• logic statements
• variables
• operations on sets and statements
• conditional statements and converses
• negations
• complements
• truth tables

II. Ordered Fields

• axioms for fields
• proofs
• indirect proofs
• axioms of order
• absolute value
• subsets of the real numbers

III. Mathematical Induction and Sequences and Series

• induction
• sequences and series
• arithmetic progressions
• geometric progressions
• the Binomial Theorem
• limits
• infinite geometric series

IV. Vectors

• ordered pairs and points
• displacements
• vector addition
• norms
• scalar mutiplication
• inner products
• parallel and perpendicular vectors
• components

V. Functions

• relations
• functions
• function arithmetic
• polynomials
• synthetic division
• the Factor Theorem
• rational roots
• bounds
• Descartes' Rule
• graphs of polynomials

VI. Complex Numbers

• field reducibility
• addition of complex numbers
• multiplication of complex numbers
• square roots
• Fundamental Theorem of Algebra

VII. Exponents and Logarithms

• rational exponents
• exponential functions
• composition of functions
• inverses of functions
• logarithms in base 10

VIII. Probability

• sample spaces
• addition of probabilities
• multiplication of probabilities
• permutations
• combinations
• probability distributions
• expected value

Semester II - Analytic Geometry

IX. Basic Concepts

• points, lines, and graphing
• slope
• divisions of line segments
• analytic proofs
• functions
• equations and graphs

X. Lines and Circles

• first degree equations
• intersections of lines
• directed distance
• families of lines
• circles
• families of circles
• translation of axes

XI. Conics

• parabolas
• ellipses
• hyperbolas

XII. Polar Coordinates

• graphing in polar coordinates
• relating rectangular and polar coordinates
• polar equations of lines and circles
• polar equation of conics
• intersections of polar coordinate graphs

XIII. Parametric Equations

XIV. Space Coordinates and Surfaces

• three dimensional graphing
• surfaces of revolution
• cylindrical and spherical coordinates