Full Year Courses
Mathematic courses in the 9th Grade explore algebra, geometry, and the connections between the two. Throughout, there is an emphasis on problem solving, reasoning, and proof. Students are sectioned by interest and ability, with the different classes varying in pace and level of abstraction. Topics for more advanced sections include Euclidean geometry and unit-circle trigonometry. Topics for all 9th Grade sections include algebra, coordinate geometry, systems of equations, trigonometry, quadratic functions, and combinatorics.
Students expand upon the understanding of algebra and geometry gained in Math 9. Students will explore exponential and logarithmic functions, combinatonics, sequences and series, graphical transformations, polynomials and rational functions, circular motion and the trigonometric functions, trigonometric identities, complex numbers, and begin the study of infinitesimal processes. Throughout the year students also develop their ability to write proofs and work on a variety of contest problems to broaden their perspective on problem-solving.
Math 10-2, Math 10-3, math 10-4
These courses examine algebra, geometry, and discrete mathematics in greater depth than the previous year, with a continuing emphasis on developing students’ ability to solve problems through a variety of approaches. Topics include graph theory, geometric sequences and series, radicals and laws of exponents, exponential functions, polynomial functions, and synthetic geometry.
Prerequisite: Math 10-1 or permission of current math teacher.
Concepts and applications of differential and integral calculus are presented. For juniors, a month-long final project, requiring considerable independent work, concludes the course. Students who complete the course successfully are prepared to take the Advanced Placement Calculus AB exam.
Math 11-2, Math 11-3, Math 11-4
These courses emphasize mathematical modeling and may include the following areas: algorithms, logarithms, trigonometric functions, transformations of functions, trigonometric identities, probability and counting methods, and/or statistics.
Advanced Calculus (Acc)
In Calculus, students were introduced to the limit as a way to study the infinite and the infinitesimally small. They used the limit to develop the integral and the derivative. In Advanced Calculus, students explore the concept of the limit in more depth and generality, applying it to the study of sequences and series and providing more applications of derivatives and integrals. New techniques for calculating integrals are explored. Topics may include differential equations, polar coordinates, vectors, calculus in three dimensions, applications of Taylor series to differential equations, the formal definition of the limit, and/or point-set topology, depending on interest. This course reaches beyond the scope of the Advanced Placement Calculus BC exam. Although not all topics on the exam may be covered, students who wish to do some extra work and take the exam should have a good foundation upon which to build.
fundamentals of complex analysis
Prerequisite: an excellent foundation in advanced calculus and an introduction to metric spaces, and permission of the department.
Complex analysis is one of the most beautiful and complete theories in all of mathematics. It is both elegant and powerful. After gaining a strong foundation in complex numbers and analytic functions, students will study elementary functions, Cauchy’s theorem and complex integration, series representation of analytic functions, introductory residue theory, and close with a study of beautiful conformal mappings and Moebius transformations.
introduction to knot theory
Knot theory — the mathematical theory of knots — is a fascinating and hands-on subject that can start from simple algebraic and geometric ideas and move to deep results and open questions in topology and mathematical modeling. Topology, one of the major branches of advanced mathematics, is an exciting, visual, sophisticated topic known for its mathematical beauty and for its surprising applications to modern biology, chemistry, physics, and engineering. One example from this course will show how modeling DNA structure with knot theory has led to some remarkable insights into how enzymes manipulate the topological structure of DNA. The class will begin by defining a knot, because if students do not know what is a knot and what is not a knot, then all their knot effort will be for naught. The main text for this class will be The Knot Book by Colin Adams.
Fall Semester Courses
Discrete Mathematics I
Discrete Mathematics is a contemporary branch of mathematics that focuses on problems with countable outcomes—this is a change from primarily studying algebra, geometry, or trigonometry. This course focuses on voting methods, apportionment, estate division, and graph theory. The course concludes with a study of matrix applications to economics and population growth.
Functions and Calculus I
Prerequisite: Math 10-1, 11-2, or permission of the current mathematics teacher.
Students begin by considering the “tangent line problem” and go on to study limits and develop a definition of the derivative, eventually applying derivative to real-life problems. Along the way, they examine polynomial and rational functions, using the language and techniques of calculus to help understand the graphs of these functions.
Students are introduced to the four key components of data exploration: observing patterns and departures from patterns, planning a study (deciding what and how to measure), anticipating patterns (producing models using probability and simulation), and statistical inference (confirming models).
Spring Semester Courses
Discrete Mathematics II
Discrete Mathematics II explores graph theory, combinatorics, and probability. (Note: Discrete Mathematics I is not a prerequisite.)
Functions and Calculus II
Prerequisite: Functions and Calculus I.
Students continue to use the lens of calculus to study functions and their graphs. Topics may include optimization problems, related rate problems, the area under a curve, the definition of an integral, and the Fundamental Theorem of Calculus.
Prerequisite: Statistics I.
Students explore statistical inference, with an emphasis on estimating the parameters of a population distribution and testing hypotheses about a population parameter. The probability models used in these inference situations are the normal distribution (bell curve), the t-distribution, and the chi-square distribution. Depending on time and interest, students may conduct a project in which they collect and analyze data.