## Full Year Courses

### Math 9

#### Grade: 9

**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.

### Math 10-1

#### Grade: 10

Students expand upon the understanding of algebra and geometry gained in Math 9. Students will explore exponential and logarithmic functions,

### Math 10-2, Math 10-3, math 10-4

#### Grade: 10

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

### Calculus (Acc)

#### Grades: 11-12

*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 ** **

#### Grade: 11

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)

#### Grade: 12

*Prerequisite: Calculus*

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

#### Grades: 10-12

*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

### introduction to knot theory

#### Grades: 10-12

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.