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.
Math 140-141 and one 400 level Math course.
What is meant by "Advanced Perspective"
Rationals & decimals: Period, delays
Complex numbers: Operations, Polar form, Exponential form, product, quotient, powers, DeMoivre's Theorem
Functions and equations
Catching up problem--Analysis
Properties of functions
Limit behavior: Classic box problem
Data analysis: Linear and exponential regression (Fathom)
Trig functions and the unit circle
Law of Sines, Cosines: Law of Sines and a geometry proof
Linear and exponential regression
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
Descartes' Rule of signs
Factorization theorems, including Eisenstein's Irreducibility Criterion