Pre-algebra lays the foundation needed for success in algebra. In this class we study the underlying properties of calculation with the real numbers, with a special emphasis on order of operations, exponents and their properties, and translating from English into the language of mathematics. We introduce variables and learn to manipulate them in simple algebraic expressions and linear equations. Students entering this course should have computational mastery of addition, subtraction, multiplication, and division of integers as well as fractions.
It will also help to have mastered prime factoring of integers.
Algebra I: $400/semester
Wednesday 3:00-4:45 (full), Thursday 1:00-2:45
Our Algebra I course begins the transition from the focus on numbers to the study of variables and equations. In addition to expanding our ability to solve equations, we introduce the notion of functions and discuss ways to use them to model situations in the real world. We focus on the relationship between equations and functions, and how we can use graphs in order to better understand both. Students should enter this course with at least basic knowledge of algebraic expressions and the ability to solve simple linear equations.
Wednesday 9:00-10:45, Thursday 3:00-4:45
This course covers the breadth of Euclidean geometry, from basic shapes in two dimensions to the study of three-dimensional solids. We will cover properties of triangles and circles, coordinate systems, and applications of algebra to solve geometric problems in the real world. A strong emphasis will be placed on proof-writing and logic, as well as geometry in real world applications. Time permitted, we will also briefly introduce the basics of non-Euclidean geometry and geometry of higher dimensions. Students should have a solid Algebra I background and willingness to work hard for this course.
Algebra II: $400/semester
Wednesday 1:00-2:45, Thursday 9:00-10:45
Building on the material covered in Algebra I, this course continues the study of functions and how we analyze them. We will introduce rational functions, logarithms, conics, and extensively study the art of building new functions out of old. Content also includes an introduction to matrices and infinite series. Students should have completed Algebra I prior to beginning this course, but Geometry is not a strict prerequisite.
This course picks up where Algebra II leaves off, with a study of advanced functions. In particular, we will focus much of our time on understanding the basic trigonometric functions, their graphs, and how to use them to solve problems in the real world. We will begin analyzing functions using limits and behavior at extremes, setting the stage for the study of Calculus. Students should have successfully completed Algebra II and Geometry prior to the beginning of the fall semester.
AP Calculus: $400/semester
In this course we develop the tools of differentiation and integration, and we learn to use them to better understand functions, their graphs, and how they change. We study applications of Calculus techniques to complicated real world problems, including finance and engineering. In addition to preparing students for the AB calculus AP exam, this class sets a solid foundation for students who wish to go on to study math or science in college. Success in calculus requires mastery of all material through the end of precalculus.
Designed to give advanced math students a good taste of a college math major, this class covers a brought slice of the topics that one usually encounters in the third or fourth year of college. In addition to introducing students to the basics of topology, abstract algebra, and advanced proof writing, we will learn to typeset with LaTeX and put substantial focus on the softer skills of presentation and independent reading of textbooks. Enrollment in this class is by invitation only. If you're interested, please email Dr. Swann at before sending in enrollment information.