# 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

A conversation with members of the Class of 2017 on their STEM experiences at St. Andrew's

Shridhar Singhania '18 on his math experiences at SAS

## Mathematics Requirement

Students are required to earn four yearlong course credits in mathematics. One of those courses must be Problem Solving in Algebra 2 **or** Honors Problem Solving in Algebra 2/Trigonometry.

# Math Courses

- Problem Solving in Algebra & Geometry
- Honors Problem Solving in Geometry & Algebra II
- Problem Solving in Geometry & Algebra II
- Honors Problem Solving Algebra II & Trigonometry
- Problem Solving in Precalculus & Trigonometry
- Honors Precalculus & Differential Calculus
- Calculus
- Advanced Study in Calculus AB
- Advanced Study in Calculus BC
- Advanced Study in Mathematical Economics
- Advanced Study in Statistics
- Advanced Study in Multivariable Calculus
- Advanced Topics Tutorial in Mathematics

## Problem Solving in Algebra & Geometry

### Open to III and IV Form students

This course introduces students to the problem-solving techniques used by mathematicians and employed throughout the St. Andrew’s math curriculum. 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. They learn that good mathematicians do not immediately see the answer to every problem but enjoy experimenting with possible solutions. The disciplines of algebra and geometry provide excellent vehicles to practice and hone the skills required for such an approach. Although students may enter the course with a variety of backgrounds in algebra and geometry, they are equally challenged in applying and synthesizing their knowledge as they collaborate with peers in class and puzzle through solutions. Students also develop resilience and good communication skills, while solidifying their skills in algebra and recognizing its connections to geometry.

## Honors Problem Solving in Geometry & Algebra II

### Open to III and IV Form students

This course develops the problem-solving skills required for advanced mathematics, with an emphasis on the in-depth study of traditional topics of geometry, such parametrics and vectors. Students explore the relationships between geometry and more advanced algebraic topics, including quadratics, transformations. Students are expected to have a mastery of basic algebra and a facility with the investigative and collaborative approach of problem solving. Placement is determined by the department.

## Problem Solving in Geometry & Algebra II

### Open to IV Form Students

### Prerequisite: Intro to Problem Solving in Algebra and Geometry

This course continues to develop the problem-solving skills introduced in Problem Solving in Algebra and Geometry with greater emphasis on traditional topics of geometry. Students explore the relationships between geometry and more advanced algebraic topics, including quadratics and transformations. Further topics are studied in depth, including parametrics and vectors. Students are expected to have a mastery of basic algebra and a facility with the investigative and collaborative approach of problem solving.

## Honors Problem Solving Algebra II & Trigonometry

### Open to IV and V Form Students

### Prerequisites: Honors Problem Solving in Geometry & Algebra II

This course covers all of the topics in Problem Solving in Geometry and Algebra 2, and adds a full treatment of trigonometry. 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. Text: Larson et al., *Algebra and Trigonometry*.

## Problem Solving in Precalculus & Trigonometry

### Open to V and VI Form students

### Prerequisite: Problem Solving in Geometry and Algebra II

This precalculus course reviews and expands on the study of functions introduced in Problem Solving in Geometry and Algebra 2. Special emphasis is placed on using functions to model real-world phenomena. Students also study bivariate data analysis and a full treatment of trigonometry. Text: Connally et al., *Functions Modeling Change: A Preparation for Calculus*.

## Honors Precalculus & Differential Calculus

### Open to V Form Students

### Prerequisite: Honors Problem Solving in Algebra II & Trigonometry

In the first half of the year, Honors Precalculus students review topics in trigonometry and study a variety of precalculus topics drawn from discrete mathematics and analysis. The second half of the course covers differential calculus and its applications to prepare students for Advanced Study in Calculus BC. Text: Hughes-Hallett et al., *Calculus* and supplementary material.

## Calculus

### Open to VI Form Students

### Prerequisites: Problem Solving in Precalculus & Trigonometry

This course is a study of the concepts and skills of differential and integral 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*.

## Advanced Study in Calculus AB

### Open to V and VI Form Students

### Prerequisites: Problem Solving in Precalculus & Trigonometry or Honors Problem Solving in Algebra II & Trigonometry

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. Text: Hughes-Hallett et al., *Calculus*.

## Advanced Study in Calculus BC

### Open to V and VI Form Students

### Prerequisites: Honors Precalculus & Differential Calculus

This course continues the study of calculus begun in the second half of Honors Precalculus. 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. Text: Hughes-Hallett et al., * Calculus*.

## Advanced Study in Mathematical Economics

### Open to V and VI Forms

### Corequisite: AS Calculus AB or AS Calculus BC

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 Study in Statistics

### Open to VI Form students

### Prerequisites: Problem Solving in Geometry & Algebra II

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.*

## Advanced Study in Multivariable Calculus

### Not Offered 2017-18 (will be incorporated into Advanced Topics Tutorial in Mathematics)

### Prerequisites: AS Calculus BC and a score of 5 on the AP Calculus BC exam

This course extends the ideas of single-variable calculus to functions of two or more variables, vector-valued functions and vector fields. Numerous applications taken from the physical, life and social sciences motivate the development of each topic. Additional topics chosen from differential equations and linear algebra are covered as time permits. Text: Larson, et al., *Calculus*.

## Advanced Topics Tutorial in Mathematics

### Open to VI Form Students

### Prerequisites: AS Calculus BC

Advanced Topics Tutorial in Mathematics has, in recent years, focused on an introduction to linear algebra. Matrices and their relationship to systems of linear equations are studied in detail. Special emphasis is given to the application of matrices to various disciplines, including economics, game theory, computer science, statistics, physics, and biology.