## Foundation I

This course is designed for beginners in mathematics. We start from counting with whole numbers and study the basic operations and types of numbers. The course emphasizes intuitive visualizations and technical algorithms to compute with numbers. We will learn about various forms of numbers and how to transfer ideas between them.

## Foundation II

The purpose of this course is to study the pattern of proportions and its ubiquity in everyday life. Students will build a practical toolkit and learn the ideas of proportions essential for algebra and beyond.

## Foundation III

This course introduces the concepts of geometry. We begin with the Euclidean concepts of two and three dimensional geometric objects along with their measurements of segments, angles, perimeter, area, and volume. Then we move to the Cartesian coordinate system and begin the connection of algebra and geometry.

## Algebra I

This course begins the transition from concrete numbers to unknown quantities represented by symbols. Students will learn to formulate and solve symbolic equations from verbal information. We will study the fundamental equations of lines and parabolas and explore connections of algebra and geometry.

## Algebra II

In this course we continue the connections between algebra and geometry as well as develop the notion of functional relation between quantities. We will study arbitrary degree polynomials and general functions.

## Algebra III

In this course we apply symbolic algebra to summations of sequences of numbers and geometric transformations.

## Computational Math I

In this course students will learn computational methods of a geometric nature. Logarithms will be introduced to solve equations involving exponents and study problems of growth and decay. Students will learn geometric methods with complex numbers and computational methods of trigonometry.

## Computational Math II

This course covers computational methods of an algebraic nature. Students will learn advanced topics about algebraic solutions of equations not covered in standard courses.

## Computational Math III

This course covers computational methods useful for engineering and computer science.

## Analytic Thinking I

In this course students will learn about logic systems and concepts of infinity. Notions such as limits and convergence are fundamental to the study of calculus and will be studied in a variety of contexts. Students will learn how to write proofs and construct logical arguments.

## Analytic Thinking II

In this course students will learn about logic systems and concepts of infinity. Notions such as limits and convergence are fundamental to the study of calculus and will be studied in a variety of contexts. Students will learn how to write proofs and construct logical arguments.

## Analytic Thinking III

This course is about understanding approximate errors of computation and inequalities. These topics are important to understand the results of computing tools and are used throughout calculus to calculate bounds and limits.

## Calculus I

In this course we study the basic objects of calculus: derivatives and integrals. The course emphasizes physical motivations and intuitive understanding of the concepts.

## Calculus II

This course focuses on the technical aspects of calculating derivatives and integrals. Students will master the technical machinery introduced in part I.

## Calculus III

This course covers applications of calculus to problems of physics and ordinary differential equations. Students will apply theoretical knowledge to analyze a variety of physical systems.

## Mathematical Methods I

This course is a standard course in vector calculus to be taken after a course in calculus. The course begins with a study of vector geometry before turning to multiple integrals.

## Mathematical Methods II

This course is a standard course in vector calculus to be taken after a course in calculus. The course begins with a study of vector geometry before turning to multiple integrals.