Mathematics

Academic advisors also use this course map to guide students in designing their most appropriate and desired selection of mathematics coursework throughout their time at St. George's.

In 1623, Galileo wrote, “The universe, that vast book which stands forever open before our eyes, cannot be read until we have learned the language and we have become familiar with the characters in which it is written. It is written in mathematical language, without which it is humanly impossible to comprehend a single word.”

The importance of mathematics in the fields of science and technology is readily apparent, but mathematics also plays an integral role in fields as diverse as psychology, economics, medicine and linguistics. Accordingly, it is important for the secondary school student to become well-grounded in mathematics. Constant attention is focused on helping students become critical thinkers in all areas of life through problem solving, decision making and analyzing. Emphasis is placed on understanding mathematics as a language with its own vocabulary, symbols and syntax. Students are encouraged to look for multiple solutions to individual problems and to explain their calculations orally. The Mathematics Department offers a rigorous program with a range of courses to meet the needs of individual students. Requirements for the school diploma include a year of Algebra I, Geometry, Algebra II and Precalculus. Beyond this basic requirement, students may elect to take courses in Calculus, Probability and Statistics, AB and BC Calculus and Multivariable Calculus.

Students are given the opportunity to progress in mathematics at a rate appropriate to their aptitude. An honors program is available for those with outstanding interests and talents. Those students who have traditionally found mathematics difficult may elect to take courses in which additional time and support are provided to facilitate comprehension.

Students are encouraged to join the school’s Math Team, which participates in mathematics contests at the local, state, regional and national levels. All department members belong to the National Council of Teachers of Mathematics.

Available Courses:

Algebra I
MATH 100
Full-Year

Open to third-formers

This three-trimester course in algebra is designed to enhance the student’s understanding of the properties and operations associated with real numbers. The course content includes the study of the real number system, linear functions and their graphs, solving linear systems and inequalities, quadratic functions, exponents, radicals, polynomial functions, factoring, and applied problem solving. Students are required to have a College-Board-approved graphing calculator. If they receive the approval of the Mathematics Department, students who take Algebra I in the third form may take both Geometry and Algebra II in their fourth-form year.

Geometry
(Prerequisite Algebra I)
MATH 210
Full-Year

Open to third- and fourth-formers; Prerequisite Algebra I

This three-trimester course in Euclidean Geometry investigates the definitions, postulates and theorems of two and three-dimensional figures. During the first trimester, study will focus on the building blocks of geometry — the various shapes and their properties, angles, parallel lines, as well as using geometric software to investigate patterns and make conjectures. Writing mathematical proofs will also be introduced. The second trimester will include advanced study of polygons, circles and area formulas. The final trimester includes the study of solid geometry, similarity and an introduction to trigonometry. The concepts of logical reasoning, problem solving skills, as well as organizational skills will be stressed throughout the year.

Honors Geometry
(Prerequisite Algebra I)
MATH 220/H
Full-Year

Open by invitation to third- and fourth-formers; Prerequisite Algebra I

This three-trimester honors course includes all of the elements of Math 210, but has a limited number of seats available, requires more and deeper preparation by students and advances through topics at a faster pace. Students who wish to enroll in the honors section should express that desire on their Course Planning Worksheets, and indicate Math 210 as an alternate. Students are enrolled based on a stated request, demonstrated motivation to tackle the course’s increased demands, achievement in other mathematics courses and standardized test scores where applicable.

Algebra II Introduction
(Prerequisite Geometry)
MATH 300
Full-Year

Open by invitation to fourth- and fifth-formers; Prerequisite Geometry

This full-year course builds on key components of Algebra I and Geometry by presenting the fundamental concepts necessary to preparation for Precalculus. Students review the real number system, linear functions and their graphs, quadratics, exponents and polynomial functions, factoring and applied problem solving. Students will also encounter new material in the graphing of polynomial functions; exponential and logarithmic functions, and the complex number system. Use of College Board-approved graphing calculators is required. Students will be enrolled based on a stated request and achievement in other mathematics courses.

Algebra II
(Prerequisite Geometry)
MATH 310
Full-Year

Open to third-, fourth- and fifth-formers; Prerequisite Geometry

In this second-year algebra course, students review and expand the study of real numbers begun in Algebra I. Students learn how to solve polynomial equations of increasing complexity and to apply their solutions to “real world” situations. New topics explored in Algebra II include graphing polynomial functions, exponential, logarithmic, and rational functions and the complex number system. Students enhance their understanding of the important features of College Board-approved graphing calculators. 

Honors Algebra II
(Prerequisite Geometry)
MATH 320/H
Full-Year

Open by invitation to third-, fourth- and fifth-formers; Prerequisite Geometry

This three-trimester honors course includes all of the elements of Math 310, but has a limited number of seats available, requires more and deeper preparation by students and advances through topics at a faster pace. An honors section of Algebra II is offered to advanced students which covers conic sections, counting principles and probability and sequences and series as time permits. Students who wish to enroll in the honors section should express that desire on their Course Planning Worksheets, and indicate Math 310 as an alternate. Students are enrolled based on a stated request, demonstrated motivation to tackle the course’s increased demands, achievement in other mathematics courses and standardized test scores where applicable.

Precalculus Introduction
(Prerequisite Algebra II)
MATH 400
Full-Year

Open by invitation to fifth- and sixth-formers; Prerequisite Algebra II

This course unifies topics previously studied in algebra and geometry and provides the foundation needed to support future coursework in calculus, discrete mathematics and statistics. During the first trimester students will study trigonometric functions, their graphs, inverses and applications. The second trimester will synthesize trigonometric functions with a review of linear, quadratic, polynomial, rational, exponential and logarithmic functions through the application of regression analysis. The final trimester will be devoted to the study of some advanced topics in precalculus. College Board- approved graphing calculators are required for this course. Students interested in taking Math 400 should indicate this on their Course Planning Worksheets and list Math 410 as an alternate. Students will be enrolled based on a stated request and achievement in other mathematics courses. Completion of 400, 410 or 420 satisfies the requirement for graduation from St. George’s School.

Precalculus
(Prerequisite Algebra II or Algebra II Honors)
MATH 410
Full-Year

Open to fifth- and sixth-formers; Prerequisite Algebra II and Algebra II Honors

Like Math 400, this course unifies topics previously studied in algebra and geometry and provides the foundation needed to support future coursework in calculus, discrete mathematics and statistics, but does so at a faster pace. During the first trimester, students will review linear, quadratic, polynomial, rational, exponential and logarithmic functions through the application of regression analysis. During the second trimester, students will study trigonometric functions, their graphs, inverses and applications. The final trimester will be devoted to the study of advanced topics in precalculus to include a focus on sequences and series, probability, topics in analytic geometry and limits. College Board-approved graphing calculators are required for this course. Completion of 400, 410 or 420 satisfies the mathematics requirement for graduation from St. George’s School.

Precalculus Honors
(Prerequisite Algebra II Honors)
MATH 420/H
Full-Year

Open by invitation to fifth- and sixth formers; Prerequisite Algebra II

This three-trimester honors course includes all of the elements of Math 410, but has a limited number of seats available, requires and more and deeper preparation by students and advances through topics at a faster pace. Like Math 400 and 410, this course unifies topics previously studied in algebra and geometry and provides the foundation needed to support future coursework in calculus, discrete mathematics and statistics. (See further details under Math 400 or 410.) College Board-approved graphing calculators are required for this course. Students who wish to enroll in the honors section should express that desire on their Course Planning Worksheets, and indicate Math 410 as an alternate. Students are enrolled based on a stated request, demonstrated motivation to tackle the course’s increased demands, achievement in other mathematics courses and standardized tests scores where applicable. Completion of 400, 410 or 420 satisfies the mathematics requirement for graduation from St. George’s School.

Design Science
(Prerequisites two trimesters Geometry, Visual Foundations)
MATH 433 (Also offered as Art 433)
Trimester: Spring

Open to all forms; Prerequisites two trimesters Geometry, Visual Foundations

This one-trimester course is intended to provide students with hands-on experience in designing, creating and analyzing two- and three-dimensional geometric structures, sculptures and models using a variety of media (including paper, wood, metal, ceramics, etc.). Students successfully completing this course would receive one trimester credit in Arts and one trimester credit in Mathematics. Possible topics and projects include tessellations, polyhedra, Platonic solids, Archimedean solids and the mathematics and design of commercial packaging. Class periods for this course would include lecture/demonstration and hands-on labs. One or two field trips to local manufacturing facilities and art museums would be included. Each student will maintain a daily journal containing research assignments, design sketches, and potential ideas relating to class projects. The resources of the Arts Center, the Welding Lab and the Fab Lab would be utilized for the hands-on part of this course. Offered spring only.

Probability and Statistics
(Prerequisite Precalculus Introduction)
MATH 500
Full-Year

Open to fifth- and sixth formers; Prerequisite Precalculus Introduction

In the world today, more and more decisions affecting the course of our lives are based, at least in part, on the results of statistical analysis. In this yearlong course, students are exposed to four broad conceptual themes: exploring and describing data, planning a statistical study, using probability to anticipate patterns in data and statistical inference. This course focuses on the statistical thinking behind data gathering and interpretation and helps students become more discerning consumers of statistics, teaching them to look closely at what numbers from surveys, election polls and medical studies really show.

Advanced Statistics
(Prerequisite Precalculus)
MATH 510/A
Full-Year

Open by invitation to fifth- and sixth-formers; Prerequisite Precalculus

The purpose of this yearlong course is to introduce students to the major concepts and tools for collecting, analyzing and drawing conclusions from data. Students are exposed to four broad conceptual themes: exploring and describing data, planning a statistical study, using probability to anticipate patterns in data and statistical inference. Specific topics to be covered include descriptive statistics, data collection, linear regression, experimental design, hypothesis testing, confidence intervals and tests of significance. A College Board-approved graphing calculator is used extensively, and students also are exposed to statistical software packages especially reading outputs from Mini-Tab.

Calculus
MATH 600
Full-Year

Open to sixth-formers, and by invitation to fifth-formers, Prerequisite Precalculus

Calculus brings together the information and skills learned in previous courses and applies that knowledge to solve a wide variety of different problems. The three-trimester Calculus course begins with the study of limits, advances through differentiation and concludes with integration. 

Advanced AB Calculus
MATH 610/A
Full-Year

Open by invitation to fifth- and sixth-formers

Calculus AB is a three-trimester course in the calculus of a single variable. Each course prepares students for successful completion of the Advanced Placement exam in the spring. AB and BC Calculus contain common topics but the BC course covers additional topics such as parametric equations, vectors and Taylor series. In both courses, students are exposed to concepts, problems and solutions in graphical, numerical, analytical and verbal form.

Advanced BC Calculus
MATH 620/A
Full-Year

Open by invitation to fifth- and sixth-formers

Calculus BC is an extended version of the three-trimester AB course. Each course prepares students for successful completion of the Advanced Placement Exam in the spring. AB and BC Calculus contain common topics but the BC course covers additional topics such as parametric equations, vectors and Taylor series. In both courses, students are exposed to concepts, problems, and solutions in graphical, numerical, analytical and verbal form.

Multi-Variable Calculus Honors
MATH 630/H
Full-Year

Open by invitation to fifth- and sixth-formers; Prerequisite AB or BC Calculus

This yearlong course is intended for students who successfully complete BC Calculus before their senior year. Exceptionally strong AB Calculus students will also be considered. This course extends the fundamental concepts of calculus to functions of more than one variable. Vectors and curves in two or more dimensions, double and triple integrals, line integrals, surface integrals, Stokes Theorem, and Green’s Theorem are among the topics covered. Students will make extensive use of appropriate software and online resources throughout the course.

Independent Study
(Prerequisite Completion of Advanced Calculus (AB or BC)
MATH 611, MATH 612, MATH 613
Trimester: Fall, Winter, Spring

Prerequisite Advanced Calculus (AB or BC)

For those students who have completed Advanced Calculus (AB or BC) and are looking to continue their math studies there is the option to take one or more trimester-long Independent Study courses. These are offered in a variety of topics and recent courses have included Game Theory, Differential Equations and Linear Algebra. These classes afford the opportunity for the student to pursue in-depth study of the material while working one-on-one with a member of the Math Department. Instructions for proposals for Independent Study appear under “Course Planning” and must be completed and received by the Academic Office by the midpoint of the trimester prior to study.

Humans & Computers
COMPUTER SCIENCE 341, 342, 343
Trimester: Fall, Winter, Spring

Open to fourth-, fifth- and sixth-formers

Cyberterrorism, human-computer interaction, communications protocols, artificial intelligence, data driven decisions: What does it all mean? This one-trimester course explores the latest computer topics and technologies. This is much more than an introduction to computers course; we explore basic computing, problem solving and ethics.

Basic computing is an introduction to computers today. Students explore the human computer interaction, including computer input, output, memory, storage, processing, software and the operating system. The “Pictures Do Lie” section introduces students to photo manipulation and image processing software to create unbelievable images. Images are then combined with text, music and animation using presentation software.

Problem solving introduces students to basic problem definition, algorithm creation and solution finding. Using a simple programming language, students will learn how to employ sequential, selection and repetitive programming statement to solve problems. Spreadsheets will then be used to teach students how to analyze and manipulate data in support of decision-making.

The final theme will be interspersed throughout the semester: computer ethics and morality. Discussion topics include: intellectual property, privacy, piracy, hackers, viruses and security. Students will research and draft position papers on these various topics. This is a stand-alone course with no prerequisites that is designed to whet a student’s appetite for computers and technology.

Robotics
COMPUTER SCIENCE 351, 352, 353
Trimester: Fall, Winter, Spring

Open to fourth-, fifth- and sixth-formers

This introductory project-based course is designed for any student who wants to learn how to approach and solve problems using computer programs. No prior programming experience is necessary. Students learn how to create digital and physical robots that interact with the world they live in. They begin the course by mastering Jeroo, a small object-oriented programming language that allows them to immediately see their digital robot executing commands on an emulator. The next step is developing physical robots that have touch, sight, sound and rotational sensors. These robots are programmed using the NXT graphical software and then the more powerful NXC programming language.

Coding, Java
COMPUTER SCIENCE 403
Trimester: Fall, Winter, Spring

Open to fifth- and sixth-formers, and by invitation to fourth-formers

This coding course uses the Java programming language to understand computer science and its applications in various fields. Building on algorithms within the language, and of students’ own creation, the course is designed to develop a basic understanding of Java as well as constructs of any programming language, to encourage enthusiasm in the field of computer science and to build confidence in creative problem-solving. Through collaborative projects, students produce tangible solutions to problems, and build practical applications through St. George’s Fab Lab. The course uses a range of online resources and has been designed for SG students by a team of teachers and mathematicians on the Hilltop.

A Coeducational Boarding and Day School for Grades 9 Through 12
St. George's School
372 Purgatory Road Middletown, Rhode Island 02842
401-847-7565
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