Geometry

This course is not the typical geometry course offered in high schools. It is rather a direct study of the writings of Euclid, namely his volume of geometrical proofs: the Elements. Being the most widely published book in history other than the Bible, Euclid’s Elements is one of the foundational works of the Western intellectual tradition, and has been consistently studied and cherished by great thinkers throughout the centuries. The study of the Elements is unique in that it allows students to witness and discover the logical foundations of all mathematics. Typical math courses require students to memorize and apply mathematical algorithms to generate correct answers, even though the students may not know where these algorithms came from or why they work. With the Elements, however, students learn the “why” behind mathematical theorems, proving their truth from the ground up using their own logical reasoning. If the foundations of Algebra, Trigonometry, and Calculus are not understood from their origins in geometry, these subsequent mathematical pursuits will lack the integrating principles that lead to true understanding.

Algebra I

This algebra course is designed to assist sophomores in gaining a full understanding of the nature of algebra and to master the skill of this powerful mathematics. Many students are asked to learn algebra in middle school but many of them are not cognitively ready for the robust logic and nuanced symbolism of algebra. Therefore, many students do not learn to think algebraically nor do they understand power, beauty, and simplicity of the discipline. Instead many students learn tricks and therefore short circuit their mathematical understanding going forward. This course carefully explains the whys of the mathematics before we move on to hows of the algorithms of algebra.

Algebra II/ Trigonometry

Pre-Calculus

Calculus

This math course is built on the assumption that each student has mastered the topics in a year longalgebra course which ranges from algebraic transformations, linear equations, systems of equations, through the basics of quadratic functions. The Algebra II & Trigonometry course is partnered with our pre-calculus course to cover all essential mathematics which creates the foundation for our students to be successful in our honor level calculus or statistics courses.

While primarily a course in trigonometry, the broader purpose of precalculus is to give the student the broader foundation in mathematical reasoning and computation necessary to approach physics, calculus, and statistics their senior year. The course begins in Euclidean geometry, deriving the law of cosines from Ptolemy’s Theorem (from the Almagest) and similar-triangle theorems from Euclid’s Elements. The formulation of (composite) trigonometric functions allows an algebraic approach to solving trigonometric problems and the derivation of trigonometric identities. The end of the year sees the application of trigonometry to matrix algebra and an introductory discussion of sequences and series, proof by mathematical induction, and limits

This upper-level math course is built on the assumption that each student has mastered the topics in a comprehensive year-long pre-calculus course. Calculus is the mathematics of non-linear change. In calculusthe major topics of limits, derivatives, and integrals are fully developed and applied. This course is the culmination of the student’s study of algebra, trigonometry, and functions.