Sub-Topics of the main topics in College Algebra

(From the same book. Only main topics listed here.)

Prerequisites 

1. Modeling the real world with Algebra - using and making algebraic models 
2. Real numbers
3. Integer exponents and scientific notation
4. Rational exponents and radicals
5. Algebraic expressions
6. Factoring 
7. Rational expressions
8. Solving basic equations
9. Modeling with equations

Equations and Graphs

1. Coordinate plane
2. Graph of equations in two variables
3. Lines
4. Solving quadratic equations
5. Complex numbers
6. Solving other types of equations
7. Solving inequalities
8. Solving absolute value equations and inequalities
9. Solving inequalities and equations graphically 
10. Modeling variation

Functions

1. About functions
2. Graphs of functions
3. Getting information from the graph of a function 
4. Average rate of change of a function
5. Linear functions and models
6. Transformations of functions
7. Combining functions 
8. One to one functions and their inverses

Polynomial and Rational Functions

1. Quadratic functions and models
2. Polynomial functions and their graphs
3. Dividing polynomials 
4. Real zeros of polynomials 
5. Complex zeros and the fundamental theorem of Algebra
6. Rational functions
7. Polynomial and rational inequalities

Exponential and Logarithmic Functions

1. Exponential functions
2. Natural exponential function
3. Logarithmic functions
4. Laws of logarithms
5. Exponential and logarithmic equations
6. Modeling with exponential functions
7. Logarithmic scales

Systems of Equations and Inequalities

1. Systems of linear equations in two variables
2. Systems of linear equations in several variables 
3. Partial fractions
4. Systems of non linear equations
5. Systems of inequalities

Matrices and Determinants

1. Matrices and systems of linear equations
2. Algebra of matrices 
3. Inverses of matrices and matrix equations
4. Determinants and Cramer's rule

Conic Sections

1. Parabolas
2. Ellipses
3. Hyperbolas
4. Shifted conics

Sequences and Series 

1. Sequences and summation notation 
2. Arithmetic sequences
3. Geometric sequences
4. Mathematics of finance
5. Mathematical induction
6. The binomial theorem

Probability and Statistics

1. Counting
2. Probability
3. Binomial probaility
4. Expected value