## MIDDLE SCHOOL COURSES

**Prealgebra**

This course reviews and extends the mathematical concepts necessary for algebra. Students investigate, discover, and apply mathematics using a variety of real-world situations. Topics include exponents, geometry, graphing, integers, linear equations, percent, probability, proportion, ratio, rational numbers, and statistics. Problem-solving techniques, cooperative learning, and critical-thinking skills are emphasized through the use of manipulatives, computer software, and calculators.

**Algebra I: Grade 7**

This fast-paced course challenges students to develop traditional first-year algebra skills and apply them to complex problems. Students must have a thorough knowledge of prealgebra and be able to work at an accelerated pace. Nonroutine problems and special investigations give students the opportunity to think critically and use the problem-solving strategies they learn in class. Nightly homework follows the forty-minute standard of an eighth-grade Algebra I course. Prerequisite: Placement test.

**Algebra**

This course investigates traditional algebraic concepts using a variety of problem-solving strategies. Connections between algebra and real-world situations are emphasized. Students are expected to become proficient at solving, writing, and graphing linear equations, inequalities, and systems as well as in solving and graphing quadratic equations. Other topics include radicals and exponents. Prerequisite: Prealgebra and permission of current instructor.

**Algebra I**

This fast-paced course, designed for students with a mastery of prealgebra skills, investigates traditional algebraic concepts using a variety of problem-solving strategies. Students must develop skills quickly and then apply them to complex problems. Students are expected to become proficient in the mechanics of a given topic and in its application to word problems. Mastery is expected in solving, writing, and graphing linear equations, inequalities, and systems as well as in solving and graphing quadratic equations. Other topics include radicals, exponents, and rational expressions. Prerequisite: Prealgebra or Algebra I: Grade 7 and permission of current instructor.

**Algebra II with Analysis**

This course reviews and extends the skills and concepts covered in algebra and geometry. Additional topics include complex numbers, polynomial and rational functions, exponential and logarithmic functions, sequences and series, and an introduction to trigonometry. Students are introduced to curve analysis, optimization arguments, and concepts of limits. Prerequisite: One year of algebra, one year of geometry, and permission of current instructor.

**Algebra II Honors**

This course provides a study of second-year algebra with greater breadth, depth, and rigor than Algebra II with Analysis. Topics include polynomial equations and inequalities; functions and their inverses; linear, quadratic, polynomial, and rational functions and their graphs; logarithmic and exponential functions; sequences and series; conics; and systems of equations, including matrix solutions. Graphing calculators are used to reinforce students' understanding of concepts. Prerequisite: Grade 8 - Algebra I: Grade 7 and permission of current instructor; Grades 9 or 10 - A- in Algebra I, A- in Geometry Honors or Geometry, and permission of current instructor.

**Geometry 9**

This course concentrates on Euclidean geometry while maintaining algebraic skills. Topics include congruent triangles, parallel lines, quadrilaterals and other polygons, the Pythagorean theorem, similar figures, circles, area, volume, coordinate geometry, an introduction to right-triangle trigonometry, and constructions. Students develop deductive reasoning skills through the use of proofs. Computer and/or other hands-on laboratory activities may be used to explore and discover geometric concepts. Prerequisite: Permission of current instructor.

**Geometry**

This fast-paced, proof-based logic course concentrates on the study of Euclidean geometry while incorporating sophisticated algebraic techniques. Geometric concepts include congruent triangles, parallel lines, quadrilaterals, circles, similar figures, the Pythagorean theorem, perimeter, area, volume, regular polygons, and right-triangle trigonometry. Algebraic methods include solving quadratic equations, solving systems of equations, and simplifying radicals as they relate to geometry problems. Students use theorems and definitions to write proofs and solve practical application problems. The underlying theme of the course is the solution of problems by creating logical, well-supported explanations. Computer and/or other hands-on laboratory activities may be used to explore and discover geometric concepts. Prerequisite: Permission of current instructor.

**Geometry Honors**

This course provides a study of Euclidean geometry and an introduction to transformational, coordinate, and three-dimensional geometries. It is fast-paced and challenges students to interpret complex written problems and write well-supported solutions to those problems and rigorous proofs. Students participate in nationwide mathematics contests. Prerequisite: Algebra I or Algebra II Honors and permission of current instructor.

**Precalculus Honors**

This course is open to students with exceptional algebra and geometry skills who show creativity in solving problems, enjoy mathematics, and are interested in exploring the subject in depth. Students study polynomial, rational, exponential, logarithmic, and trigonometric functions. Other topics include De Moivre's theorem, sequences and series, analytic geometry, conic sections, parametric and polar equations, and matrices and determinants. Graphing calculators help extend each student's ability to explore and to do more interesting and difficult problems. Prerequisite: Algebra II Honors, Geometry Honors, and permission of current instructor.

**Introduction to Programming I**

This semester elective helps students develop problem-solving skills and exercise logical abilities. Students learn programming fundamentals in Java. Topics include input, output, variables, conditional control structures, random numbers, and loops. Programming assignments include a Fahrenheit-to-Celsius converter, a multiplication tutoring program, and rock-paper-scissors and Nim number games. Students produce simple graphics on the screen and learn how to output colorful geometric shapes and the fractal Sierpinski's triangle. Students use BlueJ, a visual and interactive Java programming environment. Programming involves mathematical and logical reasoning; therefore, successful completion of, or concurrent enrollment in, Algebra I or higher is recommended.

**Introduction to Programming II**

This semester elective is a continuation of Introduction to Programming I. Students write Java programs using Karel J. Robot, a robot simulator that introduces students to object-oriented programming concepts. Topics include methods, constructors, classes, objects, and inheritance. Tasks include programming a robot to complete a steeplechase and to escape a maze. Students write programs to determine if a word is a palindrome and to simulate the game of hangman. Students use BlueJ, a visual and interactive Java programming environment. Programming involves mathematical and logical reasoning; therefore, successful completion of Algebra I or higher is recommended. Prerequisite: Introduction to Programming I.

**Middle School Robotics**

In this interdisciplinary elective, students use LEGO's EV3 and other systems to build robots. ROBOTC, a C-based language, is used to program them. Students practice real-world engineering, computer science, design, mathematics, and applied physics concepts. They learn hands-on building techniques combined with electronics and problem solving. Note that students who join the middle school's robotics team are not required to take this course; conversely, students can take this course without joining the team.

## UPPER SCHOOL COURSES

**Algebra II**

This course reviews and extends the concepts covered in the first year of algebra and geometry. Increasingly advanced algebraic skills are developed through the integration of principles introduced in those courses. Students solve a wide variety of equations and approach problems using different methods. They solve linear and non-linear systems using algebraic and graphical methods. Topics include linear and quadratic equations; polynomial, exponential, logarithmic, and introductory rational functions; and analyses of sequences and series. Prerequisite: Algebra, Algebra I, Geometry 9, or Geometry.

**Algebra II with Analysis**

This course reviews and extends the skills and concepts covered in algebra and geometry. Additional topics include complex numbers, polynomial and rational functions, exponential and logarithmic functions, sequences and series, and an introduction to trigonometry. Students are introduced to curve analysis, optimization arguments, and concepts of limits. Prerequisite: One year of algebra, one year of geometry, and permission of current instructor.

**Algebra II Honors**

This course provides a study of second-year algebra with greater breadth, depth, and rigor than Algebra II with Analysis. Topics include polynomial equations and inequalities; functions and their inverses; linear, quadratic, polynomial, and rational functions and their graphs; logarithmic and exponential functions; sequences and series; conics; and systems of equations, including matrix solutions. Graphing calculators are used to reinforce students' understanding of concepts. Prerequisite: Grade 8 - Algebra I: Grade 7 and permission of current instructor; Grades 9 or 10 - A- in Algebra I, A- in Geometry Honors or Geometry, and permission of current instructor.

**Mathematical Analysis Honors**

This course is for students who have completed a second year of algebra and wish to continue their study of mathematics in the honors program. It prepares students to take Introduction to Calculus Honors. The course emphasizes advanced problem-solving skills and thorough analysis of elementary functions. Topics include an in-depth study of linear, quadratic, polynomial, rational, exponential, and logarithmic functions as well as matrices, sequences and series, conic sections, and mathematical induction. Prerequisite: Algebra II with Analysis or Algebra II Honors, Geometry Honors, and permission of current instructor.

**Precalculus Honors**

This course is open to students with exceptional algebra and geometry skills who show creativity in solving problems, enjoy mathematics, and are interested in exploring the subject in depth. Students study polynomial, rational, exponential, logarithmic, and trigonometric functions. Other topics include De Moivre's theorem, sequences and series, analytic geometry, conic sections, parametric and polar equations, and matrices and determinants. Graphing calculators help extend each student's ability to explore and to do more interesting and difficult problems. Prerequisite: Algebra II Honors, Geometry Honors, and permission of current instructor.

**Precalculus: Trigonometry and Functions**

This course introduces the study of trigonometric functions using both right-triangle and circular-function approaches. Trigonometric graphs and identities are examined as tools for solving trigonometric equations. The progression of skills taught in algebra and geometry is continued with topics including polynomial, exponential, rational, and logarithmic functions. Graphing techniques of translations, reflections, and scale changes are studied with respect to fundamental functions. The goal of this course is to prepare students for first-year college-level work in mathematics or an advanced placement course, such as Advanced Placement Statistics. Prerequisite: Algebra II or Algebra II with Analysis.

**Precalculus**

This course is for students who anticipate enrolling in any of the following Advanced Placement courses: Calculus AB, Statistics, Microeconomics/Macroeconomics, Physics 1, and Physics C. Topics include the properties of the real number system, the theory of equations, coordinate geometry, relations, functions and their graphs, exponential and logarithmic functions, circular and trigonometric functions, sequences and series, and conic sections. The calculus ideas of limits and slopes of curves are introduced. The graphing calculator is used extensively throughout the course. Prerequisite: Mathematical Analysis Honors, Algebra II Honors, or B in Algebra II with Analysis and permission of current instructor.

**Introduction to Calculus Honors**

This course allows students to complete precalculus and start calculus. Students begin with an intensive study of trigonometric functions and then are taught calculus at the level expected of university science and engineering departments. Topics include limits, the definition of continuity, and the derivative. Students calculate derivatives and integrals. They solve separable differential equations. Students apply these tools to solve problems such as local linearization, related rates, optimization, and analysis of graphs of functions. Students develop their problem-solving skills and ability to generate clear, precise mathematical arguments. Students are expected to communicate their mathematical thinking through numeric, graphic, and analytic avenues. This course requires the use of a graphing calculator or a computer. Prerequisite: Mathematical Analysis Honors or B+ in Algebra II Honors and permission of current instructor.

**AP Calculus BC 11**

This is a college-level course in preparation for the BC-level Advanced Placement examination in mathematics. Topics include the precise definition of limits and continuity, the derivative, techniques of differentiation for the elementary functions, application of the derivative, area under a curve, integrals and the fundamental theorem, numerical methods of integration, integration techniques and applications, analysis of parametric and polar curves, improper integrals, vector-valued functions, infinite series, and elementary differential equations. Students must know the language of functions and be familiar with the properties, algebra, and graphs of functions. Prerequisite: Precalculus Honors and permission of current instructor.

**Calculus and Statistics**

This course introduces students to branches of mathematics that may be studied further in college. The essential themes of calculus (the limit, derivative, and integral) are introduced conceptually and reinforced through discussions, graphical analysis, and real-world problems. Sequences and series are examined algebraically and with spreadsheets. Statistical topics include describing and comparing data, sampling and experimental design, confidence intervals, probability, and normal and binomial distributions. Prerequisite: Precalculus: Trigonometry and Functions or Precalculus.

**AP Statistics**

Advanced Placement Statistics prepares students to master the theory and practice of four broad themes in statistics: describing data (exploratory data analysis), collecting data (sampling, experimental design, sampling design), understanding random behavior (constructing simulations, probability), and making conclusions from data (inference). Students analyze case studies and instructive examples. They also spend one day per week in a laboratory session, analyzing real data on the computer. Students gain proficiency with computer-based statistics packages. Prerequisite: B in Precalculus, B+ in Algebra II Honors, or A- in Algebra II with Analysis or Precalculus: Trigonometry and Functions.

**AP Calculus AB**

This is a college-level course in preparation for the AB-level Advanced Placement examination in calculus. Topics include the algebra of functions and advanced graphing techniques, limits and continuity, the derivative and its applications, techniques of differentiation for the elementary functions, area under a curve, integrals and their applications, and the fundamental theorem of calculus. Concepts are presented on an intuitive level without rigorous proof. A graphing calculator is used throughout the year. Tests and quizzes rely heavily on problem-solving ability; graded problems will not always be exactly like homework or in-class problems. Students are expected to apply general concepts in new situations. Prerequisite: Precalculus or Introduction to Calculus Honors and permission of current instructor.

**AP Calculus BC 12**

This course prepares students to take the BC-level Advanced Placement examination. After reviewing material from the prerequisite course, students learn precise definition of limits, numerical methods of integration, advanced integration techniques, analysis of parametric and polar curves, improper integrals, vector-valued functions, infinite series, and elementary differential equations. Additional numerical and calculator methods, including slope fields and Euler's method, are introduced. Tests and quizzes rely heavily on problem-solving ability; graded problems will not always be exactly like homework or in-class problems. Students are expected to apply general concepts in new situations. The approach is more mathematically rigorous and includes more proof than in AB calculus. Prerequisite: Introduction to Calculus Honors and permission of current instructor.

**Advanced Seminar in Mathematics Honors**

This seminar is for students who have demonstrated ability and interest in studying mathematics beyond the level of calculus. Topics include multivariable calculus and linear algebra. Differential equations, constructing proofs, topology, elementary real analysis, and elementary number theory may also be covered. The focus is on exposing students to different branches of mathematics and developing their ability to think and communicate mathematical ideas at the advanced level. Students participate in a variety of mathematics problem-solving competitions throughout the year. The majority of class time is spent in discussion and working with peers and the instructor. Prerequisite: An Advanced Placement Calculus BC course.

**AP Microeconomics/AP Macroeconomics**

This course introduces students to the principles of micro- and macroeconomics. The microeconomic portion of the course focuses on the pervasive problem of scarcity and how individual choices, incentives, and systems of prices affect the allocation of limited resources among competing uses. This includes an analysis of the effect of competition, cartels, monopolies, and government regulation on resource allocation and human welfare. The macroeconomic portion of this course is an introductory study of the domestic and international factors affecting national income, inflation, and unemployment. Among these factors, the role of money and government taxation and expenditure policy is emphasized. Students must take the Advanced Placement examinations in microeconomics and macroeconomics in May. Prerequisite: B in Precalculus, A- in Precalculus: Trigonometry and Functions, or higher.

**AP Computer Science A**

This course introduces students to the principles of computer science. Students learn the guiding principles of object-oriented software design and programming in Java. They apply concepts such as abstraction, encapsulation, inheritance, and arrays to solve problems. Topics include algorithm design, writing classes, programming principles, class hierarchy, inheritance, and interfaces. Material is introduced in presentations that are reinforced through homework. Students are assigned laboratory exercises to develop their ability to create solutions to problems in realistic situations. Students may not take Advanced Placement Computer Science A and Advanced Placement Computer Science Principles concurrently. Prerequisite: Introduction to Programming II or Advanced Placement Computer Science Principles and permission of current instructor.

**AP Computer Science Principles**

This course introduces seven big ideas in computing: creativity in arts and science, abstraction, problem analysis using data, algorithms, programming, the Internet, and the societal impact of computing. Students develop simulations to explore questions that interest them. They submit two creative works for the College Board examination. These measure: 1) students' exploration of the impact of computing on social, economic, and cultural life and 2) their creation of a computational artifact through the design, development, and testing of software. Students may not take Advanced Placement Computer Science Principles and Advanced Placement Computer Science A concurrently.

**Design and Data Structures Honors**

Students extend skills learned in the prerequisite course through an investigation of abstract data structures and practical program design. The Java programming language is used, but the course stresses universal programming concepts that can be applied to most languages. The course covers implementations and performance analyses of arrays, lists, stacks, queues, trees, heaps, maps, and graphs, including Java's implementation through the Java collections framework. Practical skills, such as basic graphical user interfaces and I/O, complement these theoretical topics. Critical programming concepts such as abstraction, encapsulation, inheritance, polymorphism, and top-down design are reinforced as students create complete executable programs from start to finish. Students choose the proper data structures to create solutions to tasks such as spell-checking, lossless data compression, and Markov chain-based text generation. Prerequisite: Advanced Placement Computer Science A.

**Advanced Topics in Computer Science Honors**

This course for students who wish to extend their knowledge of computer science and sample a variety of advanced topics includes computer security and hacking, artificial intelligence and machine learning, advanced algorithmic techniques (such as dynamic programming and divide-and-conquer), multithreading and concurrency, and the unsolved P vs. NP problem. Throughout the year, students give presentations related to each of these subjects. They are exposed to C and Python programming languages and learn to code in Swift and C#. Students also learn programming for iOS and UNITY, enabling them to develop advanced projects independently. Students are evaluated on the quality and overall design of these projects and present them at the end of the year. Topics may change depending on advances in computer science as well as the interests and needs of the class. Prerequisite: Design and Data Structures Honors.

**Directed Study: Number Theory**

Students continue to develop proof-writing skills and are introduced to concepts of number theory. Topics include primes, polygonal numbers, divisor-counting functions, amicable pairs, perfect numbers, the Mobius function, quadratic residues, and an introduction to sieve theory. Material is presented in chronological order, beginning with Pythagoras. The Java programming language and the PARI/GP computer algebra system are used in solving number-theoretic problems. Students are expected to use, and develop a proficiency in, LaTeX typesetting software to format their homework. Applications to music and the twelve-tone scale are also discussed. Necessary topics from other areas of mathematics are developed as the course progresses. Previous experience in Java, PARI/GP, LaTeX, and music is not required. Prerequisite: Advanced Seminar in Mathematics Honors.