final project, students will design and contribute a collaborative project build to aid the School community.

## App Development in Swift

### Open to IV, V, VI Form students

### Prerequisite: Intro to Computer Science or instructor permission

This course introduces students to the practice of software engineering by using design thinking and the agile methodology to develop iOS and macOS apps in Swift. In addition to learning the Swift programming language, and programming tools like XCode and GitHub, students will study event-driven programming, user interface design, using programming libraries, and data storage. Students will work in small teams to identify users within our community who have a need that could be solved with an app, and then work to iteratively design, implement, and refine their application using Agile Methodology. The goal of the course is for each student team to produce an app of lasting value for the School community.