Prealgebra and Introductory Algebra

Marvin Bittinger has been teaching math at the university level for more than thirty-eight years. Since 1968, he has been employed at Indiana University Purdue University Indianapolis, and is now professor emeritus of mathematics education. Professor Bittinger has authored over 190 publications on topics ranging from basic mathematics to algebra and trigonometry to applied calculus. He received his BA in mathematics from Manchester College and his PhD in mathematics education from Purdue University. Special honors include Distinguished Visiting Professor at the United States Air Force Academy and his election to the Manchester College Board of Trustees from 1992 to 1999. Professor Bittinger has also had the privilege of speaking at many mathematics conventions, most recently giving a lecture entitled "Baseball and Mathematics." His hobbies include hiking in Utah, baseball, golf, and bowling. In addition, he also has an interest in philosophy and theology, in particular, apologetics. Professor Bittinger currently lives in Carmel, Indiana with his wife Elaine. He has two grown and married sons, Lowell and Chris, and four granddaughters.

1. Whole Numbers

1.1 Standard Notation

1.2 Addition

1.3 Subtraction

1.4 Multiplication

1.5 Division

1.6 Rounding and Estimating; Order

1.7 Solving Equations

1.8 Applications and Problem Solving

1.9 Exponential Notation and Order of Operations

 

2. Introduction to Integers and Algebraic Expressions

2.1 Integers and the Number Line

2.2 Addition of Integers

2.3 Subtraction of Integers

2.4 Multiplication of Integers

2.5 Division of Integers and Order of Operations

2.6 Introduction to Algebra and Expressions

2.7 Like Terms and Perimeter

2.8 Solving Equations

 

3. Fraction Notation: Multiplication and Division

3.1 Multiples and Divisibility

3.2 Factorizations

3.3 Fractions and Fraction Notation

3.4 Multiplication and Applications

3.5 Simplifying

3.6 Multiplying, Simplifying, and More with Area

3.7 Reciprocals and Division

3.8 Solving Equations: The Multiplication Principle

 

4. Fraction Notation: Addition, Subtraction, and Mixed Numerals

4.1 Least Common Multiples

4.2 Addition, Order, and Applications

4.3 Subtraction, Equations, and Applications

4.4 Solving Equations: Using the Principles Together

4.5 Mixed Numerals

4.6 Addition and Subtraction of Mixed Numerals; Applications

4.7 Multiplication and Division of Mixed Numerals; Applications

4.8 Order of Operations and Complex Fractions

 

5. Decimal Notation

5.1 Decimal Notation, Order, and Rounding

5.2 Addition and Subtraction of Decimals

5.3 Multiplication of Decimals

5.4 Division of Decimals

5.5 Using Fraction Notation with Decimal Notation

5.6 Estimating

5.7 Solving Equations

5.8 Applications and Problem Solving

 

6. Percent Notation

6.1 Ratio and Proportion

6.2 Percent Notation

6.3 Percent Notation and Fraction Notation

6.4 Solving Percent Problems Using Percent Equations

6.5 Solving Percent Problems Using Proportions

6.6 Applications of Percent

6.7 Sales Tax, Commission and Discount

6.8 Simple Interest and Compound Interest; Credit Cards

 

7. Data, Graphs, and Statistics

7.1 Averages, Medians, and Modes

7.2 Tables and Pictographs

7.3 Bar Graphs and Line Graphs

7.4 Circle Graphs

 

8. Geometry

8.1 Basic Geometric Features

8.2 Perimeter

8.3 Area

8.4 Circles

8.5 Volume and Surface Area

8.6 Relationships between Angle Measures

8.7 Congruent Triangles and Properties of Parallelograms

8.8 Similar Triangles

 

9. Introduction to Real Numbers and Algebraic Expressions

9.1 Introduction to Algebra

9.2 The Real Numbers

9.3 Addition of Real Numbers

9.4 Subtraction of Real Numbers

9.5 Multiplication of Real Numbers

9.6 Division of Real Numbers

9.7 Properties of Real Numbers

9.8 Simplifying Expressions; Order of Operations

 

10. Solving Equations and Inequalities

10.1 Solving Equations: The Addition Principle

10.2 Solving Equations: The Multiplication Principle

10.3 Using the Principles Together

10.4 Formulas

10.5 Applications of Percent

10.6 Applications and Problem Solving

10.7 Solving Inequalities

10.8 Applications and Problem Solving with Inequalities

 

11. Graphs of Linear Equations

11.1 Graphs and Applications of Linear Equations

11.2 More with Graphing and Intercepts

11.3 Slope and Applications

11.4 Equations of Lines

11.5 Graphing Using the Slope and y-intercept

11.6 Parallel and Perpendicular Lines

11.7 Graphing Inequalities in Two Variables

 

12. Polynomials: Operations

12.1 Integers as Exponents

12.2 Exponents and Scientific Notation

12.3 Introduction to Polynomials

12.4 Addition and Subtraction of Polynomials

12.5 Multiplication of Polynomials

12.6 Special Products

12.7 Operations with Polynomials in Several Variables

12.8 Division of Polynomials

 

13. Polynomials: Factoring

13.1 Introduction to Factoring

13.2 Factoring Trinomials of the Type x² + bx + c

13.3 Factoring ax² + bx + c, a ≠ 1; The FOIL Method

13.4 Factoring ax² + bx + c, a ≠ 1; The ac-Method

13.5 Factoring Trinomial Squares and Differences of Squares

13.6 Factoring: A General Strategy

13.7 Solving Quadratic Equations by Factoring

13.8 Applications of Quadratic Equations

 

14. Rational Expressions and Equations

14.1 Multiplying and Simplifying Rational Expressions

14.2 Division and Reciprocals

14.3 Least Common Multiples and Denominators

14.4 Adding Rational Expressions

14.5 Subtracting Rational Expressions

14.6 Solving Rational Equations

14.7 Applications Using Rational Equations and Proportions

14.8 Complex Rational Expressions

14.9 Direct Variation and Inverse Variation

 

15. Systems of Equations

15.1 Systems of Equations in Two Variables

15.2 The Substitution Method

15.3 The Elimination Method

15.4 Applications and Problem Solving

15.5 Applications with Motion

 

16. Radical Expressions and Equations

16.1 Introduction to Radical Expressions

16.2 Multiplying and Simplifying with Radical Expressions

16.3 Quotients Involving Radical Expressions

16.4 Addition, Subtraction, and More Multiplication

16.5 Radical Equations

16.6 Applications with Right Triangles

 

17. Quadratic Equations

17.1 Introduction to Quadratic Equations

17.2 Solving Quadratic Equations by Completing the Square

17.3 The Quadratic Formula

17.4 Formulas

17.5 Applications and Problem Solving

17.6 Graphs of Quadratic Equations

17.7 Functions

 

Appendices

A. Linear Measures: American and Metric Units

B. Weight and Mass; Medical Applications

C. Capacity; Medical Applications

D. Time and Temperature

E. Sets

F. Factoring Sums or Differences of Cubes

G. Finding Equations of Lines: Point-Slope Equation

H. Equations Involving Absolute Value

I. The Distance formula and Midpoints

J. Higher Roots, and Rational Numbers as Exponents

K. Inequalities and Interval Notation

L. Nonlinear Inequalities

M. Systems of Linear Inequalities

N. Probability

O. The Complex Numbers