The mathematics curriculum is built around a core sequence of eight trimester courses: three of elementary algebra, two of geometry, one of intermediate algebra, and two of precalculus topics. The completion of these eight trimesters will satisfy diploma requirements, but two additional trimesters are required before a student may enter calculus. Placement of new students in the appropriate first course is made by the department, which considers the record in previous schools, the results of a self-administered placement test in elementary algebra that is sent to newly admitted students in the spring, and the course program chosen by the entering student.

Typically students entering with no prior study of algebra start with Mathematics 100; those with a partial year of algebra enter Mathematics 150. Students entering with a full year of algebra typically start with Mathematics 210. If the results of placement testing indicate a need for algebra review, then students who have not taken geometry start with Mathematics 190 and continue to Mathematics 210 in the winter.

New students who have taken one year of elementary algebra and one year of geometry will satisfy diploma requirements by taking Mathematics 320, 330, and 340. Those with a strong background in intermediate algebra may enroll directly in Mathematics 330. On the basis of our placement test, Mathematics 250/4 may be required for some students before Mathematics 330 and 340.

The department recognizes that it is appropriate for some students to accelerate their study of mathematics and consequently offers bypass exams in Mathematics 320, 330, 360, and 580. These exams are usually, although not always, taken after summer study. A student can prepare for a bypass exam by taking a summer school course, by being tutored, or through self-study. Note that no credit for any summer school course is automatically granted. All students must demonstrate proficiency on a departmental exam. Permission of the department must be obtained before attempting to bypass any other course.

Students who plan to take a College Board SAT II Subject Test in mathematics should schedule the exam at the test date as close to the end of the appropriate math course as possible. Students who plan to take the SAT II Math Level IIC should do so after finishing Mathematics 360; those who plan to take the Level IC exam should do so after finishing Mathematics 340.

The majority of students take courses beyond the required level. Mathematics 350 and Mathematics 360 complete the precalculus sequence. The department offers many electives beyond precalculus, some of which lead up to and beyond Advanced Placement examinations of the College Board in calculus, statistics, and computer science.

Every student enrolled in a mathematics course must have a TI-83 or TI-84 graphing calculator. No other models will be used or supported by the department. Students may purchase TI-84 calculators by check or cash from the Phillips Academy Department of Mathematics. The purchase price for scholarship students is less than for others. No calculator that has CAS (Computer Algebra System) capabilities, including but not limited to the TI- 89, TI-92, and TI-Voyager, may be used for departmental exams.

COURSES LEADING TO SATISFACTION
OF THE DIPLOMA REQUIREMENT

MATH-100/0 Elementary Algebra
(a yearlong commitment)
Five class periods. A yearlong course for students who have had little or no algebra. Stress is placed on an understanding of the elementary structure and language of the real number system, on the manipulative skills of simplifying expressions and solving first- and second-degree equations, and on the study and graphing of polynomial functions. Work is done with word problems, inequalities, irrational numbers, and right triangle trigonometry. Prerequisite: None.

MATH-150/4 Elementary Algebra (T2)
(a two-term commitment)
Five class periods. A two-term course for those new students whose knowledge and skills are not strong enough to enter the one-term Algebra Review or Geometry. Prerequisite: A half to a full year of algebra.

MATH-190 Algebra Review
(F)
Five class periods. A course for students who enter with a full year of algebra and whose knowledge and confidence indicate they need a brief review of algebra. Prerequisite: A full year of algebra.

MATH-210 Geometry
(F-W-S)
Five class periods. A course for students who have had a strong ninth-grade algebra course but little or no geometry. This course is a thorough and systematic presentation of standard synthetic Euclidean geometry. Emphasis is placed on the need for precision and clarity in the writing of formal proofs. Prerequisites: A complete course in elementary algebra and good algebraic skills.

MATH-220 Geometry
(F-W-S)
Five class periods. This course continues the work of Mathematics 210, with increased emphasis on the algebraic and numerical aspects of geometry. Prerequisite: Mathematics 210.

MATH-250/4 Algebra Consolidation (T2)
(a two-term commitment)
Five class periods. A two-term course primarily for new students who have completed a yearlong geometry course but whose algebraic skills are not strong enough to place them in Mathematics 320 or 330. The course begins with a comprehensive review of elementary algebra and concludes with topics in intermediate algebra (as listed in the course description ofMathematics 320). Students with a (T2) grade of “4” or higher in this course enter Mathematics 330 in the spring. Students with a (T2) grade of “3” or below inMathematics 250 enter Mathematics 320 in the spring.

MATH-310/0 Geometry and Precalculus
(a yearlong commitment)
Five class periods. A yearlong course for extremely able entering students who have completed with distinction an intermediate algebra course but have not completed a yearlong geometry course. The course covers Euclidean geometry (both synthetic and coordinate) and elementary functions. This course completes the diploma requirement and prepares students to enroll in Mathematics 350. Prerequisite: Credit for one year of elementary algebra and one year of intermediate algebra.

MATH-320 Intermediate Algebra
(F-W-S)
Five class periods. For returning students, this course is taken after Mathematics 220, Geometry. Topics include sets; properties of real numbers; factoring; fractional and negative exponents; radicals; absolute value; solutions of linear, quadratic, and radical equations; and word problems. In addition, students are introduced to the more advanced features of the TI-83 Plus graphing calculator. Prerequisite: Mathematics 220 or its equivalent.

MATH-330 Precalculus
(F-W-S)
Five class periods. An exploration of relations and functions with the TI-83 Plus graphing calculator. The uses of graphs and tables to solve equations, systems of equations, and inequalities are introduced. Students have the opportunity to collect data and create functions to describe the behavior. Prerequisite: Mathematics 320 or its equivalent.

MATH-340 Precalculus
(F-W-S)
Five class periods. An exploration of functions in greater detail and with more abstraction. Multiple representations of a function—as a table of values, as a graph, and as an algebraic rule—are a central theme. Elementary functions (polynomial functions and inverse functions, in particular) and their transformations, compositions, and applications are emphasized. Completion of this course satisfies the diploma requirement. Prerequisite: Mathematics 330 or its equivalent.

Entering Seniors whose prior work has not satisfied the diploma requirement must complete Mathematics 340 or Mathematics 400.

MATH-400 Elementary Functions II
(F)
Five class periods. A course primarily for entering Seniors who need to satisfy the diploma requirements in mathematics. The course focuses on functions and their applications, including polynomial, exponential, logarithmic, circular, and trigonometric functions. Strong emphasis is placed on graphing and the use of graphs as an aid in problem solving. Prerequisite: Credit for three years of high school mathematics or permission of the department.

ELECTIVE COURSES

Only courses with sufficient enrollment will be
given.

MATH-350 Precalculus
(F-W-S)
Five class periods. This course focuses on rational, exponential, and logarithmic functions. The TI-83 Plus graphing calculator is used for continued study of non-linear data sets with special attention to sets that grow exponentially and logarithmically. Elementary work with arithmetic and geometric sequences is included. Prerequisite: Mathematics 340 or its equivalent.

MATH-360 Precalculus Trigonometry
(F-W-S)
Five class periods. An exploration of the circular functions: sine, cosine, and tangent. Topics include right triangle trigonometry, simple harmonic motion, applications and proofs of trigonometric identities, polar and parametric graphs, and complex numbers. Mathematics 360 is the final course in the precalculus sequence. Prerequisite: Mathematics 350 or permission of the department.

MATH-410 Probability
(W)
Four class periods. Includes sample spaces, counting problems, sampling, conditional probability, random variables, expected value, variance, standard deviation, binomial and normal distributions. The computer is used on applications that are too time-consuming to performby hand and to simulate experiments for which there are no models. Prerequisite: Mathematics 350 or its equivalent.

MATH-470 Discrete Mathematics
(W)
Four class periods. This course covers selected topics of discrete mathematics and their applications to engineering, computer science, and the real world, including combinatorics, sets, mathematical logic, recursion, graphs, and networks. Prerequisite: Mathematics 360 or its equivalent.

MATH-480 Analytic Geometry
(W)
Four class periods. This course is an extension of earlier work on lines and curves in the plane. It includes extended locus problems and further study of the conic sections: parabolas, ellipses, and hyperbolas, and their simple rotations. The course includes an introduction to the algebraic description of three-space: vectors, curves, planes, simple surfaces, and their intersections. Prerequisite: Mathematics 360 or its equivalent.

MATH-500/5 Advanced Mathematics (T2)
(a two-term commitment)
Four class periods. Primarily for Seniors, but open to other students who want to continue the study of functions and get an introduction to calculus. The calculus topics will include limits, problems of optimization, rates of change, areas under curves, and lengths of curves. Prerequisite: Mathematics 360, Mathematics 400, or an equivalent course in trigonometry and elementary functions.

MATH-510 Calculus
(F)
Five class periods. Primarily for Seniors. Topics covered include a review of functions and graphing, limits, continuity, determination of derivatives and integrals from graphs of functions (not from their formal definitions). Prerequisite:Mathematics 360 or the equivalent, or Mathematics 500.

MATH-520/5 Calculus (T2)
(a two-term commitment)
Five class periods. This is a continuation of Mathematics 510. Topics covered include the definite integral, the Fundamental Theorem of Calculus, further differentiation of functions, techniques and applications of integration. The most successful students will be in a position to do the AB Advanced Placement examination in calculus. Prerequisite: A grade of “3” or higher in Mathematics 510 or permission of the department.

MATH-530 AP Statistics I
(F)
Five class periods. The first term of a yearlong sequence that prepares for the Advanced Placement Examination in Statistics. This term primarily covers the exploratory analysis of data, making use of graphical and numerical techniques to study patterns, and developing plans for data collection of valid information. Prerequisite: Mathematics 360 or permission of the department.

MATH-530/5 AP Statistics II (T2)
(a two-term commitment)
Five class periods. A continuation of Mathematics 530, finishing the syllabus for the Advanced Placement examination in May. Topics include probability as the tool for producing models, random variables, independence, normal distribution, simulation, sampling, statistical inference, confidence intervals, and tests of significance. Prerequisite: A grade of “3” or higher in Mathematics 530.

MATH-560 AB Calculus I
(S)
Five class periods. This is the beginning of the four-term calculus sequence that, together with Mathematics 570, covers the syllabus of the AB Advanced Placement examination. This term focuses primarily on differential calculus: limits, continuity, derivatives, and applications of derivatives. Some integral calculus may be covered if time permits. Graphical, numerical, and analytic methods will be used throughout the course. Prerequisite: Mathematics 360 or its equivalent, with no grade lower than a “3” in Mathematics 340, 350, and 360.

MATH-570 AB Calculus II
(F)
Five class periods. This course continues the work of Mathematics 560 in preparation for the AB Advanced Placement examination. Topics include integration and applications of integral calculus. Prerequisite: Mathematics 560 completed with at least a “3” or Mathematics 580.

MATH-570/5 AB Calculus II (T2)
(a two-term commitment)
Five class periods. A continuation of Mathematics 570, finishing the syllabus for the AB Advanced Placement examination. Prerequisite: Mathematics 570 completed with at least a “3” or Mathematics 590.

MATH-575/0 Accelerated AB Calculus
(a yearlong commitment)
Five class periods. A yearlong course in calculus that begins only in the fall. Satisfactory completion of this course prepares students for the College Board AB Advanced Placement examination. This course does not prepare students for Mathematics 650. This course may require more than the standard four to five hours of homework per week. Prerequisite: Mathematics 360 or its equivalent, with no grade lower than a “4” in Mathematics 340, 350, and 360. Those students who do not meet this requirement should take either Mathematics 510 or 560.

MATH-580 BC Calculus I
(S)
Five class periods. This is the beginning of a four-term calculus sequence recommended for students who are well prepared in precalculus. With Mathematics 590 it covers the syllabus of the BC Calculus Advanced Placement examination. Topics covered include primarily differential calculus: limits, continuity, derivatives, the Chain Rule, related rates, and the Mean Value Theorem. Some integral calculus is also covered. Graphical, numerical, and analytic methods are used throughout the course. Prerequisite: Mathematics 360 or its equivalent, with no grade lower than a “4” in Mathematics 340, 350, and 360. Those students who do not meet this requirement should either takeMathematics 510 or 560.

MATH-590 BC Calculus II
(F)
Five class periods. This course continues the work ofMathematics 580 in preparation for the BC Advanced Placement examination. Topics include integration and applications of integral calculus. Prerequisite: Mathematics 580 completed with a grade of at least a “4,” or departmental permission.

MATH-590/5 BC Calculus II (T2)
(a two-term commitment)
Five class periods. A continuation of Mathematics 590, finishing the syllabus for the BC Advanced Placement examination. Prerequisite: Mathematics 590 completed with a grade of “3” or better.

MATH-600/0 Accelerated BC Calculus
(a yearlong commitment)
Five class periods. A yearlong course in calculus that begins only in the fall. Enrollment is limited to the most able mathematics students. Satisfactory completion of this course prepares students for the College Board BC Advanced Placement examination. This course may require more than the standard four to five hours per week of homework. In order to qualify for this course, returning students must perform satisfactorily on a special precalculus qualifying examination given the previous spring term. Prerequisite: Mathematics 360 or its equivalent, with no grade lower than a “5” in Mathematics 340, 350, and 360, plus departmental permission and demonstrated excellence on entrance tests.

MATH-630/1 Honors Mathematics
MATH-630/2 Seminar
MATH-630/3
Four class periods. Each term’s seminar will be devoted to one topic, which will be developed in depth. The term’s topic will be announced the previous term and might be Topics in the History of Mathematics; Numerical Methods and Approximations; Non-Linear Dynamical Systems—Instability, Chaos, and Fractals; Complex Analysis; Abstract Algebra—Groups, Rings, and Fields; Mathematical Models in the World Around Us; Topics in Discrete Mathematics; or Number Theory. Participants need to be prepared to work on one topic in great detail and, in some seminars, to work as part of a team on the solution of problems. Prerequisite: Three terms of calculus or departmental permission.

MATH-650 Linear Algebra
(F)
Four class periods. For students of demonstrated ability and interest. Vectors, lines, and planes in space, and an introduction to linear algebra, includingmatrices, Gaussian elimination, vector spaces, and eigenvectors. Prerequisite: Mathematics 590 or Mathematics 600, and departmental permission.

MATH-650/5 Calculus of Vector Functions (T2)
(a two-term commitment)
Four class periods. A continuation of Mathematics 650 covering functions of many variables, partial differentiation, gradients, vector valued functions, multiple integration and its applications, line integrals, and Green’s Theorem. Prerequisite: Mathematics 650.

The mathematics department teaches introductory and advanced computer science courses and supports some more advanced independent study.

COMP-310 Business Applications and Web Page Design
(F-W-S)
Five class periods. This one-term course exposes students to using a personal computer with business productivity applications such as Microsoft Excel and PowerPoint, as well as to the design of simpleWeb pages. The first half of the course will cover the design of spreadsheets (data entry, formulas and functions, graphing, databases) and the creation of presentations (templates, inclusion of graphics and data, animation). After an overview of the hardware and software architecture of a PC and the Web to start the second half of the class, students will learn the HTML language, allowing them to design their own Web pages. This course does not qualify a student for COMP-500. Prerequisite: None.

COMP-350 Introduction to
Programming and Computer Science
(F-W-S)
Five class periods. This one-term course introduces students to computer hardware and software, and then focuses on the fundamentals of programming using the Java language. The course will cover Java syntax and style, data types, conditional statements, and loops. It also will introduce the concepts of objectoriented programming, relating them to Java classes, fields, and methods. Students will learn how to write and test short programs, design simple algorithms, and use software development tools. A grade of “4” or higher in this course qualifies a student for COMP-500 (AP Computer Science I). Prerequisite: Enrollment in Math 210 or demonstration of some degree of abstract thinking and formal logical reasoning.

COMP-500 Advanced Placement Computer Science I
(F)
Five class periods. The first term of a yearlong course in algorithms, object-oriented programming, and data structures, guided by the course description of the College Board’s AB-level Advanced Placement exam in computer science. The course covers Java language syntax and style, classes and interfaces, lists and iterators. This course may require more than the standard four to five hours per week of homework. Prerequisite: A grade of at least “4” in COMP-350 or permission of the department.

COMP-500/5 Computer Science (T2)
(a two-term commitment)
Five class periods. This course is the continuation of COMP-500 in Java. The emphasis is on data structures and the design of larger programs. This course completes the preparation for the AB-level Advanced Placement exam in computer science. The students will study abstract data types (stacks, queues, binary trees, priority queues, etc.), recursion, and algorithms (searching, sorting, hashing, etc.). The course may require more than the standard four or five hours per week of homework. Prerequisite:COMP-500.

COMP-630 Advanced Topics in Computer Science
(F-W-S)
Four class periods. This class offers students with experience and advanced knowledge of computer science the opportunity to explore specific topics beyond the College Board’s AP curriculum. Topics will vary from year to year and may include Graphical User Interface design, introduction to computer graphics, or introduction to database design. This course may require more than the standard four or five hours per week of homework. Prerequisite: A grade of at least “5” in COMP-500 or permission of the department.