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Introductory Algebra

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Language:  English
Introductory Algebra is a primer for students considering an entrance level college algebra course. The textbook’s goal is to teach a set of problem solving skills in fundamental areas of algebra.
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Introductory Algebra is a primer for students considering an entrance level college algebra course. The textbook should not be considered a comprehensive treatment of algebra. The goal of the textbook is to teach a set of problem solving skills in some of the more fundamental areas of algebra.

The author uses a step-by-step problem solving technique that is demonstrated in an exacting format. These formats can often take an entire page to demonstrate the solution to a problem. Additional examples of problems are worked out completely using the exact problem solving format originally demonstrated.

  1. The Real Number System
    1. Natural Numbers
    2. Whole Numbers
    3. Integers
    4. Rational Numbers
    5. Irrational Numbers
    6. Real Numbers
  2. Mathematical Properties
    1. The Distributive Property
    2. The Associative Properties
    3. The Commutative Properties
    4. The Identity Property
    5. A Statement on Mathematical Properties
  3. Arithmetic Operations
    1. Orders of Operations
    2. Fractions, Decimals, and Percentages
    3. Common Denominators
    4. Positive and Negative Numbers
    5. Exponents
    6. Chapter 3 End of Chapter Exercises
  4. Expressions, Variables, and Equations
    1. Algebraic Expressions
    2. Algebraic Variables and Equations
    3. The Language of Algebraic Equations
    4. Solving Linear Equations
    5. Chapter 4 End of Chapter Exercises
  5. Polynomial Expressions
    1. Polynomial Expressions of Variables
    2. Degrees of Polynomials
    3. Addition and Subtraction of Polynomials
    4. Multiplication and Division of Monomials
    5. Chapter 5 End of Chapter Exercises
  6. Factoring of Polynomials
    1. The Concept of Common Factors
    2. Factoring by Grouping
    3. Factoring Second Degree Polynomials
    4. Special Factors
    5. Long Division of Polynomials
    6. Chapter 6 End of Chapter Exercises
  7. Rational Expressions
    1. Simplification of Rational Expression
    2. Addition and Subtraction of Rational Expressions
    3. Multiplication and Division of Rational Expressions
    4. Simplifying Complex Fractions
    5. Solving Equations with Fractions
    6. Ratios and Proportions
    7. Chapter 7 End of Chapter Exercises
  8. Inequalities and Absolute Values
    1. Inequality Expressions
    2. Graphing Inequalities on the Number Line
    3. Absolute Values
    4. Graphing Absolute Values of Inequalities on the Number Line
    5. Chapter 8 End of Chapter Exercises
  9. Graphing in the Rectangular Coordinate System
    1. The Rectangular Coordinate System
    2. Linear Equations: The Slope Intercept Form
    3. Linear Equations: The Point-Slope Form
    4. Horizontal and Vertical Graphs
    5. Parallel and Perpendicular Graphs
    6. Graphing Linear Inequalities
    7. Chapter 9 End of Chapter Exercises
  10. Exponents and Radicals
    1. Whole Integer Positive Exponents
    2. Negative and Zero Exponents
    3. Rational Exponents: The nth Root
    4. Mathematical Operations with Exponents and Radicals
    5. Chapter 10 End of Chapter Exercises
  11. Systems of Equations
    1. Systems of Linear Equations in Two Unknowns: Solutions by Graphing
    2. Systems of Linear Equations in Two Unknowns: Solutions by Substitution
    3. Systems of Linear Equations in Two Unknowns: Solutions by Elimination
    4. Systems of Linear Equations in Three Unknowns: Solutions by Elimination and Back Substitution
    5. Chapter 11 End of Chapter Exercises
  12. Appendix A
    1. Answers to End of Chapter Exercises
About the Author

Edward W. Pitzer

Edward W. Pitzer is an Assistant Professor of Chemistry and Mathematics at Marian University in Indianapolis, Indiana in the USA.

Professor Pitzer’s specialty is introductory courses in chemistry and mathematics for non-science and non-mathematics majors.

His present research interest is in the pedagogical construct of these non-major courses. He insists that making a non-science major excited about, or at least intrigued by, a science or mathematics course is a worthwhile effort.

Professor Pitzer has published works describing mathematical properties of organic molecules. Among these are his works describing topological constructs of organic molecules and a recent work on a general formulization of hydrocarbons. These types of works show both his predilection for chemistry and mathematics.