Academics: The Curriculum
Math
M-125 Algebra I
Year 1 unit
In this course, students expand their notion of a variable and connect it to algebraic and problem-solving techniques. This is a comprehensive course that lays the foundation for both Algebraic Geometry and Algebra II/Trigonometry. Topics studied include signed numbers, radicals and radical operations, linear equations, systems of linear equations, exponents, the quadratic formula, polynomials, and factoring. Students in this course learn to translate verbal statements into mathematical statements, clarify procedural questions, solidify arithmetic skills, and comprehend the abstraction of the coordinate plane. Class time is used for discussion, developing initiative in problem solving and perfecting study skills.
Open to: 9/10
M-225 Algebraic Geometry
Year 1 unit
This course uses a problem-based curriculum that enables students to investigate and prove geometric concepts. Topics include distance in a coordinate plane, the Pythagorean Theorem, angles, parallel and perpendicular lines, planes, vectors, properties of triangles, properties of quadrilaterals, regular polygons, transformations, congruence, similarity, right triangle trigonometry, circles, area, perimeter, volume, and surface area. Proficiency in basic algebra is expected and necessary. Geometry students are active learners, engaging the problem-solving skills learned in Algebra I. The course stresses the connections between algebra and the new geometric topics covered. Each student develops the practice of self-assessment so that she is better able to critique her understanding. Class discussion centers around problem sets and students employ graphing calculators, dynamic computer software, the Internet, and journals as tools in the learning process.
Prerequisite: Algebra I (M-125)
Open to: 9/10/11
M-315 Essential Topics in Functions and Trigonometry
Year 1 unit
This course is a one-year algebra and trigonometry course that satisfies the mathematics graduation requirement for juniors and seniors. Its syllabus is based on the mathematics SAT outline, and it includes topics to prepare students for mathematical applications at the college level. If recommended by the department, a student may follow this course with M-325. If M-315 is taken before the junior year, another year of mathematics must be taken to fulfill the graduation requirement. This course does not serve as a prerequisite for Advanced Math (M-450).
Prerequisite: Placement by recommendation of department
Open to: 10/11/12
M-325 Algebra II and Trigonometry
Year 1 unit
After a brief review of basic algebra concepts such as solving and graphing linear and quadratic equations, the course addresses new concepts such as functions, logarithms, rational functions, and trigonometry. Some concepts and mechanics of data analysis are included. To promote students’ development of original ideas, these topics are introduced from an applications perspective. At this level, students begin to reason independently and formulate questions based on insights into applications of the algebra previously studied. Functions introduce an abstract thought process, and challenging, open-ended problems foster independent work.
Prerequisite: Algebraic Geometry (M-225)
Open to: 9/10/11/12
M-410 The Heart of Mathematics I
Fall .5 unit Schettino
Wondering what there is in mathematics that is beyond algebra and trigonometry? Do mathematical puzzles and concepts inspire you? The Heart of Mathematics is based on the best-selling book, Coincidences, Chaos, and All that Math Jazz, co-authored by Professor Ed Burger. In this course, students work on problems that require techniques and thinking skills that pertain to many other subjects and real life. Students discuss mathematical games and contemplate our number system, the concept of infinity, and problems long considered “geometric gems.” This course is very different from any other math course. It involves substantial reading and writing, along with problem solving and open risk-taking.
Prerequisite: Algebra II and Trigonometry (M-325) for rising juniors or Essential Topics in Functions and Trigonometry (M-315) for rising seniors
Open to: 11/12
M-420 The Heart of Mathematics II
Spring .5 unit Schettino
This continuation of The Heart of Mathematics I covers intriguing topics in topology, graph theory, chaos theory, fractals, and probability and uncertainty. The year ends with students applying rigorous thinking skills to make decisions related to personal responsibility, public policy and resource management. The Heart of Mathematics I (M-410) is not a prerequisite, but is encouraged. An extensive project is required of students at the end of the semester.
This course does not satisfy the mathematics graduation requirement.
Prerequisite:Algebra II and Trigonometry (M-325) for rising juniors or Essential Topics in Functions and Trigonometry (M-315) for rising seniors
Open to: 11/12
M-450 Advanced Math
Year 1 unit
This elective course is designed for students who have completed the study of basic trigonometry and algebra. In Advanced Math, students are introduced to different courses of study in higher level mathematics. Topics include advanced trigonometry, vectors, applications to physics, functions, modeling, statistics, analytic geometry, series, and limits. The course assumes that students will employ effective questioning skills: not just procedural, but analytical. In addition, students apply a range of methods when problem solving. This course involves significant independent work, and students are responsible for assessing their progress, seeking help in the Math Learning Center as necessary.
Prerequisite: Algebra II and Trigonometry (M-325)
Open to: 10/11/12
M-500 Calculus
Year 1 unit
This course is designed for students looking for a moderately paced course in calculus. The course covers the traditional topics of differential and integral calculus with special emphasis on applications, and it prepares students well for college and/or continual study in mathematics. This course is not intended to prepare students for the AP examination.
Prerequisite: Advanced Math (M-450) and recommendation of the department
Open to: 11/12
M-540 Advanced Placement Statistics
Year 1.5 units
This course offers a thorough examination of data analysis, data production, and statistical inference. Topics include the normal distribution, correlation and regression, experimental design, sampling distributions, probability theory, confidence intervals, tests of significance, and the Chi-Square Test. Diverse areas such as economics, medicine, and politics are incorporated into discussions of statistical topics. Solution methods for the Advanced Placement exam and for assessments in this class employ technology. Also, students should expect significant reading, written analysis, and interpretation as parts of statistical inference. As with other AP courses, additional work is assigned over school vacations.
Prerequisites: Advanced Math (M-450) and recommendation of the department
Open to: 11/12
M-550 Advanced Placement Calculus AB
Year 1.5 units
This course prepares students for the AP Calculus AB exam. It offers a thorough exposure to differential and integral calculus. The course begins with a review of functions and their graphs, followed by derivative functions, limits, continuity, and the definite integral. Derivative rules and applications complete the study of differential calculus, and this is followed by further work with integrals and their applications. The course finishes with the topics of differential equations and slope fields. All students who take this course are expected to take the AP exam in May. As with other AP courses, additional assignments should be expected over school vacations., and summer work is required.
Prerequisites: Advanced Math (M-450) and recommendation of the department
Open to: 11/12
M-560 Advanced Placement Calculus BC with Additional Advanced Topics (AP optional)
Year 1.5 units
This advanced elective course deals with single-variable calculus and includes all the topics of AP Calculus AB plus additional topics in differential and integral calculus (including parametric, polar, and vector functions) and series (including Taylor polynomial approximation and McClaurin Series). It is equivalent to more than a year of calculus at most colleges and universities. Because of this, it moves at a very rapid pace and requires much independent work. Although a textbook is used for practice problems, the course is run in a seminar style, emphasizing students’ discussion of problems. Algebraic, numerical, and graphical representations are employed throughout the course. Enrichment topics are covered as well, including advanced differential equations, hyperbolic functions, polar equation derivatives, and surface area of solids of rotation. As with other AP courses, additional assignments should be expected over school vacations. Students who have not completed AP Calculus AB (M-550) are required to complete work during the summer and take the AP Calculus BC exam. All other students are encouraged, but not required to sit for the AP BC exam.
Prerequisites: AP Calculus AB (M-550) or Calculus (M-500) and/or recommendation of the department
Open to: 11/12
