Developmental Mathematics through Applications

Geoffrey Akst and Sadie Bragg have worked together for many years as professors of mathematics at Borough of Manhattan Community College/City University of New York. They met as graduate students at Teachers College, Columbia University, where they were both working on degrees in the teaching of college mathematics. The emphasis on applications in their texts reflects a concern they share for helping students understand why the topics to be studied are useful. Dr. Akst for years has begun his classes with the payoff question:­ Why is this material worth learning? A native New Yorker, he enjoys surfing the Web, listening to good music, and traveling to exciting places. Dr. Bragg, who began her career in math education as a high school geometry teacher, credits her teachers with inspiring her love for mathematics and an appreciation of its utility. A transplanted Virginian, she spends her time with her family and her beautiful grandchildren.

• 1. Whole Numbers 1.1 Introduction to Whole Numbers1.2 Adding and Subtracting Whole Numbers 1.3 Multiplying Whole Numbers 1.4 Dividing Whole Numbers 1.5 Exponents, Order of Operations, and Averages 1.6 More on Solving Word Problems  2. Fractions 2.1 Factors and Prime Numbers 2.2 Introduction to Fractions 2.3 Adding and Subtracting Fractions 2.4 Multiplying and Dividing Fractions  3. Decimals 3.1 Introduction to Decimals 3.2 Adding and Subtracting Decimals 3.3 Multiplying Decimals 3.4 Dividing Decimals  4. Basic Algebra: Solving Simple Equations4.1 Introduction to Basic Algebra 4.2 Solving Addition and Subtraction Equations 4.3 Solving Multiplication and Division Equations  5. Ratio and Proportion 5.1 Introduction to Ratios 5.2 Solving Proportions  6. Percents 6.1 Introduction to Percents 6.2 Solving Percent Problems 6.3 More on Percents  7. Signed Numbers 7.1 Introduction to Signed Numbers 7.2 Adding Signed Numbers 7.3 Subtracting Signed Numbers 7.4 Multiplying Signed Numbers 7.5 Dividing Signed Numbers  8. Basic Statistics 8.1 Introduction to Basic Statistics 8.2 Tables and Graphs  9. Measurement and Units 9.1 U.S. Customary Units 9.2 Metric Units and Metric/U.S. Customary Unit Conversions  10. Basic Geometry 10.1 Introduction to Basic Geometry 10.2 Perimeter and Circumference 10.3 Area 10.4 Volume 10.5 Similar Triangles 10.6 Square Roots and the Pythagorean Theorem  11. Introduction to Real Numbers and Algebraic Expressions 11.1 Real Numbers 11.2 Using Properties to Add and Subtract Real Numbers 11.3 Using Properties to Multiply and Divide Real Numbers 11.4 Algebraic Expressions and Exponents 11.5 Evaluating Algebraic Expressions and Formulas 11.6 Simplifying Algebraic Expressions  12. Solving Linear Equations and Inequalities 12.1 Solving Linear Equations: The Addition Property 12.2 Solving Linear Equations: The Multiplication Property 12.3 Solving Linear Equations by Combining Properties 12.4 Solving Literal Equations and Formulas 12.5 Solving Linear Inequalities  13. Graphing Linear Equations and Inequalities 13.1 Introduction to Graphing 13.2 Slope 13.3 Linear Equations and Their Graphs 13.4 More on Linear Equations and Their Graphs 13.5 Linear Inequalities and Their Graphs  14. Solving Systems of Linear Equations 14.1 Introduction to Systems of Linear Equations: Solving by Graphing 14.2 Solving Systems of Linear Equations by Substitution 14.3 Solving Systems of Linear Equations by Elimination  15. Exponents and Polynomials 15.1 Laws of Exponents 15.2 More Laws of Exponents and Scientific Notation 15.3 Basic Concepts of Polynomials 15.4 Adding and Subtracting Polynomials 15.5 Multiplying Polynomials 15.6 Special Products 15.7 Dividing Polynomials  16. Factoring Polynomials 16.1 Common Factoring and Factoring by Grouping 16.2 Factoring Trinomials Whose Leading Coefficient Is 1 16.3 Factoring Trinomials Whose Leading Coefficient Is Not 1 16.4 Factoring Perfect Square Trinomials and the Difference of Squares 16.5 Solving Quadratic Equations by Factoring  17. Rational Expressions and Equations 17.1 Rational Expressions 17.2 Multiplying and Dividing Rational Expressions 17.3 Adding and Subtracting Rational Expressions 17.4 Complex Rational Expressions 17.5 Solving Rational Equations  18. Radical Expressions and Equations 18.1 Introduction to Radical Expressions 18.2 Adding and Subtracting Radical Expressions 18.3 Multiplying and Dividing Radical Expressions 18.4 Solving Radical Equations  19. Quadratic Equations 19.1 Solving Quadratic Equations by Using the Square Root Property 19.2 Solving Quadratic Equations by Completing the Square 19.3 Solving Quadratic Equations by Using the Quadratic Formula 19.4 Graphing Quadratic Equations in Two Variables  AppendixesA. Table of Symbols B. Review of Basic Mathematics C. Introduction to Graphing Calculators D. Factoring the Sum of Cubes and the Difference of Cubes Online Bonus Material:E. Solving Compound InequalitiesF. Solving Absolute Value Equations and InequalitiesG. Introduction to Functions H. Solving Systems of Linear Inequalities I. Variation J. Radical Expressions and Rational Exponents K. The Distance and Midpoint Formulas; the Circle