- Part 1 | Adjusting to Algebra
Topics include: the Cartesian coordinate system, qualitative graphs, algebraic expressions, algebraic equations involving a single variable, and sequences.
- Part 2 | Developmental Linear Algebra\(^1\)
Topics include: solving linear equations in one variable, graphing equations in two variables, exploring applications involving linear equations in two variables, direct variation (with single powers), arithmetic sequences, systems of linear equations and inequalities, matrices (as well as determinants and Cramer's Rule), applications of larger systems, and solving absolute-value linear equations and inequalities.
- Part 3 | Functions
Topics include: introduction to functions, graphs of functions, piecewise-defined functions, inspecting the graph of a function, base graphs, transformations of graphs of functions, arithmetic of functions, one-to-one functions and their inverses, linear functions, and difference quotients involving linear functions.
- Part 4 | Exponential Algebra
Topics include: exponents, scientific notation, radicals and roots, complex numbers (revisited), rational exponents, simplifying radical expressions, solving radical equations, arithmetic of radical expressions, exponential functions, graphs of exponential functions, logarithmic functions and their graphs, properties of logarithms, solving exponential and logarithmic equations, applications involving exponential and logarithmic models, exponential and logarithmic inequalities, geometric sequences and series, and data analysis with exponential and logarithmic functions.
- Part 5 | Polynomial Algebra
Topics include: polynomials and their functions, polynomial arithmetic, polynomial factorizations (including sum and difference of cubes, and factoring quadratic-like expressions), synthetic division, the Fundamental Theorem of Algebra, the Binomial Theorem, the Remainder and Factor theorems, solving polynomial equations (including those derived from exponential and logarithmic equations), the discriminant, direct variation with a power, quadratic functions, optimization problems involving quadratic functions, difference quotients involving polynomial functions, curve fitting, polynomial inequalities, conic sections, the Rational Roots theorem and Descartes' Rule of Signs, using technology to solve polynomial equations and inequalities, and solving systems of non-linear equations and inequalities.
- Part 6 | Rational Algebra
Topics include: simplifying rational expressions, arithmetic involving rational expressions, complex fractions, difference quotients involving rational functions, solving rational equations, applications involving rational functions, inverse, joint, and combined variation, similar triangles, and graphing rational functions.
\(^1\) This is not to be confused with Linear Algebra, which is a course beyond Differential Equations.