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