US Mathematics

Advanced Topics in Mathematics is a one-semester course, which follows Multivariate Calculus. Selected by the students and the instructor, the topic for the semester will be one of the following: Linear Algebra, Differential Equations, Cryptography, Number Theory or Game Theory.

Algebra I emphasizes algebraic language, structure, concepts, and skills needed for success in future math courses.  Topics covered include variables in polynomials and number sequences; graphing one and two variable equations and inequalities; algebraic functions and problem-solving; systems of equations and inequalities; exponents and radicals.

Algebra II is designed to reinforce and extend the concepts presented in Algebra I. Topics include solutions to all algebraic functions as well as their graphical analysis. Polynomials and the Fundamental Theorem of Algebra are studied. The conic relations are studied and presented in graphical form. 

All topics presented in Algebra II are covered in greater depth and at an accelerated pace. Sequences and series; matrix and linear algebra; statistics; probability; and exponential and logarithmic functions are introduced.

Analysis Honors is an advanced study of precalculus. The topics are the same as in Precalculus Honors but include the study of: polar coordinates; complex numbers; analytic geometry; matrix algebra; sequences and series; basic probability and statistics; and limits and derivatives. This course is designed to prepare students for Calculus AP (BC).

The curriculum for AP Calculus (AB) is designed by the College Board. Our purpose is to prepare students for the AP exam so that they may earn credit for the first semester of college-level calculus. Presentation of the material includes the traditional approach to the study of calculus and the more recent reform of using technology to enhance the understanding of calculus. Concepts of differential and integral calculus are developed through an analytic, graphical and numerical presentation; emphasis is on applications.

The curriculum for AP Calculus (BC) is designed by the College Board. Our purpose is to prepare students for the AP exam so that they may earn credit for a full year of college-level calculus. The BC course includes all of the topics of the AB course and extends the applications to include Taylor series, vector functions and parametric and polar curves.

The curriculum for AP Statistics is designed by the College Board. Our purpose is to prepare students for the AP exam so that they may earn credit for the first semester of an introductory, non-calculus-based, college statistics course. Three big ideas serve as overarching concepts that run throughout the course: variation and distribution; patterns and uncertainty; data-based predictions, decisions, and conclusions. Topics covered include selecting statistical methods; data analysis; experimental and sampling design; regression analysis; probability and simulation; confidence intervals; and hypothesis tests.

Calculus Honors covers the fundamental concepts of differential and integral calculus but is less rigorous than the AP courses. Initially, concepts and applications are introduced by study of the algebraic functions; later, the transcendental functions are presented. Emphasis is on intuitive understanding of calculus, not on formal proof. Technology is used whenever it enhances the study of the concepts.

The Discrete Math course is one distinct semester and may be followed in the spring by Probability and Statistics. The two semesters are independent, as Discrete Math is a stand-alone course and not a pre-requisite for the second-semester Probability and Statistics course. Students work in small groups or individually to solve theoretical and real-life problems, communicate useful mathematical reasoning and employ technology to assist in decision-making. Topics covered include: election theory; fair division; graph theory including circuits, paths, trees and graph coloring; counting techniques and basic probability theory.

Geometry is presented as a formal deductive process. Students study basic definitions and postulates and derive theorems. Student-designed proofs are emphasized in the first semester. The physical attributes of two- and three-dimensional figures are studied. Problem solving includes the proper use of algebraic principles and includes irrational numbers. This Euclidean approach includes congruence, similarity, parallelism, perpendicularity and right-triangle trigonometry. In the honors-level course, all topics are covered in greater depth and at an accelerated pace; this course also extends the formal proof throughout both semesters.

Multivariate Calculus is a one-semester course completing the standard three-semester calculus sequence. It is open to students who have completed Calculus AP (BC). Topics covered include basic vector calculus, partial derivatives, multiple integrals, line integrals and surface integrals. The course ends with a discussion of topics such as Green’s, Stokes’ and Divergence Theorems.

Precalculus is designed to develop a sound understanding of the topics in algebra and trigonometry needed for success in later courses, particularly the study of calculus. Additional topics include exponential and logarithmic functions as well as solving systems of equations through matrices; probability and statistics are introduced. Students become proficient in using the TI graphing calculator.

Precalculus Honors is a mid-level honors course emphasizing problem solving and analytical skills. Concepts explored include function theory and extensive graphing. The transcendental functions such as trigonometric, inverse trigonometric, exponential and logarithmic functions are studied in depth with an emphasis on graphing.

Probability and Statistics is a one-semester course that introduces the basic concepts of probability and descriptive statistics and their applications to data analysis. Topics include: selecting statistical methods; data analysis; experimental and sampling design; regression analysis; conditional probability; binomial and Normal distributions. Emphasis is placed on understanding key concepts and not on memorizing complicated formulas. Technology is used extensively throughout the course.