Algebra: Form and Function, 2nd Edition
November 2014, ©2015
Algebra: Form and Function, 2nd Edition 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, 2nd Edition 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
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)
- A new organization that moves quickly through early material. The former chapters 2 and 3 on rules for expressions and rules for equations, and the former chapter 6 on exponent rules, has been moved to appendices, complete with exercises, for those instructors who still want to cover this material.
- Problems organized according to the three aspects of algebraic knowledge—recognizing building blocks, fluency, and modeling encourage students first to look inside and then to think ahead.
- Suggested by current users, a simplified presentation throughout the text and clarifications of wording in text, examples, and exercises help student comprehension of the materials being presented.
- A Balanced Approach: Form, Function, and Fluency. To use algebra in later courses, students need not only manipulative skill, but fluency in the language of algebra, including an ability to recognize algebraic form and an understanding of the purpose of different forms. Algebra achieves this through unique examples and exercises.
- Restoring Meaning to Expressions and Equations. After introducing each type of function--linear, power, quadratic, exponential, polynomial--the text encourages students to pause and examine the basic forms of expressions for that function, see how they are constructed, and consider the different properties of the function that the different forms reveal.
- Maintaining Manipulative Skills: Review and Practice. Acquiring the skills to perform basic algebraic manipulations is as important as recognizing algebraic forms. Algebra: Form and Function provides sections reviewing the rules of algebra, and the reasons for them, throughout the book, numerous exercises to reinforce skills in each chapter, and a section of drill problems on solving equations at the end of the chapters on linear, power, and quadratic functions.
- Students with Varying Backgrounds. Algebra: Form and Function is thought-provoking for well-prepared students while still accessible to students with weaker backgrounds, making it understandable to students of all ability levels.
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