# Mathematics

The study of calculus provides the backdrop for the use of statistical measures,

derivations, rigorous proof, and real world applications.

Mathematics is a combination of science, language and art. The math department strongly believes that it is only through early discipline that creativity is possible. Students learn formulas, translate words into symbols, and finally graph the results. Introductory courses teach the fundamentals, enabling students to manipulate numbers and formulas with confidence. Intermediate courses reiterate previously learned concepts while building upon definitions and terminology. In the process, students develop models, turning data into equations, defining their meanings, and depicting them on graphs. From this a larger picture appears, one in which individual topics merge into a coherent whole. At the upper level, the study of calculus provides the backdrop for the use of statistical measures, derivations, rigorous proof, and real world applications.

## Math Courses

- First Year Algebra
- Geometry
- Second-Year Algebra
- Pre-Calculus
- Statistics
- Discrete Math
- Advanced Pre-Calculus
- Honors Advanced Pre-Calculus and Differential Calculus
- Calculus
- AP Statistics
- AP Calculus (AB)
- AP Calculus (BC)
- Multivariable Calculus
- Product Design Engineering: From CAD to Products/Prototypes Through 3D Printing
- Digital Design: Introduction to Digital Logic
- Computer Programming & Coding Through Apps
- Independent Study

## First Year Algebra

The first semester introduces the language of algebra and functions while emphasizing reading, writing, and evaluating algebraic expressions. In addition, it deals with the fundamental operations of polynomials, linear equations, and linear inequalities. The second semester covers linear systems, quadratic equations, factoring, fractional equations, radicals, and radical equations.

## Geometry

The first semester introduces students to the terms, definitions, postulates, and theorems that form the basis of Euclidean geometry. It also explores the notion of formal proofs. Topics covered include parallel lines, congruent triangles, similar triangles, right triangles, and polygons. The second semester covers right triangle trigonometry, oblique triangle trigonometry, circles, area of planar figures, surface areas and volumes of three-dimensional objects, and an introduction to vectors and/or matrices. In both semesters, students utilize Geometer Sketchpad. An honors section of this course is also offered.

## Second-Year Algebra

The first semester reviews, reinforces, and explores more deeply the concepts of a first-year algebra course. The concept of functions, particularly linear and quadratic functions, is more fully developed. The second semester explores the logarithmic, exponential, rational, irrational, and variation functions. The study of sequences, series, and probability completes the course. There is an emphasis on modeling realistic examples from life and using the full capabilities of the graphing calculator. An honors section of this course is also offered.

## Pre-Calculus

This is a two-semester course that serves as an introduction to the elements of Pre-Calculus. It is designed for students who have not been recommended for the Advanced Pre-Calculus course. It is also designed for those who may be interested in pursuing the non-Advanced Placement Calculus course or math electives during the following year. Topics include the study of polynomial, exponential, logarithmic and trigonometric functions. The graphing calculator is used extensively, and students create mathematical models to solve realistic problems. The syllabus also includes some preparation for the SAT subject tests.

## Statistics

Students develop the skills to collect, analyze and interpret data, as well as develop proficiency in the use of MS Excel. We are inundated by numbers that communicate powerful messages. As a citizen in today's society, one must be able to interpret the ‘real' story behind the numbers. Likewise, given the overwhelming amount of data available to us, we must be able to make sense of the data – to tell its story. This is not a math-intensive course, but rather a class focused on building analytic skills and writing stories about data. Students complete several projects, at least one of which is based on data of the student's own choosing.

## Discrete Math

This course provides an overview of the branch of mathematics commonly known as discrete mathematics. It is an applications based course and focuses on problem solving for common issues in contemporary society. Some of the topics included for study are election theory, fair division algorithms for estates, matrix applications, population growth models, graph theory, probability and others. Students work together on projects and develop their problem solving skills.

## Advanced Pre-Calculus

The first semester of this course continues the study begun in second year algebra of the modeling of linear, quadratic, logarithmic, exponential, and variation functions. Composite and inverse functions are also examined. The trigonometric and circular functions are also introduced in this course. The second semester studies trigonometric equations and identities; non-right triangle trigonometry; conic sections; complex numbers; polar numbers, equations and graphs; parametric equations and graphs; sequences and series; probability; and vectors.

## Honors Advanced Pre-Calculus and Differential Calculus

## Calculus

## AP Statistics

This year long course introduces students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. There are four themes in the AP Statistics course: exploring data, sampling and experimentation, anticipating patterns, and statistical inference. Students use technology, investigations, problem solving, and writing as they build conceptual understanding. All students are required to take the Advanced Placement examination.

## AP Calculus (AB)

This course follows closely the syllabus as outlined by the Advanced Placement program of The College Board. The first semester includes the topics of limits and derivatives with attention given to the concept of rate of change, optimization and graphing techniques. The second semester continues with work in the trigonometric, exponential and logarithmic functions. It also explores the concept of the integral and all of its applications including the fundamental theorem of calculus. Students need to have done honors-level work in Pre-Calculus and must have departmental permission to gain entrance to this course. All students are required to take the Advanced Placement examination.

## AP Calculus (BC)

This course continues the study of calculus begun in the second semester of Honors Advanced Pre-Calculus and Differential Calculus. After completing the course work as defined in AP Calculus (AB), students proceed to the more advanced topics for the Advanced Placement BC examination. These topics include infinite series, Taylor series, differential equations, delta-epsilon proofs, vector analysis, length of curves, surface area, advanced integration techniques, and parametric functions.

## Multivariable Calculus

The first semester of this full-year course includes vector algebra and geometry, cylindrical and spherical coordinates, three-dimensional surfaces, vector functions, velocity and acceleration, speed, tangent and normal vectors, arc length and curvature. The second semester covers functions of several variables, partial differentiation, grad, div, curl, tangent plane, normal line, level curves/surfaces, extrema and Lagrange's method, multiple integrals, change of variables, Jacobian applications, vector analysis, and more complex differential equations.

## Product Design Engineering: From CAD to Products/Prototypes Through 3D Printing

Students have a hands-on introduction to the product design process from conceptualization to prototype construction through 3D printer and testing. Students learn many skills including engineering graphics communications, technical sketching, and CAD (Computer-Aided Design. Students work in groups and learn to function effectively in a team.

## Digital Design: Introduction to Digital Logic

Students have a hands-on introduction to the principles and practices of digital design, one of the first core courses in the discipline of electrical and computer engineering in college. Students study topics such as analog vs. digital, different number systems, Boolean algebra, transistor network design, combinational circuits, sequential circuits and more. Design methodology using both discrete components (using breadboard) and hardware description languages (using FPGA) is implemented in the laboratory portion of the course. (Not offered in 2017-2018).

## Computer Programming & Coding Through Apps

Students are introduced to programming with creating an app in mind, either iOS or Android. Students explore simple coding through their TI calculators and transition to learning MIT’s AppInventor, a GUI-based coding. After gaining some experience in simple programming, students learn Java or Objective-C and eventually create apps starting with classic games such as Tic-Tac-Toe or Flappy Bird.