This is a list of all courses offered by the Math Department.  Not all courses are offered each year.  What is provided is a general description of the courses and the prerequisites.  The actual content may vary.

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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

Math 140-141 and one 400 level Math course.

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