The focus of this course is the foundational ideas of grades K-8 mathematics. The purpose is to engage prospective teachers in (re)discovering the real number system in order to develop a deep understanding of number meanings, representation, operations, algorithms, and properties. Through intuition and imagination, rather than rigidly following prescribed methods, students will explore models for arithmetic, consideration of children’s thinking about numbers, and investigations with technology.

This course investigates foundational ideas of grades K-8 mathematics. The focus is on thinking about mathematical concepts that are currently prominent in elementary schools from the perspective of teaching. Mathematical tasks include a deep analysis of concepts, consideration of children’s thinking, and investigations with technology. Topics include two and three dimensional geometry, transformations,area, volume, surface area, measurements, statistics, and probability.

For students with one or two years of high school algebra. This course is at the level of college algebra, but is not focused on algebra. It stresses application of mathematics in careers of non-scientists and in the everyday lives of educated citizens, covering basic mathematics, logic, and problem solving in the context of real-world applications.

Algebra review, functions and graphs, logarithmic and exponential functions, analytic geometry, trigonometric functions, trigonometric identities and equations, mathematical induction, complex numbers. Students completing this course are prepared to enter calculus.

Limits and continuity for functions of one real variable. Derivatives and integrals of algebraic, trigonometric, exponential, and logarithmic functions. Applications of the derivative. Introduction to related numerical methods.

Techniques of integration, numerical integration, and applications of integrals. Infinite series including Taylor series. Introduction to differential equations. Calculus in polar coordinates.

The calculus of vector-valued functions, functions of several variables, and vector fields. Includes vector operations, equations of curves and surfaces in space, partial derivatives, multiple integrals, line integrals, surface integrals, and applications.