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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 not only to understand 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. 

REQUIREMENTS

A minimum of three credits and successful completion of any Precalculus course is required in mathematics. A junior is required to take a full year of math and EHS strongly encourages students to take mathematics every semester during their time at Episcopal. 

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.

  • Adv 3D Modeling, Computer Aided Design & Manufacturing

    Coursework will cover introductory and advanced 3D modeling, introduction to simulation, manufacturing design principles, and project management. This course uses the open-source modeling software Autodesk Fusion 360 to create multifaceted designs. Students will explore real-world applications to devise models from an initial design to a final physical product. The projects will guide students through an exploration of computer science, mathematics, science, and engineering. Sample projects include developing mechanical components, creating full-scale blueprints of a modular house, and analyzing production output data to optimize efficiency. In addition, students will be given opportunities to gain skills and knowledge needed in the product development and manufacturing industry. Corequisite: Precalculus or higher. (One-half Credit)

  • Adv Calculus AB

    This course mirrors a college-level Calculus course that covers limit, differential, and integral calculus. A strong understanding of algebraic skills and Precalculus functions is expected and needed to find success. Students will need to apply skills and concepts learned in various ways. All topics in this course fall under the AP Calculus AB curriculum, though additional study and preparation are advised for those wishing to take the AP exam. Familiarity with the following topics is expected: solving quadratic equations by factoring, identifying parent functions & their properties, identifying & solving polynomial, logarithmic, exponential, rational, & radical equations, familiarity with basic trigonometry & physics. Prerequisite: Precalculus or Honors Precalculus. Department Permission Required. (One Credit)

  • Adv Calculus BC

    This course mirrors a college-level Calculus course that covers limit, differential, integral polar, parametric, and vector calculus, as well as sequences and series. This course has greater breadth, pace, and depth than AB Calculus. Students are expected to apply skills and concepts learned in various novel and challenging ways throughout the course. This course prepares students to take the AP Calculus BC Exam. Familiarity with the following topics is expected: solving quadratic equations by factoring, identifying parent functions & their properties, identifying & solving polynomial, logarithmic, exponential, rational, & radical equations, familiarity with basic trigonometry & physics. Prerequisite: Honors Precalculus. Department permission required (One Credit)

  • Adv 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)

  • Adv Linear Algebra

    An undergraduate-level exploration of topics in Linear Algebra, including matrix Algebra, vector spaces, linear transformations, determinants, eigenvectors, and  orthogonality. Students should expect both traditional summative assessments as well as collaborative problem sets and projects exploring applications in Calculus, statistics, probability, and computer science. Students will also develop rudimentary programming skills using MatLab. This course is designed for students who have completed single variable Calculus and are excited to pursue challenging higher level topics in mathematics. It is appropriate for students interested in majoring in math, engineering, or computer science. Familiarity with the following topics is expected: derivative Calculus, integration, Taylor series, and basic vector operations. Prerequisite: Advanced Calculus AB/BC. By department permission. (One Credit)

  • Adv Multivariable/Vector Calculus

    An undergraduate-level exploration of topics in Multivariable Calculus, including multivariable functions, vectors and vector fields, differentiation and integration in multiple variables, line integrals, flux, curl, and Stokes’ Theorem. Students should expect both traditional summative assessments and collaborative problem sets and projects. This course is designed for students who have completed single variable Calculus and are excited to pursue challenging higher level topics in mathematics. It is appropriate for students interested in majoring in math, engineering, or computer science. Familiarity with the following topics is expected: derivative Calculus, integration, Taylor series, and basic vector operations. Prerequisite: Advanced Calculus AB/BC, Department permission required. (One Credit)

  • Adv Statistics

    This course is an introduction to the major concepts of a college-level introductory course in statistics. Students will be expected to select methods for collecting and/or analyzing data for statistical inference, describe patterns, trends, associations, and relationships in data, explore random phenomena using probability and simulation, and develop an explanation or justify a conclusion using evidence from data, definitions, or statistical inference. Units include one and two-variable statistics, collecting data, probability and sampling distributions, and statistical inference for categorical and quantitative data. This course prepares students to take the AP Statistics Exam. Prerequisite: Honors Algebra 2, Precalculus, or Honors Precalculus, Department permission required. (One Credit)

  • Advanced Linear Algebra

    An undergraduate-level exploration of topics in Linear Algebra, including matrix Algebra, vector spaces, linear transformations, determinants, eigenvectors, and orthogonality. Students should expect both traditional summative assessments as well as collaborative problem sets and projects exploring applications in Calculus, statistics, probability, and computer science. Students will also develop rudimentary programming skills using MatLab. This course is designed for students who have completed single variable Calculus and are excited to pursue challenging higher level topics in mathematics. It is appropriate for students interested in majoring in math, engineering, or computer science. Familiarity with the following topics is expected: Derivative Calculus, integration, Taylor series, and basic vector operations. (One Credit)

  • Algebra 1

    This course introduces students to the essential concepts of Algebra as they develop reasoning and problem-solving skills. Major topics will include Solving equations, inequalities, and systems of equations; the fundamentals of exponents, radicals, and factoring; graphing and understanding linear and quadratic functions. This course will also emphasize the skills necessary to be successful in any math classroom. Students will be encouraged to develop the initiative necessary to work through challenging problems individually and cooperatively, making appropriate use of resources. (One Credit)

  • Algebra 2

    This course continues the study of algebra, reviews concepts seen in Algebra 1, and serves as a natural extension of the topics covered in Algebra 1. The course prepares students to complete Fundamentals of Precalculus successfully. Topics include proportions, factoring, solving equations and inequalities (including absolute values), solving linear systems with graphing, substitution, elimination, and linear programming. This course’s major focus is solving linear and quadratic functions and equations, along with basic exponential and logarithmic functions and equations. A study of rational and radical functions will also be introduced. Familiarity with the following topics is expected: identifying & graphing linear equations, solving linear equations, identifying & solving basic systems of equations, solving inequalities, simplifying expressions, and using ratios & proportions. Prerequisite: Algebra 1, Geometry. (One Credit)

  • Algebra 2/Trig

    Designed for students with one or more years of algebra and one full year of geometry, this course continues the study of algebra and reviews work with linear functions and systems. The course introduces various function families, including absolute value, quadratics, exponential, logarithmic, radical, and rational functions. The second semester of the course will introduce the fundamentals of trigonometry and will aim to prepare students for Precalculus. Familiarity with the following topics is expected: solving single variable and systems of equations, graphing linear equations, ratios, and proportions, and solving quadratic equations by factoring. Solving Right Triangles using trigonometry. 
    Prerequisite: Algebra 1, Geometry. (One Credit)

  • Calculus

    This course explores topics in differential calculus and simultaneously reinforces algebraic skills. Understanding and mastery of intermediate skills in algebra and precalculus are expected. Topics include limits, continuity, differential and introductory integral calculus and their applications, including problems in the area of physics, and the role of calculus as a tool for problem-solving is emphasized. This course is open to all students who have completed Precalculus or Honors Precalculus. Familiarity with the following topics is expected: solving quadratic equations by factoring, identifying parent functions & their properties, identifying & solving polynomial, logarithmic, exponential, rational, & radical equations, familiarity with basic trigonometry & physics. Prerequisite: Precalculus. (One Credit)

  • Fundamentals of Precalculus

    This course begins with a review of linear functions and then moves on to the graphs and transformations of various functions (quadratic, rational, radical, and absolute value). The course continues into a study of the basics of trigonometry. Emphasis is placed on equation solving, graphing, and reinforcing algebraic skills and concepts. Familiarity with the following topics is expected: solving systems of equations, graphing linear equations, ratios, and proportions, and solving quadratic equations by factoring. Prerequisite: Algebra 2 (One Credit)

  • Geometry

    Students will study Euclidean Geometry, emphasizing problem-solving, proofs, and graphing in the coordinate plane. Topics include properties of figures in two and three dimensions, similarity, congruence, area, and right triangle trigonometry. Students will work collaboratively and be expected to justify and explain their reasoning – especially in the context of two-column proofs – and use tools like the free-to-use Geogebra. Though the course will review many algebra topics, a strong foundation in solving and graphing linear equations is expected. Familiarity with the following topics is expected: solving single variable equations and systems of equations. Graphing lines, identifying slopes, and y-intercepts. Prerequisite: Algebra 1 (One Credit)

  • Honors Algebra 2/Trig

    This two-semester, highly accelerated discussion-based course covers a vast breadth of advanced algebra topics. The pace is demanding, and the dense problem sets that students will encounter will be challenging. For students who have completed a thorough study of Algebra I and Geometry, some topics will be familiar, though likely presented in novel contexts; other ideas and techniques will be new. This course is designed to prepare highly motivated students who are interested in striving for EHS’ advanced offerings, including BC Calculus and higher levels. Familiarity with the following topics is expected: solving systems of equations, graphing linear equations, ratios, and proportions, and solving quadratic equations by factoring. Knowledge of functions and function notation. Basic understanding of trigonometry including: Sine, Cosine, and Tangent. Prerequisite: Algebra 1, Geometry or Honors Geometry. Department Permission Required. (One Credit)

  • Honors Geometry

    Students will study Euclidean Geometry with an emphasis on problem-solving, construction, proofs, and graphing in the coordinate plane. Topics include properties of figures in two and three dimensions, similarity, area, volume, and right triangle trigonometry. Students will frequently work collaboratively and be expected to justify and explain their reasoning using tools like a geometer’s compass and the free-to-use graphing software Geogebra. The course is heavily problem-based and designed to develop skills, conceptual understanding, and synthesis of content across topics. Students should be prepared to meet honors-level expectations of challenge and rigor, with homework requirements frequently reaching three hours per week. Familiarity with the following Algebra 1 topics is expected: solving systems of equations, graphing linear equations, ratios and proportions, irrational numbers, and solving quadratic equations by factoring. Prerequisite: Algebra 1, Department Permission Required. (One Credit)

  • Honors Precalculus

    This course studies the real and complex number systems and analysis of functions (polynomial, rational, circular, trigonometric, exponential, logarithmic, and logistic). It introduces and reinforces the study of vectors in two and three dimensions, parametric functions, analytic geometry, and polar functions. The course introduces calculus through optimization, asymptotic behavior, and limits. Students are expected to apply skills and concepts learned in various novel and challenging ways throughout the course. Familiarity with the following topics is expected: solving systems of equations, graphing linear equations, ratios, and proportions, and solving quadratic equations by factoring. Basic understanding of trigonometry including: Sine, Cosine, and Tangent. Prerequisite: Algebra 2/Trig or Honors Algebra 2/Trig. Department Permission Required (One Credit)

  • Introduction to Big Data Analytics

    Blending mathematics, statistics, and computer programming, this course provides an introduction to the emerging field of data science. Students will analyze large sets of data from areas such as the financial sector, retail sales, sports analytics, healthcare industry, and social networking platforms looking for patterns and trends. Using the open-source computer language R, students will identify regularities within a data set, exposing secrets and making original discoveries. Sample projects include gathering vast amounts of data about consumers to predict shopping habits and analyzing sports statistics to evaluate an athlete’s value and performance. Prerequisite: Algebra 2. No previous statistics or computer science courses are required to take this course. (One-half 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 Fundamentals of Precalculus, Precalculus or Honors Precalculus. (One Credit).

  • Precalculus

    This course is designed to bridge the connection from Algebra to Calculus. Topics and concepts learned in prior Algebra classes are reinforced, and new topics are introduced. The goal is to deepen mathematical understanding and the ability to synthesize concepts. Topics include functions (polynomial, rational, exponential, and logarithmic) and trigonometry (solving equations, graphing functions, and verifying identities). Familiarity with the following topics is expected: solving systems of equations, graphing linear equations, ratios, and proportions, and solving quadratic equations by factoring. Basic understanding of trigonometry including: Sine, Cosine, and Tangent. Prerequisite: Algebra 2/Trig. (One credit)

  • GOA: Computer Science 1: Computational Thinking

    Computational thinking centers on solving problems, designing systems, and understanding human behavior. It has applications not only in computer science but also myriad other fields of study. This introductory-level course focuses on thinking like a computer scientist, especially understanding how computer scientists define and solve problems. Students begin the course by developing an understanding of what computer science is, how it can be used by people who are not programmers, and why it’s a useful skill for all people to cultivate. Within this context, students are exposed to the power and limits of computational thinking. Students are introduced to entry-level programming constructs that help them apply their knowledge of computational thinking in practical ways. They learn how to read code and pseudocode as well as begin to develop strategies for debugging programs. By developing computational thinking and programming skills, students will have the core knowledge to define and solve problems in future computer science courses. While this course would be beneficial for any student without formal training as a programmer or computer scientist, it is intended for those with no programming experience. Prerequisite: Honors Geometry, Algebra 2 (One-half credit)

  • GOA: Computer Science 2: Analyzing Data with Python

    In this course, students utilize the Python programming language to read, analyze, and visualize data. The course emphasizes using real-world datasets, which are often large, messy, and inconsistent. Because of the powerful data structures and clear syntax of Python, it is one of the most widely used programming languages in scientific computing. Students explore the multitude of practical applications of Python in fields like biology, engineering, and statistics. Prerequisite: Computer Science I: Computational Thinking or its equivalent. (One-half credit)

  • GOA: Computer Science 2: Game Design & Development

    In this course, students practice designing and developing games through hands-on work. Through the creation of small “toys,” the course asks students to solve problems and create content, building the design and technical skills necessary to build their own games. Throughout the course, students come to understand 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 Godot, 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 GDScript programming language, which is modeled after Python. In the last two modules of the course, students 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: Computer Science 2: Java

    This course teaches students how to write programs in the Java programming language. Java is the backbone of many web applications, especially eCommerce and government sites. It is also the foundational code of the Android operating system and many tools of the financial sector. Students learn the major syntactical elements of the Java language through object-oriented design. The emphasis in the course is on creating intelligent systems through the fundamentals of Computer Science. Students write working programs through short lab assignments and more extended projects that incorporate graphics and animation. Prerequisite: Computer Science I: Computational Thinking or its equivalent

  • GOA: Game Theory

    In this course, students explore a branch of mathematics known as game theory, which uses mathematical models to inform decision making. There are many applications to everyday dilemmas and conflicts, many of which can be treated as mathematical games. Students consider significant global events from fields like diplomacy, political science, anthropology, philosophy, economics, and popular culture. They examine models of world conflicts and scheduling of professional athletic contests. Specific topics include two-person zero-sum games, two-person non-zero sum games, sequential games, multiplayer games, linear optimization, and voting theory. (One-half credit)

  • GOA: Geometry (Summer)

    This intensive summer course is designed to provide an accelerated path through the traditional high school geometry curriculum. Focusing on Euclidian geometry, students examine topics relating to parallel lines, similar and congruent triangles, quadrilaterals, polygons, and circles. Students can expect to analyze lengths, areas, and volumes of two- and three-dimensional figures and explore transformations and other manipulations. Particular attention is paid to introductory trigonometry with right triangles and the study of circles (radians, sectors, arc length, etc.). In addition, the development of a mature, logical thought process will begin through a formal introduction to arguments, deductions, theorems, and proofs. Because this course covers topics that are typically presented in a yearlong course, students should expect to dedicate 15-20 hours per week during the intensive seven-week summer session. Prerequisite: Algebra 1, Department Permission Required (One Credit)

  • GOA: Introduction to AI

    Aspects of artificial intelligence permeate our lives and the algorithms power your favorite apps. How much do you really know about how AI works or how it is changing the world around us? This course explores the history of research into artificial general intelligence and the subsequent focus on the subfields of narrow AI: neural networks, machine learning and expert systems, deep learning, natural language processing, and machine vision and facial recognition. Students also learn how AI training datasets cause bias and focus on the ethics and principles of responsible AI: fairness, transparency and explainability, human centeredness, and privacy and security. (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. Students progressively develop the tools needed to understand the RSA algorithm, the most common encryption scheme used worldwide. Along the way, they invent some encryption schemes of their own and discover how to play games using number theory. Students also get a taste of the history of the subject, which involves the most famous mathematicians from antiquity to the present day, and see parts of the story of Fermat’s Last Theorem, a 350-year-old statement that was fully proven only 20 years ago. While most calculations are simple enough to do by hand, students 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)

Department Faculty

1200 North Quaker Lane
Alexandria, Virginia 22302
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