# Algebra for College Students

## 1st Edition

**Authors:**Bernard Kolman Arnold Shapiro

**eBook ISBN:**9781483271217

**Imprint:**Academic Press

**Published Date:**1st January 1982

**Page Count:**550

## Description

Algebra for College Students, Revised and Expanded Edition is a complete and self-contained presentation of the fundamentals of algebra which has been designed for use by the student. The book provides sufficient materials for use in many courses in college algebra. It contains chapters that are devoted to various mathematical concepts, such as the real number system, sets and set notation, matrices and their application in solving linear systems, and notation of functions. The theory of polynomial equations, formulas for factoring a sum and a difference of cubes, roots of polynomials, and the geometric definition of each conic are likewise included in the book. College students will find the book very useful and invaluable.

## Table of Contents

Preface

Acknowledgments

To the Student

Chapter One the REAL Number System

1.1 The Real Number System

1.2 Arithmetic Operations: Fractions

1.3 Algebraic Expressions

1.4 Operating with Signed Numbers

1.5 Properties of Real Numbers

1.6 Absolute Value and Inequalities

Chapter Two Polynomials

2.1 Polynomials

2.2 Addition and Subtraction of Polynomials

2.3 Multiplication of Polynomials

2.4 Factoring

2.5 Special Factors

Chapter Three Linear Equations and Inequalities

3.1 Linear Equations in One Variable

3.2 Applications

3.3 Linear Inequalities

3.4 Absolute Value in Equations and Inequalities

Chapter Four Word Problems

4.1 From Words to Algebra

4.2 Coin Problems

4.3 Investment Problems

4.4 Distance (Uniform Motion) Problems

4.5 Mixture Problems

Chapter Five Algebraic Fractions

5.1 Multiplication and Division of Fractions

5.2 Addition and Subtraction of Fractions

5.3 Complex Fractions

5.4 Ratio and Proportion

5.5 Equations and Inequalities with Fractions

5.6 Applications; Work Problems

Chapter Six Functions

6.1 Rectangular Coordinate Systems

6.2 Functions and Function Notation

6.3 Graphs of Functions

6.4 Increasing and Decreasing Functions

6.5 Direct and Inverse Variation

Chapter Seven the Straight Line

7.1 Slope of the Straight Line

7.2 Equations of the Straight Line

7.3 Further Properties of the Straight Line

7.4 Linear Inequalities in Two Variables

Chapter Eight Exponents, Radicals, and Complex Numbers

8.1 Positive Integer Exponents

8.2 Integer Exponents

8.3 Rational Exponents and Radicals

8.4 Evaluating and Simplifying Radicals

8.5 Operations with Radicals

8.6 Complex Numbers

Chapter Nine Second-Degree Equations and Inequalities

9.1 Solving Quadratic Equations

9.2 The Quadratic Formula

9.3 Roots of a Quadratic Equation: The Discriminant

9.4 Applications

9.5 Forms Leading to Quadratics

9.6 Second-Degree Inequalities

Chapter Ten Roots of Polynomials

10.1 Polynomial Division and Synthetic Division

10.2 The Remainder and Factor Theorems

10.3 Factors and Roots

10.4 Real and Rational Roots

Chapter Eleven Exponential and Logarithmic Functions

11.1 Combining Functions; Inverse Functions

11.2 Exponential Functions

11.3 Logarithmic Functions

11.4 Properties of Logarithms

11.5 Computing with Logarithms

11.6 Exponential and Logarithmic Equations

Chapter Twelve Analytic Geometry: The Conic Sections

12.1 Distance and Midpoint Formulas

12.2 Symmetry

12.3 The Circle

12.4 The Parabola

12.5 The Ellipse and Hyperbola

12.6 Identifying the Conic Sections

Chapter Thirteen Systems of Equations

13.1 Systems of Linear Equations

13.2 Solving by Elimination

13.3 Applications

13.4 Systems of Linear Equations in Three Unknowns

13.5 Systems Involving Nonlinear Equations

Chapter Fourteen Matrices and Determinants

14.1 Matrices and Linear Systems

14.2 Determinants

14.3 Cramer's Rule

Chapter Fifteen Topics in Algebra

15.1 Arithmetic Progressions

15.2 Geometric Progressions

15.3 The Binomial Theorem

15.4 Counting: Permutations and Combinations

Appendix/Tables

Answers to Odd-Numbered Exercises and Progress Tests

Index

## Details

- No. of pages:
- 550

- Language:
- English

- Copyright:
- © Academic Press 1982

- Published:
- 1st January 1982

- Imprint:
- Academic Press

- eBook ISBN:
- 9781483271217

## About the Authors

### Bernard Kolman

### Affiliations and Expertise

Drexel University