Basic College Mathematics

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. Fraction Notation: Multiplication and Division

2.1 Factorizations

2.2 Divisibility

2.3 Fractions and Fraction Notation

2.4 Multiplication and Applications

2.5 Simplifying

2.6 Multiplying, Simplifying, and Applications

2.7 Division and Applications

 

3. Fraction Notation and Mixed Numerals

3.1 Least Common Multiples

3.2 Addition and Applications

3.3 Subtraction, Order, and Applications

3.4 Mixed Numerals

3.5 Addition and Subtraction Using Mixed Numerals; Applications

3.6 Multiplication and Division Using Mixed Numerals; Applications

3.7 Order of Operations; Estimation

 

4. Decimal Notation

4.1 Decimal Notation, Order, and Rounding

4.2 Addition and Subtraction

4.3 Multiplication

4.4 Division

4.5 Converting from Fraction Notation to Decimal Notation

4.6 Estimating

4.7 Applications and Problem Solving

 

5. Ratio and Proportion

5.1 Introduction to Ratios

5.2 Rates and Unit Prices

5.3 Proportions

5.4 Applications of Proportions

5.5 Geometric Applications

 

6. Percent Notation

6.1 Percent Notation

6.2 Percent and Fraction Notation

6.3 Solving Percent Problems Using Percent Equations

6.4 Solving Percent Problems Using Proportions

6.5 Applications of Percent

6.6 Sales Tax, Commission, and Discount

6.7 Simple 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. Measurement

8.1 Linear Measures: American Units

8.2 Linear Measures: The Metric System

8.3 Converting Between American Units and Metric Units

8.4 Weight and Mass; Medical Applications

8.5 Capacity; Medical Applications

8.6 Time and Temperature

8.7 Converting Units of Area

 

9. Geometry

9.1 Perimeter

9.2 Area

9.3 Circles

9.4 Volume

9.5 Angles and Triangles

9.6 Square Roots and the Pythagorean Theorem

 

10. Real Numbers

10.1 The Real Numbers

10.2 Addition of Real Numbers

10.3 Subtraction of Real Numbers

10.4 Multiplication of Real Numbers

10.5 Division of Real Numbers and Order of Operations

 

11. Algebra: Solving Equations and Problems

11.1 Introduction to Algebra

11.2 Solving Equations: The Addition Principle

11.3 Solving Equations: The Multiplication Principle

11.4 Using the Principles Together

11.5 Applications and Problem Solving