|
Participants will study topics in high school mathematics from a mature perspective. Topics include algebraic structures, vectors, complex numbers, and trigonometry. Connections to classroom practice will be included. Prerequisite: Math X464B (Perspectives on Functions 2)
INTRODUCTION TO TRIGONOMETRIC FUNCTIONS
Participants develop the radian system of angle measurement using circular objects and string. They find the ratios of the sides of special triangles, and they use these values to graph the sine, cosine, and tangent functions.
VECTORS
Participants use the polar and rectangular form of a vector. Participants add vectors, and use them to find map distance and direction.
PROJECTILE MOTION
Participants use vectors to represent position, velocity, and acceleration as they analyze data gathered from a ball tossing experiment.
ALGEBRAIC STRUCTURES: GROUPS
Participants learn about the properties of groups as they investigate the properties of the symmetries of a triangle under the operation of composition. They analyze various sets of numbers with an operation to determine if they are groups.
ALGEBRAIC STRUCTURES: RINGS AND FIELDS
Participants use modular arithmetic to investigate the properties of Groups, Rings and Fields. They relate these ideas to familiar number sets such as integers, and rational, irrational, and real numbers. They prove theorems using the field properties.
AN INTRODUCTION TO COMPLEX NUMBERS
Participants explore solutions to quadratic equations with complex roots. Participants learn to compute with complex numbers as they explore some interesting properties of them.
COMPLEX NUMBERS: POLAR FORM
Participants write complex numbers in rectangular and polar form. They perform operations with complex numbers using both rectangular and polar form. Participants learn to use DeMoivre's theorem to find powers and roots of complex numbers.
DIVISION
Participants use the division algorithm and the Euclidean algorithm to find the greatest common factors of numbers. Participants test various rules for divisibility and explain why they work.
Back to Course Descriptions | 
