Introductory and Intermediate 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. Introduction to Real Numbers and Algebraic Expressions

1.1 Introduction to Algebra

1.2 The Real Numbers

1.3 Addition of Real Numbers

1.4 Subtraction of Real Numbers

1.5 Multiplication of Real Numbers

1.6 Division of Real Numbers

1.7 Properties of Real Numbers

1.8 Simplifying Expressions; Order of Operations

 

2. Solving Equations and Inequalities

2.1 Solving Equations: The Addition Principle

2.2 Solving Equations: The Multiplication Principle

2.3 Using the Principles Together

2.4 Formulas

2.5 Applications of Percent

2.6 Applications and Problem Solving

2.7 Solving Inequalities

2.8 Applications and Problem Solving with Inequalities

 

3. Graphs of Linear Equations

3.1 Graphs and Applications of Linear Equations

3.2 Graphing Linear Equations

3.3 More with Graphing and Intercepts

3.4 Slope and Applications

 

4. Polynomials: Operations

4.1 Integers as Exponents

4.2 Exponents and Scientific Notation

4.3 Introduction to Polynomials

4.4 Addition and Subtraction of Polynomials

4.5 Multiplication of Polynomials

4.6 Special Products

4.7 Operations with Polynomials in Several Variables

4.8 Division of Polynomials

 

5. Polynomials: Factoring

5.1 Introduction to Factoring

5.2 Factoring Trinomials of the Type x2 + bx + c

5.3 Factoring ax2 + bx + c, a ≠ 1:

The FOIL Method

5.4 Factoring ax2 + bx + c, a ≠ 1:

The ac-Method

5.5 Factoring Trinomial Squares and Differences of Squares

5.6 Factoring Sums or Differences of Cubes

5.7 Factoring: A General Strategy

5.8 Solving Quadratic Equations by Factoring

5.9 Applications of Quadratic Equations

 

6. Rational Expressions and Equations

6.1 Multiplying and Simplifying Rational Expressions

6.2 Division and Reciprocals

6.3 Least Common Multiples and Denominators

6.4 Adding Rational Expressions

6.5 Subtracting Rational Expressions

6.6 Complex Rational Expressions

6.7 Solving Rational Equations

6.8 Applications Using Rational Equations and Proportions

6.9 Variation and Applications

 

7. Graphs, Functions, and Applications

7.1 Functions and Graphs

7.2 Finding Domain and Range

7.3 Linear Functions: Graphs and Slope

7.4 More on Graphing Linear Equations

7.5 Finding Equations of Lines: Applications

 

8. Systems of Equations

8.1 Systems of Equations in Two Variables

8.2 Solving by Substitution

8.3 Solving by Elimination

8.4 Solving Applied Problems: Two Equations

8.5 Systems of Equations in Three Variables

8.6 Solving Applied Problems: Three Equations

 

9. More on Inequalities

9.1 Sets, Inequalities, and Interval Notation

9.2 Intersections, Unions, and Compound Inequalities

9.3 Absolute-Value Equations and Inequalities

9.4 Systems of Inequalities in Two Variables

 

10. Radical Expressions, Equations, and Functions

10.1 Radical Expressions and Functions

10.2 Rational Numbers as Exponents

10.3 Simplifying Radical Expressions

10.4 Addition, Subtraction, and More Multiplication

10.5 More on Division of Radical Expressions

10.6 Solving Radical Equations

10.7 Applications Involving Powers and Roots

10.8 The Complex Numbers

 

11. Quadratic Equations and Functions

11.1 The Basics of Solving Quadratic Equations

11.2 The Quadratic Formula

11.3 Applications Involving Quadratic Equations

11.4 More on Quadratic Equations

11.5 Graphing f(x) = a(x -  h)2 + k

11.6 Graphing f(x) = ax2 + bx + c

11.7 Mathematical Modeling with Quadratic Functions

11.8 Polynomial and Rational Inequalities

 

12. Exponential and Logarithmic Functions

12.1 Exponential Functions

12.2 Inverse and Composite Functions

12.3 Logarithmic Functions

12.4 Properties of Logarithmic Functions

12.5 Natural Logarithmic Functions

12.6 Solving Exponential and Logarithmic Equations

12.7 Mathematical Modeling with Exponential and Logarithmic Functions

 

Appendices

A:  Factoring and LCMs

B:  Fraction Notation

C:  Exponential Notation and Order of Operations

D:  Review of Factoring Polynomials

E:  Introductory Algebra Review

F:  Handling Dimension Symbols

G:  Mean, Median, and Mode

H:  Synthetic Division

I:    Determinants and Cramer’s Rule

J:   Elimination Using Matrices

K:  The Algebra of Functions

L:   Distance, Midpoints, and Circles