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Mathematics/Computer Science

DEPARTMENT PHILOSOPHY

The Mathematics Department at Episcopal High School strives to offer each student both a challenge and an opportunity to succeed. Emphasis is placed on using applications of “real world” problems to provide a context for students to understand not only the traditional facts and techniques of mathematics, but also to develop the logical reasoning and problem-solving skills that will allow them to approach and solve unfamiliar problems throughout their lives. The Mathematics Department believes strongly that students should use technology, such as computers and graphing calculators, as problem-solving tools, and it encourages students to pursue the study of mathematics throughout all four years of high school.

REQUIREMENTS

A minimum of three credits is required in mathematics including successful completion of trigonometry, either as part of the full-year Algebra 2 with Trigonometry course or in a one-semester course (Algebra 3 with Trigonometry). A junior is required to take a full year of math and EHS strongly encourages students to take mathematics every semester. Seniors have several Advanced Placement math options.

OBJECTIVES

  • Create a positive attitude toward the study and learning of mathematics
  • Foster confidence, competence, and creativity in the learning and execution of mathematics, so that students can become independent self-learners
  • Expect mastery of identified course-specific skills in problem solving, algebraic manipulation, proof, and mathematical theory
  • Teach the mathematical skills necessary to support other academic disciplines
  • Provide students with frequent assessment and feedback so that faculty, students, and parents can get a good sense of a student’s progress at almost any time
  • Encourage department members to continue their study of mathematics and education through coursework, workshops, and conferences
  • Teach the "art of learning," including note taking, daily self-evaluation, test preparation, and using available resources to be a better learner of mathematics
  • Achieve consistency of content and depth across the mathematics curriculum through detailed course syllabi, course meetings, and common examinations, while honoring the individual strengths and styles of department members.
  • Advanced 3D Modeling and Robotic Programming

    This course covers basic and advanced 3D modeling, and an introduction to computer programming (Python) using robotic projects. This course uses hands-on projects to implement inquiry learning in which each student takes a series of projects from design to completion. The projects guide students through an exploration of computer science, mathematics, science and engineering. In addition, students have opportunities to gain skills and knowledge needed in the product development and manufacturing industry. (One-Half Credit)
  • Advanced Calculus AB

    This course prepares students to take the AP Exam. Students deal with limits and the basic material of differential and integral Calculus. First-year college course for those desiring more than the basic four years of math. By department permission. (One Credit)
  • Advanced Calculus BC

    This course is of greater breadth and depth than AB Calculus and is directed toward the BC level AP Examination. Students normally are selected from Honors Precalculus. This course prepares students to take the AP Exam. By department permission. (One Credit)
  • Advanced Computer Science

    This course, which uses the Java language, is designed to meet the requirements of the AP Exam. Students who have completed Algebra 2 are encouraged to take this course. By department permission. (One Credit)
  • Advanced Linear Algebra

    A continuation of AB/BC Calculus. Offered alternately with Multivariable Calculus. By department permission. (One Credit)
  • Advanced Multivariable/Vector Calculus

    A continuation of AB/BC Calculus. Topics may include linear algebra, multivariable calculus and differential equations. By department permission. (One Credit)
  • Advanced Projects in Computer Science

    This course gives students with some prior experience in technology an opportunity to dive deeper into programming, operating systems, and networking. Using the Python programming language and Raspberry Pi computers, students code their own projects in networking, databases, gaming, graphical user interfaces, gaming, and the web. Students interested in this course should have previously completed 3D Modeling and Robotic Programming, Advanced Computer Science, or have prior coding experience. (One-Half Credit)
  • Advanced Statistics

    This course is an introduction to the major concepts and tools for collecting, analyzing and drawing conclusions from data. The four broad conceptual themes are: exploring data, planning a study, anticipating patterns, and statistical inference. This course prepares students to take the AP Exam. Prerequisite: Honors Algebra 2/Trig or higher. By department permission. (One Credit)
  • Algebra 1

    This course introduces students to the axiomatic basis of elementary algebra, while at the same time developing reasoning skills and the ability to use algebra to solve problems, laying a foundation for knowledge needed in subsequent mathematics courses. An introduction to the use of spreadsheets is also provided. (One Credit)
  • Algebra 2 (Fall)

    This course continues the study of algebra and introduces reviewing concepts seen in Algebra 1. Topics include solving equations and inequalities (including absolute value), solving linear systems with a specific focus on linear programming, solving quadratic functions and matrices. (One-half credit)
  • Algebra 2 (spring)

    This course is the continuation of Algebra 2. Topics covered include a review of exponent rules, exponential, logarithmic, and rational functions. A study of probability will include the counting principle, permutations and combinations. (One-half Credit)
  • Algebra 2: Functions & Transformations

    This course is the continuation of Algebra 2 with the specific focus on how functions are transformed. Topics covered include a review of exponent rules, exponential, logarithmic, and rational functions. A study of probability will include the counting principle, permutations and combinations. A problem-based approach will be used to solve application problems. By department permission. (One-half Credit)
  • Calculus

    This course is an introduction to the techniques and applications of calculus. Students will study both differential and integral calculus and their applications, including problems in the area of business, physics, and geometry. The role of calculus as a tool for problem-solving is emphasized. This course is open to all students who have successfully completed Precalculus or Honors Precalculus. (One Credit)
  • Fundamentals of Precalculus

    This course begins with a review of linear relations and functions before continuing with the theory of equations, trigonometry and its applications, and exponential and logarithmic functions. The second semester emphasizes the topics of matrices, sequences and series, and probability and statistics. Emphasis is placed on fundamentals and problem solving. (One Credit)
  • Geometry

    This course familiarizes students with the properties of two- and three-dimensional figures and provides a foundation for presenting mathematical arguments and logical reasoning. Students work with computers and software—specifically Geometer's Sketchpad. (One Credit)
  • GOA: Computer Science 2: Game Design & Development

    In this course, students design and develop games through hands-on practice. Comprised of a series of “game jams,” the course asks students to solve problems and create content, developing the design and technical skills necessary to build their own games. The first month of the course is dedicated to understanding game design through game designer Jesse Schell’s “lenses”: different ways of looking at the same problem and answering questions that provide direction and refinement of a game’s theme and structure. During this time, students also learn how to use Unity, the professional game development tool they use throughout the class. They become familiar with the methodologies of constructing a game using such assets as graphics, sounds, and effects, and controlling events and behavior within the game using the C# programming language. Throughout the remainder of the course, students will work in teams to brainstorm and develop new games in response to a theme or challenge. Students will develop their skills in communication, project- and time- management, and creative problem-solving while focusing on different aspects of asset creation, design, and coding. Prerequisite: Computer Science I: Computational Thinking or its equivalent.
  • GOA: Cybersecurity

    Cyber criminals leverage technology and human behavior to attack our online security. This course explores the fundamentals of and vulnerabilities in the design of computers, networks, and the internet. Course content includes the basics of computer components, connectivity, virtualization, and hardening. Students will learn about network design, Domain Name Services, and TCP/IP. They will understand switching, routing and access control for internet devices, and how denial of service, spoofing and flood attacks work. Basic programming introduced in the course will inform hashing strategies, while an introduction to ciphers and cryptography will show how shared-key encryption works for HTTPS and TLS traffic. Students will explore the fundamentals of data forensics and incident response protocols. The course includes analysis of current threats and best practice modelling for cyber defense, including password complexity, security, management, breach analysis, and hash cracking. Computational thinking and programming skills developed in this course will help students solve a variety of cyber security issues. There is no computer science prerequisite for this course, though students with some background will certainly find avenues to flex their knowledge in this course. (One-half credit)
  • GOA: Data Visualization

    Through today's fog of overwhelming data, visualizations provide meaning. This course trains students to collect, organize, interpret, and communicate massive amounts of information. Students will begin wrangling data into spreadsheets, learning the basic ways professionals translate information into comprehensible formats. They will explore charts, distinguishing between effective and misleading visualizations. Employing principles from information graphics, graphic design, visual art, and cognitive science, students will then create their own stunning and informative visualizations using Datawrapper, Tableau Public and/or Python. From spreadsheets to graphics, students in this course will practice the crucial skills of using data to decide, inform, and convince. There is no computer science, math or statistics prerequisite for this course, though students with backgrounds in those areas will certainly find avenues to flex their knowledge in this course. (One-Half Credit)
  • GOA: Game Theory

    Do you play games? Do you ever wonder if you’re using “the right” strategy? What makes one strategy better than another? In this course, we explore a branch of mathematics known as game theory, which answers these questions and many more. Game theory has many applications as we face dilemmas and conflicts every day, most of which we can treat as mathematical games. We consider significant global events from fields like diplomacy, political science, anthropology, philosophy, economics, and popular culture. Specific topics include two-person zero-sum games, two person non-zero-sum games, sequential games, multiplayer games, linear optimization, and voting and power theory. (One-half credit)
  • GOA: iOS App Design

    Learn how to design and build apps for the iPhone and iPad and prepare to publish them in the App Store. Students will work much like a small startup: collaborating as a team, sharing designs, and learning to communicate with each other throughout the course. Students will learn the valuable skills of creativity, collaboration, and communication as they create something amazing, challenging, and worthwhile. Coding experience is NOT required and does not play a significant role in this course. Prerequisite: For this course, it is required that students have access to a computer running the most current Mac or Windows operating system. An iOS device that can run apps (iPhone or iPad) is also highly recommended. (One-half credit)
  • GOA: Number Theory

    Once thought of as the purest but least applicable part of mathematics, number theory is now by far the most commonly applied: every one of the millions of secure internet transmissions occurring each second is encrypted using ideas from number theory. This course covers the fundamentals of this classical, elegant, yet supremely relevant subject. It provides a foundation for further study of number theory, but even more, it develops the skills of mathematical reasoning and proof in a concrete and intuitive way and is necessary preparation for any future course in upper-level college mathematics or theoretical computer science. We progressively develop the tools needed to understand the RSA algorithm, the most common encryption scheme used worldwide. Along the way we invent some encryption schemes of our own and discover how to play games using number theory. We also get a taste of the history of the subject, which involves the most famous mathematicians from antiquity to the present day, and we see parts of the story of Fermat’s Last Theorem, a 350-year-old statement that was fully proven only twenty years ago. While most calculations will be simple enough to do by hand, we will sometimes use the computer to see how the fundamental ideas can be applied to the huge numbers needed for modern applications. Prerequisite: A strong background in precalculus and above, as well as a desire to do rigorous mathematics and proofs.
    (One-half credit)
  • Honors Algebra 2/Trig

    This course continues the study of algebra and introduces work with linear functions, exponential functions and logarithms, trigonometry, and matrices. This course employs a non-traditional, problem-based approach to a curriculum developed by Phillips Exeter Academy. By department permission. (One Credit)
  • Honors Geometry

    This course familiarizes students with the properties of two- and three-dimensional figures and provides a foundation for presenting mathematical arguments and logical reasoning. In addition, students work with trigonometry and vectors. This course employs a non-traditional, problem-based approach to a curriculum developed by Phillips Exeter Academy. By department permission. (One Credit)
  • Honors Precalculus

    This course studies the real and complex number systems and analysis of functions – linear, quadratic, polynomial, rational, circular, trigonometric, exponential, logarithmic, logistic, and more. It introduces and reinforces the study of vectors in two and three dimensions, parametric functions, analytic geometry, and polar functions. It also provides an introduction to statistics via probability. The course concludes with an introduction to calculus through the lenses of optimization, asymptotic behavior, and limits. By department permission.(One Credit)
  • Introduction to Statistics

    This elective course explores how to collect, display, interpret and analyze statistical data. The course centers around applying statistical methods to real world, current data sets. In addition to traditional assessments, students will be expected to collaborate with their peers to design their own surveys, collect and analyze the results, and present their findings. Other topics covered include probability, displaying sampling distributions, confidence intervals, and testing hypotheses. Simulation software packages and other technology will be used to assist when investigating large data sets. This course is open to all students who have completed Algebra 3/Trig, Precalculus or Honors Precalculus. (One Credit).
  • Precalculus

    This course is designed to bring the connection between Algebra and Calculus. Topics and concepts learned in prior Algebra classes are reinforced, while additional techniques are introduced to enhance the depth of study. Topics include exponential and logarithmic functions, probability, conic Sections, as well as an immersion in the concepts of Trigonometry that include right angle trigonometry, solving and graphing functions, and identities. (One credit)

Department Faculty