The Harvard‑Westlake Mathematics department provides a challenging and diverse six-year college preparatory program that meets the needs of students at different stages of development with different levels of ability and interest. The curriculum is technologically current and has both the breadth and depth to provide the mathematical tools for success in a changing society. The program is designed to develop students who will:

• have good number sense and reasoning ability;
• be proficient in the appropriate use of the technological tools currently associated with mathematical thinking in varied real-life situations;
• be able to communicate in the language of mathematics and be able to perform basic algorithms by hand if required;
• be creative problem solvers who are willing to take risks, try alternative approaches when the first attempt fails, and stick with it until the solution is found;
• be able to work successfully in individual or cooperative situations;
• appreciate the value of mathematical thinking and study mathematics for their entire Harvard‑Westlake career.

All students are required to study mathematics each year through the eleventh grade and are strongly encouraged to continue their study in the senior year. Each student is advised by his or her current teacher as to the best program of study. Most courses have two-hour examinations at the end of each semester. Students in Advanced Placement courses take the College Board Advanced Placement examination at the end of the second semester in lieu of an internal examination. Other exceptions to this general policy are noted under individual courses.

MATHEMATICS

This course concentrates on the study of Euclidean geometry while maintaining algebraic skills. Concepts include congruent triangles, parallel lines, quadrilaterals, circles, similar figures, the Pythagorean theorem and special triangles, perimeter, area, volume, regular polygons, and right-triangle trigonometry. During the first semester, students concentrate on proof techniques; the second semester shifts the emphasis to exploration and discovery of the concepts. Most of the material is presented through teacher-directed lessons and reading assignments. Students are evaluated on tests (50%), homework and quizzes (30%), and the final examinations (20%).
Prerequisite: Algebra I.

This course reviews and develops a deeper understanding of fundamental principles in algebra and geometry. Students study linear functions, quadratic functions, rational functions, systems of equations, roots, exponents, probability, and data analysis. Activities and lessons are designed to help students develop not only a better understanding of algebra and geometry but also the specific organization, problem-solving, and communication skills necessary for future success in mathematics. A typical class consists of discussing homework problems (10 minutes), learning new material through lessons and activities (20–25 minutes), and practicing the skills covered through individual, paired, and group work (10 minutes). Quizzes are given on each chapter, and at least one class period is devoted to review before each major test. Students are evaluated (with approximate relative weight) through tests (45%), quizzes (25%), semester examinations (20%), and homework (10%).
Prerequisite: Algebra I.

This is a second-year algebra course that reviews and extends the skills and concepts of Algebra I. Additional topics include complex numbers, polynomial and rational functions, exponential and logarithmic functions, sequences and series, and an introduction to trigonometry. This information is presented in several ways: about 80% of the material is presented through lecture and multimedia presentations; the balance is presented to students as they work through problems and exercises in groups or independently. Students are evaluated (with approximate relative weight) through tests (55%), homework and quizzes (25%), and semester examinations (20%).
Prerequisite: Geometry, Algebra I, and permission of the department.

This course provides an in-depth study of second-year algebra with greater breadth, depth, and rigor required than in Algebra II. Topics include polynomial equations and inequalities; functions and their inverses; linear, quadratic, polynomial, and rational functions and their graphs; logarithmic and exponential functions; mathematical induction, sequences, and series; and systems of equations, including matrix solutions. The material is presented through teacher-directed lessons, and students are expected to derive answers analytically, numerically, and graphically. Students are evaluated on tests (50%), homework and quizzes (30%), and the final examinations (20%).
Prerequisite: Geometry, Algebra I, and permission of the department.

This is a tenth-grade honors math course that focuses on topics taught in a precalculus class. The course is intended for students who have already had a second algebra course and want to continue working in an honors program to prepare for Introductory Calculus, which is taken in the junior year. It emphasizes advanced problem-solving skills. Topics include polynomial equations and inequalities; functions and their inverses; linear, quadratic, polynomial, and rational functions; logarithmic and exponential functions; systems of equations; mathematical induction, sequences, and series; and conic sections. The material is presented through lecture and classroom discussions. Students are expected to derive answers analytically, numerically, and graphically. Occasionally, students work in groups. All work is reinforced by daily homework assignments. Students are evaluated on tests (50%), homework and quizzes (30%), and semester examinations (20%).
Prerequisite: Advanced Algebra Honors and Geometry Honors.

This course is open to students of outstanding ability with strong algebra and geometry skills who show creativity in solving problems, enjoy mathematics, and are interested in studying the subject in depth. In addition to a review of algebra, all of the elementary functions are studied. These functions include polynomials, rational functions, exponential and logarithmic functions, and the circular and trigonometric functions. Other topics are complex numbers, sequences and series, analytic geometry, matrices and determinants, and inductive proofs. The material is presented primarily through lecture and classroom discussion. Worksheets, group activities, and daily assignments reinforce the material. Graphing calculators help to explore and extend each student’s ability to do more interesting and difficult problems. Class preparation at home entails completion of homework exercises, review of class notes, and preparation for written examinations. Students are evaluated (with approximate relative weight) through tests (50%), quizzes (20%), fall and spring final examinations (20%), and homework (10%).
Prerequisite: Permission of the department.

This course covers a series of topics that use skills learned in Algebra and Geometry. Students study trigonometric, polynomial, exponential, rational, and logarithmic functions. Emphasis is placed on the trigonometric functions. Students are introduced to right-triangle trigonometric relationships, which are used to solve problems and develop the trigonometric functions. Students work with trigonometric identities and use them to solve trigonometric equations. Trigonometric representation of complex numbers is studied. Graphing techniques involving basic functions with respect to translations, reflections, and scale changes are presented. Material is presented through lecture, discussion, and discovery activities. Students are evaluated (with approximate relative weight) through tests (50%), homework and quizzes (30%), and semester examinations (20%).
Prerequisite: Algebra II or Algebra II: The Fundamentals.

This course is for students who anticipate enrolling in any of the following Advanced Placement courses at Harvard‑Westlake: Calculus AB, Statistics, Economics, Physics B, and Physics C. Topics include the properties of the real number system, coordinate geometry, relations, functions and their graphs, theory of equations, exponential and logarithmic functions, circular and trigonometric functions, complex numbers, polar coordinates, DeMoivre’s theorem, sequences and series, elementary probability, and conic sections. The calculus ideas of limits and slopes of curves are introduced. The material is presented primarily through lecture and classroom discussion, occasionally through worksheets and group activities, and is reinforced by the students’ daily assignments. Class preparation at home entails completion of homework exercises, review of class notes, and preparation for written examinations. The graphing calculator is used extensively throughout the course. Students are evaluated (with approximate relative weight) through chapter tests (55%), quizzes and homework (25%), and fall and spring final examinations (20%).
Prerequisite: Algebra II or Algebra II Honors and permission of the department.

This eleventh-grade honors course allows students to complete precalculus and start calculus. In the first semester, students begin with an intensive study of trigonometric functions. In the second semester, students are taught calculus at the very rigorous level expected of university science and engineering departments. Topics covered include limits, the definition of continuity, and the derivative. Students develop skill calculating derivatives and integrals. They learn to solve separable differential equations. Students apply these tools to solve several classes of problems: 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. All work is reinforced by daily assignments. Students are evaluated through tests (50%), homework and quizzes (30%), and semester examinations (20%).
Prerequisite: Mathematical Analysis Honors or Algebra II Honors and permission of the department.

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. The material is presented through teacher-directed lessons, worksheets, and computer simulations. Students are expected to know the language of functions and be familiar with the properties, algebra, and graphs of functions. Students are evaluated on tests (50%), homework and quizzes (30%), and the final examinations (20%).
Prerequisite: Precalculus Honors 10 and permission of the department.

This is a college-level course in preparation for the AB-level Advanced Placement examination in mathematics. Topics include the algebra of functions and advanced graphing techniques, 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, and applications of the integral. Many concepts are presented on an intuitive level without rigorous proof. Material is presented through lecture, worksheets, and computer simulations. Students are evaluated (with approximate relative weight) on tests and a first-semester examination (70%) and homework and quizzes (30%) . Tests and quizzes rely heavily on problem-solving ability; that is, 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 and permission of the department.

This course is for students who have completed Introduction to Calculus Honors in the previous year and who wish to complete preparation for the BC-level Advanced Placement examination. The material from Introduction to Calculus Honors is reviewed followed by the 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. Material is presented through lecture, worksheets, and computer simulations. Students are evaluated (with approximate relative weight) on tests and a fall-semester examination (70%) and homework and quizzes (30%). Tests and quizzes rely heavily on problem-solving ability; that is, 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 in this course is more mathematically rigorous and includes more proof than in AB calculus.
Prerequisite: Introduction to Calculus Honors and permission of the department.

This course covers a variety of topics which include probability, statistics, elementary set theory, and principles of logic along with sequences and series. The essential themes of calculus (the limit, derivative, and integral) are introduced conceptually and reinforced through discussions, graphing, and real-world problems. Graphing calculators, spreadsheets, and other applicable software are used extensively for the development of a variety of projects and presentations of financial case studies. Other topics of interest are examined as time permits. Concepts are presented in a variety of ways, including lectures, small-group work, guided discoveries, and computer-based laboratories. Consistency of work habits is emphasized. Students are evaluated (with approximate relative weight) through tests (45%), homework and quizzes (20%), various multimedia projects (15%), a fall-semester examination (10%), and a spring-semester project (10%).
Prerequisite: Precalculus or Precalculus: Trigonometry and Functions.

Equivalent to a college-level introductory statistics course, 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). In addition to learning from teacher instruction, students analyze case studies and instructive examples. Students also spend one day per week in a laboratory session, analyzing real data on the computer. This activity-based approach to learning requires increased proficiency with the TI‑83/TI-84 calculator and computer-based statistics packages. Strong reading and writing skills are needed for success in the course. The course grade is based on daily work (40%), tests and projects (40%), and the semester examination (20%). It is helpful to have computer and Internet access. Students who miss classes because of extracurricular events may be at a disadvantage in this course.
Prerequisite: Successful performance in Precalculus and approval of the department. Exceptional students in Precalculus: Trigonometry and Functions may be approved after consultation with the instructor.

This seminar is designed for those students who have proven their ability and interest in studying mathematics beyond the level of calculus. Students encounter a variety of topics in advanced mathematics. Topics include multivariable calculus and linear algebra. Differential equations, constructing proofs, topology, elementary real analysis, and elementary number theory are additional topics that may also be covered. The focus is not only on exposing students to different branches of mathematics, but also on developing their ability to think and communicate mathematical ideas at the advanced level. In addition, members of the course participate in a variety of mathematics problem-solving competitions throughout the year. The teacher presents illuminating or instructive problems once per week. The majority of class time is spent in discussion and work with peers and the instructor. Students keep a “log book” of ongoing problems and turn in their solutions when requested. Students are evaluated on tests (40%), their solutions (20%), a midterm examination (20%), and a final project (20%).
Prerequisite: Advanced Placement Calculus BC 11.

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ECONOMICS

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. Methods of presentation include class lecture, student-initiated discussion and debate, computer simulations and tutorials, and student presentations. Methods of evaluation include daily homework assignments, quizzes (two to three per week), unit tests (four to five per semester), one- to two-page current event essays (four to five per semester), and a cumulative first-semester examination. Students must take the Advanced Placement examinations in Microeconomics and Macroeconomics in May.
Prerequisite: Permission of the instructor based on completion of Precalculus with a final grade of B+ or higher. Exceptional students in Precalculus: Trigonometry and Functions may be approved after consultation with the instructor.

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COMPUTER SCIENCE

The primary objective of the Harvard‑Westlake Computer Science program is to enable students to use computers for future academic needs. Our computer courses cover a broad range of topics, from creating a web page to advanced computer science techniques, and provide experience in art, music, writing, publishing, data access, science, mathematics, and analytic computer science. In the computer science courses, students are introduced to programming through the study of Java, although other languages are discussed. Other courses allow students the chance to explore the vast world of computers, from developing parts of the Internet to building robots.

* Indicates a course that does not fulfill the University of California system’s Subject requirement.

This course focuses on planning, designing, and executing a website. Students design websites, taking into consideration graphics, content, and programming issues. Students also gain an introduction to object-oriented programming through the use of the JavaScript language. Classes are held in the computer lab. The teacher either leads students through instructive examples or works with them as they develop their projects. Evaluation is based on: a final project (30%); small projects (20%); in-class exercises, which focus on team building and discussion (20%); quizzes, which are intended to test specific software and programming skills (15%); and homework, which is primarily to do project research, planning, and documentation (15%).

This course covers the fundamentals of programming and gives students an appreciation for the task of organizing and writing programs using methods and objects. While Java is the primary language used, JavaScript and HTML are employed to construct web pages. Most of the material is presented through in-class exercises and programming assignments. Many of these exercises are introduced to students through lecture and multimedia presentations. At least weekly, students work in small groups to use the introductory material to solve more complex problems. Programming assignments, which are completed in the computer lab, further extend the complexity of the problems to be solved. Students are evaluated (with approximate relative weight) through tests (45%), projects (35%), and semester examinations (20%). No previous computer experience is required.

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. This information is presented in several ways. About 50% of the material is introduced through lectures and multimedia presentations. At least weekly, students work in small groups to use the introductory material to solve problems and, in doing so, develop another 25% of the material. The final 25% of the material is covered in programming assignments, which are completed in the computer lab. Students are evaluated (with approximate relative weight) through unit tests and an Advanced Placement practice test (55%); homework, quizzes, and programs (35%); and a fall-semester examination (10%).
Prerequisite: Permission of the instructor.

This course provides an introduction to the field of computer science for students who have a strong interest in the subject and a solid background in Java programming. Students learn the guiding principles of object-oriented software design. They apply concepts such as abstraction, encapsulation, inheritance, and polymorphism to solve problems. Topics include algorithm design and analysis, programming principles, class hierarchy, and abstract data types. About 60% of the material is introduced through lectures and multimedia presentations. At least weekly, students work in small groups to use the introductory material to solve problems and, in doing so, develop another 15% of the material. The final 25% of the material is covered in programming assignments, which are completed in the computer lab. Students are evaluated (with approximate relative weight) through unit tests and an Advanced Placement practice test (55%), homework, quizzes, and labs (35%), and a fall-semester examination (10%).
Prerequisite: Advanced Placement Computer Science A or permission of the department.

This course is intended for students who have completed Advanced Placement Computer Science AB and wish to extend their knowledge of computer science while working independently on advanced projects of their own design. Topics may include machine architecture, assembly language, robotics, artificial intelligence, the uniform modeling language, operating system and networking theory, and client/server programming. Topics may change from year to year depending on advances in computer science as well as the interests and needs of the class. This information is presented in several ways. About 30% of the material is introduced through lectures and multimedia presentations. Other presentations, covering 30% of the material, are made by students. Students also work in small groups to develop software systems and robots to complete the remaining 40% of the material. Students are evaluated (with approximate relative weight) through projects (75%), quizzes (15%), and homework (10%).
Prerequisite: Advanced Placement Computer Science AB.

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(from the 2008-2009 Curriculum Guide)