Description

An advanced perspective on some of the core mathematics underlying high school mathematics courses. Topics include number systems, functions of one variable, equations, inequalities, trigonometric functions, curve fitting, and polynomials. The course includes an analysis of alternate approaches to mathematical ideas and problems, and makes connections between ideas that may have been studied separately in different high school and college courses.

Prerequisites

MATH141 and MATH140; and must have completed one 400-level MATH course (not to include MATH461, 478, and 480's).

Topics

What is meant by "Advanced Perspective"

Average problems

Mixture problems

Number systems

Decimal representation

Rationals & decimals: Period, delays

Countability

Complex numbers: Operations, Polar form, Exponential form, product, quotient, powers, DeMoivre's Theorem

Functions and equations

Catching up problem--Analysis

Properties of functions

Composition, inverse

Limit behavior: Classic box problem

Data analysis: Linear and exponential regression (Fathom)

Trig functions and the unit circle

Definitions

Properties (proofs)

Identities

Law of Sines, Cosines: Law of Sines and a geometry proof

Curve fitting

Linear and exponential regression

Equality, inequality

The solving process

Solving inequalities: Table of signs, Inequalities and increasing or decreasing functions

Averages of speeds (connection to different types of means)

Solving equations with cups and cubes, algebra tiles

Polynomials (Geller notes)

Division algorithm for Polynomials

Unique prime factorization for polynomials

Synthetic division

Descartes' Rule of signs

Factorization theorems, including Eisenstein's Irreducibility Criterion