Algebra: Form and Function

Algebra: Form and Function offers a fresh approach to algebra that focuses on teaching readers how to truly understand the principles, rather than viewing them merely as tools for other forms of mathematics. Meant for a College Algebra course, Algebra: Form and Function is an introduction to one of the fundamental aspects of modern society. Algebraic equations describe the laws of science, the principles of engineering, and the rules of business. The power of algebra lies in the efficient symbolic representation of complex ideas, which also presents the main difficulty in learning it. It is easy to forget the underlying structure of algebra and rely instead on a surface knowledge of algebraic manipulations. Most students rely on surface knowledge of algebraic manipulations without understanding the underlying structure of algebra that allows them to see patterns and apply it to multiple situations: McCallum focuses on the structure from the start.

1: Functions and Algebraic Structure

2: Linear Functions

3: Quadratic Functions

4: Power Functions

5: More on Functions

6: Exponential Functions

7: Logarithms

8: Polynomial Functions

9: Rational Functions

Appendix A: Expressions

Appendix B: Equations

Appendix C: Inequalities

Appendix D: Quadratics

Appendix E: Algebraic Fractions

Appendix F: Absolute Value

Appendix G: Exponents

10 Summation Notation (Online Only)

11 Sequences and Series (Online Only)