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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; Order
1.2 Addition and Subtraction
1.3 Multiplication and Division; Rounding and Estimating
1.4 Solving Equations
1.5 Applications and Problem Solving
1.6 Exponential Notation and Order of Operations
1.7 Factorizations
1.8 Divisibility
1.9 Least Common Multiples
2. Fraction Notation
2.1 Fraction Notation and Simplifying
2.2 Multiplication and Division
2.3 Addition and Subtraction; Order
2.4 Mixed Numerals
2.5 Applications and Problem Solving
2.6 Order of Operations; Estimation
3. Decimal Notation
3.1 Decimal Notation, Order, and Rounding
3.2 Addition and Subtraction
3.3 Multiplication
3.4 Division
3.5 Converting from Fraction Notation to Decimal Notation
3.6 Estimating
3.7 Applications and Problem Solving
4. Percent Notation
4.1 Ratio and Proportion
4.2 Percent Notation
4.3 Percent Notation and Fraction Notation
4.4 Solving Percent Problems Using Percent Equations
4.5 Solving Percent Problems Using Proportions
4.6 Applications of Percent
4.7 Sales Tax, Commission, and Discount
4.8 Simple Interest and Compound Interest; Credit Cards
5. Data, Graphs, and Statistics
5.1 Averages, Medians, and Modes
5.2 Tables and Pictographs
5.3 Bar Graphs and Line Graphs
5.4 Circle Graphs
6. Geometry
6.1 Basic Geometric Figures
6.2 Perimeter
6.3 Area
6.4 Circles
6.5 Volume and Surface Area
6.6 Relationships Between Angle Measures
6.7 Congruent Triangles and Properties of Parallelograms
6.8 Similar Triangles
7. Introduction to Real Numbers and Algebraic Expressions
7.1 Introduction to Algebra
7.2 The Real Numbers
7.3 Addition of Real Numbers
7.4 Subtraction of Real Numbers
7.5 Multiplication of Real Numbers
7.6 Division of Real Numbers
7.7 Properties of Real Numbers
7.8 Simplifying Expressions; Order of Operations
8. Solving Equations and Inequalities
8.1 Solving Equations: The Addition Principle
8.2 Solving Equations: The Multiplication Principle
8.3 Using the Principles Together
8.4 Formulas
8.5 Applications of Percent
8.6 Applications and Problem Solving
8.7 Solving Inequalities
8.8 Applications and Problem Solving with Inequalities
9. Graphs of Linear Equations
9.1 Graphs and Applications of Linear Equations
9.2 More with Graphing and Intercepts
9.3 Slope and Applications
9.4 Equations of Lines
9.5 Graphing Using the Slope and the y-intercept
9.6 Parallel and Perpendicular Lines
9.7 Graphing Inequalities in Two Variables
10. Polynomials: Operations
10.1 Integers as Exponents
10.2 Exponents and Scientific Notation
10.3 Introduction to Polynomials
10.4 Addition and Subtraction of Polynomials
10.5 Multiplication of Polynomials
10.6 Special Products
10.7 Operations with Polynomials in Several Variables
10.8 Division of Polynomials
11. Polynomials: Factoring
11.1 Introduction to Factoring
11.2 Factoring Trinomials of the type x² + bx + c
11.3 Factoring ax² + bx + c, a ≠ 1; The FOIL Method
11.4 Factoring ax² + bx + c, a ≠ 1; The ac-Method
11.5 Factoring Trinomial Squares and Differences of Squares
11.6 Factoring: A General Strategy
11.7 Solving Quadratic Equations by Factoring
11.8 Applications of Quadratic Equations
12. Rational Expressions and Equations
12.1 Multiplying and Simplifying Rational Expressions
12.2 Division and Reciprocals
12.3 Least Common Multiples and Denominators
12.4 Adding Rational Expressions
12.5 Subtracting Rational Expressions
12.6 Solving Rational Equations
12.7 Applications Using Rational Equations and Proportions
12.8 Complex Rational Expressions
12.9 Direct Variation and Inverse Variation
13. Systems of Equations
13.1 Systems of Equations in Two Variables
13.2 The Substitution Method
13.3 The Elimination Method
13.4 Applications and Problem Solving
13.5 Applications with Motion
14. Radical Expressions and Equations
14.1 Introduction to Radical Expressions
14.2 Multiplying and Simplifying with Radical Expressions
14.3 Quotients Involving Radical Expressions
14.4 Addition, Subtraction, and More Multiplication
14.5 Radical Equations
14.6 Applications with Right Triangles
15. Quadratic Equations
15.1 Introduction to Quadratic Equations
15.2 Solving Quadratic Equations by Completing the Square
15.3 The Quadratic Formula
15.4 Formulas
15.5 Applications and Problem Solving
15.6 Graphs of Quadratic Equations
15.7 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 and 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. Complex Numbers