Topics in Algebra, Trigonometry, and Pre-Calculus

This is a need-based flexible-credit course leading up to standard college calculus. It serves several purposes: preparation for one-variable differential calculus, studying for standardized tests such as the GRE, brushing up basic quantitative skills, or just taking a break from writing opinion-dependent papers.

Topic One: Algebra and Analytic Geometry

• Polynomial Arithmetic
• Factoring Polynomials Part 1
• Factoring Polynomials Part 2
• Lines and Parabolas
• Quadratic Roots and Tangent Line
• Circles Centered at the Origin
• Circles and Completing the Square

Topic Two: Trigonometry and 3D Geometry

• Trigonometry with Right Triangles
• Problem Solving with Trig Values
• Trig Identities and the Law of Cosines
• Trigonometry with Circles
• Polar Coordinates
• Problem Session

Topic Three: Lots of Functions and Their Properties.

• Introduction to Functions
• Domain and Range (of polynomial and rational functions)
• Modeling with Linear Functions
• Basic Algebra with Functions
• Compositions of Functions
• Geometric Transformations of Functions
• Inverse Functions
• Trigonometric Functions

Other topics to consider: mathematical logic, discrete mathematics, Euclidean geometry