● Mathematics

MATHEMATICS

The mathematics program is designed to fulfill these goals: ● To develop in students an appreciation for the essential character of mathematics as an intellectual discipline ● To foster development of logical reasoning skills, both inductive and deductive, and the ability to use these skills in general problem solving tasks beyond the mathematics classroom. ● To give students a mathematical foundation that is sufficient for all levels of further study ● To help students master technical skills that will be needed in their future studies

Moses Brown offers up to three levels of full year courses. All students are placed in a level based on the recommendation of their current math teacher. Students are placed into AP courses based on the recommendation of the department.

All upper school math courses require a TI-83 or TI-84 (or equivalent) graphing calculator. Moses Brown does not provide calculators to students.

Yearlong Courses (2 credits)

Algebra 1 Geometry, Accelerated Geometry, Honors Geometry Algebra 2, Accelerated Algebra 2, Honors Algebra 2 Precalculus, Accelerated Precalculus, Honors Precalculus Accelerated Calculus, AP Calculus AB, AP Calculus BC Multivariable Calculus* Linear Algebra/Differential Equations* Statistics in Action AP Statistics

Fall Semester Courses (1 credit)

Economics of Business** International Economics**

Spring Semester Courses (1 credit)

Problem Solving with Python Programming

*Note: Multivariable Calculus and LinearAlgebra/Differential Equations are offered on an alternating schedule. In the 2022-2023 school year, the department will offer Multivariable Calculus.

**Note: Economics of Business and International Economics are offered on an alternating schedule. In the 2022-2023 school year, the department will offer International Economics.

YEARLONG COURSES (2 credits)

ALGEBRA 1

This course reviews number systems and covers fundamental operations, including fractions, exponents, square roots, functions, solving linear and quadratic equations, polynomials, factoring, graphing, and general problem-solving skills. Students are placed in Algebra 1 based on grades and teacher recommendations.

GEOMETRY

This course studies traditional Euclidean geometry in two and three dimensions. Topics include lines and planes, congruency, polygons, similarity, Pythagorean relationships, circles, triangle trigonometry, area, and volume. The honors course will put increased emphasis on the concept of formal proof. Levels: Geometry, Accelerated Geometry, Honors Geometry Prerequisite: Algebra 1 and department permission

ALGEBRA 2

This course is a continuation of first year Algebra and emphasizes skill development and critical thinking. Topics include factoring and operations with rational, irrational and polynomial expressions, graphing of relations and various functions, solutions of linear and quadratic equations, inequalities and systems, rational and real exponents, logarithms, and rational functions. The honors course will include an introduction to circle trigonometry. Levels: Algebra 2, Accelerated Algebra 2, Honors Algebra 2 Prerequisite: Algebra 1 and department permission; (Geometry can be taken as a prerequisite or co-requisite with department permission).

PRECALCULUS

This course is an in-depth survey of the fundamental mathematical functions used to model real phenomena, including polynomial, rational, exponential and trigonometric functions and their applications. The course is designed to enhance inferential thinking skills. Students enrolling in Precalculus Honors and Accelerated can expect little to no review of linear and quadratic functions. In addition, Honors students can expect a faster pace that covers more material such as polar coordinates, math on the complex plane, sequences and series, and the derivative, as well as a more in-depth treatment of all function types. Facility with a TI-83 or TI-84 graphing calculator is required for this course. Levels: Precalculus, Accelerated Precalculus, Honors Precalculus Prerequisite: Algebra 2 and department permission

CALCULUS

The main topics covered in this course include limits, derivatives, and integrals. Students learn to compute derivatives of a variety of functions, and apply them to solve problems, including those involving optimization and motion. Students also learn methods of computing integrals as well as their applications. Accelerated Calculus begins with further development of selected Precalculus topics. Facility with a TI-83 or TI-84 graphing calculator is required for this course. Levels: Accelerated Calculus, AP Calculus AB, AP Calculus BC Prerequisite: Accelerated Precalculus or Honors Precalculus, and department permission

LINEAR ALGEBRA/DIFFERENTIAL EQUATIONS

This honors-level course will focus on linear algebra for one semester and differential equations for the other semester. The linear algebra portion of the course will take students from the concrete ideas to the more abstract ideas. Beginning with a review of matrix operations and solving linear systems and observing the solution sets, they will work towards the general idea of vector spaces, including eigenvalues and eigenvectors, and linear mappings. Once a base of theory is established students will look at popular applications of the subject including linear regression and graph theory. The differential equations portion of the course will build upon the work done in calculus on separable differential equations. Students will learn about ordinary differential equations and use this knowledge to solve a variety of types of differential equations and explore their applications through common modeling problems, including predator/prey models and circuit systems. Prerequisite: AP Calculus BC, AP Calculus AB with summer work

*This course is offered in alternating years with Multivariable Calculus. It will not be offered for the 2022 – 2023 school year.

MULTIVARIABLE CALCULUS

This honors-level course covers techniques of calculus in two and three dimensions. Topics may include, but are not limited to: vectors, parametric curves, partial derivatives and multiple integrals. Prerequisite: AP Calculus BC, AP Calculus AB with summer work

*This course is offered in alternating years with LinearAlgebra/Differential Equations. It will be offered for the 2022 – 2023 school year.

STATISTICS IN ACTION

In this year-long course, students will study descriptive statistics, research study design, basic probability, and inferential statistics. The first half of the course focuses on educating and empowering students to be critical consumers of statistical information who can create and interpret graphs and summary statistics in both qualitative and quantitative contexts.

The second half of the course gives students the opportunity to see statistics in action, allowing them to further their understanding of the statistical research process and its implications for greater insight into social issues. Students will apply their knowledge of statistics to address real-time questions that need to be explored at Moses Brown and across the state of RI. This course will allow students to further develop their sense of the power of statistics with a focus on engaged scholarship, through reciprocal collaborations between students and the community. Students will collect, organize, interpret and analyze real data and will share their findings with our school leadership or leaders of non-profit organizations in RI. Prerequisite: Algebra 2 or Precalculus.

AP STATISTICS

This course follows the curriculum for the Advanced Placement curriculum as established by the College Board. It is generally equivalent to a half year of college statistics. Major topics include exploratory data analysis, experimental design, probability, and statistical inference. All students will be prepared to take the optional AP Statistics exam. Technology used includes TI-84 calculators. Prerequisite: Honors Precalculus or Honors Algebra 2 OR Honors Geometry or Accelerated Precalculus with department permission

FALL SEMESTER COURSES (1 credit)

ECONOMICS OF BUSINESS (open to 11th and 12th graders only)

What will you eat today? What will you wear? What college will you go to? You make choices every single day. Economics is a social science that focuses on decision making by individuals, businesses, and countries. All of these groups are limited in terms of the types and amounts of resources (time, money, land, etc.) available to them. In this class, students will explore the art of making optimal choices by analyzing market data, participating in dynamic in-class simulations, exploring the stock market, and investigating case studies of actual companies. The class will culminate with the students being put in charge of virtual companies and competing and/or collaborating with each other across various markets. Prerequisite: Algebra 2

*This course is offered in alternating years with International Economics. It will not be offered for the 2022 – 2023 school year.

INTERNATIONAL ECONOMICS (open to 11th and 12th graders only)

Globalization has had a lasting impact on our world - but what keeps this fine global balance in order? This course begins with fundamental economic principles and works through major micro- & macroeconomic topics, including supply and demand, debt/deficits, economic growth, income distribution, and basic economic policy. Students then dive deep into international economics: balance of trade/payments, benefits and challenges of international trade, economic development & currency exchange. The final section of the course will address current events and challenges related to international economics. Students will use case studies to explore international negotiations, marketing strategies, free-trade agreements, policy making and corporate meeting dynamics. Students will be asked to complete a capstone for an international business, including designing a corporate strategy and public policy proposals. Prerequisite: Algebra 2

*This course is offered in alternating years with Economics of Business. It will be offered for the 2022 – 2023 school year.

SPRING SEMESTER COURSES (1 credit)

PROBLEM SOLVING WITH PYTHON PROGRAMMING (Open to 10th , 11th & 12th graders)

From using Monte Carlo simulation to predict sporting outcomes, to machine learning algorithms that can teach a computer to drive a car, it is abundantly clear that computers have completely changed the way we approach challenging tasks. In this semester-long course, students will learn to use the Python programming language to explore real world problems. Many problems that are difficult, tedious, or impossible to solve by hand can be made trivial with clever use of computer programming. No previous programming experience is necessary. Prerequisite: Algebra 2