by Lewis R. Hirsch and Arthur Goodman
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Hirsch and Goodman offer a mathematically sound, rigorous text to those instructors who believe students should be challenged. The text prepares students for future study in higher-level courses by gradually building students' confidence without sacrificing rigor. To help students move beyond the "how" of algebra (computational proficiency) to the "why" (conceptual understanding), the authors introduce topics at an elementary level and return to them at increasing levels of complexity. Their gradual introduction of concepts, rules, and definitions through a wealth of illustrative examples -- both numerical and algebraic--helps students compare and contrast related ideas and understand the sometimes-subtle distinctions among a variety of situations. This author team carefully prepares students to succeed in higher-level mathematics.
1. THE INTEGERS.
What is Algebra? Introduction and Basic Notation. Integers. Adding Integers. Subtracting Integers. Multiplying and Dividing Integers. The Real Number System.
2. ALGEBRAIC EXPRESSIONS.
Variables and Exponents. Algebraic Substitution. The Distributive Property and Combining Like Terms. Simplifying Algebraic Expressions. Translating Phrases and Sentences Algebraically.
3. FIRST-DEGREE EQUATIONS AND INEQUALITIES.
Types of Equations. Solving First-Degree Equations in One Variable and Applications. More First-Degree Equations and Applications. Types of Inequalities and Basic Properties of Inequalities. Solving First-Degree Inequalities in One Variable and Applications.
4. RATIONAL EXPRESSIONS.
Fundamental Principle of Fractions. Multiplying and Dividing Rational Expressions. Adding and Subtracting Rational Expressions. Solving Fractional Equations and Inequalities. Ratio and Proportion. Applications.
5. GRAPHING STRAIGHT LINES.
The Rectangular (Cartesian) Coordinate System. Graphing a Linear Equation in Two Variables. The Slope. The Equation of a Line.
6. INTERPRETING GRAPHS AND SYSTEMS OF LINEAR EQUATIONS.
Interpreting Graphs. Solving Systems of Linear Equations: Graphical Method. Solving Systems of Linear Equations: Algebraic Methods. Applications.
7. EXPONENTS AND POLYNOMIALS.
Exponent Rules. Zero and Negative Exponents. Scientific Notation. Introduction to Polynomials. Multiplying Polynomials. Special Products.
8. FACTORING.
Common Factors. Factoring Trinomials. More Factoring. Solving Polynomial Equations by Factoring. Dividing Polynomials.
9. MORE RATIONAL EXPRESSIONS.
Reducing Rational Expressions. Multiplying and Dividing Rational Expressions. Adding and Subtracting Rational Expressions. Fractional Equations. Literal Equations. Applications.
10. RADICAL EXPRESSIONS AND EQUATIONS.
Definitions and Basic Notation. Properties of Radicals and Simplest Radical Form. Adding and Subtracting Radical Expressions. Multiplying and Dividing Radical Expressions. Radical Equations.
11. QUADRATIC EQUATIONS.
The Factoring and Square Root Methods. The Method of Completing the Square. The Quadratic Formula. Choosing a Method. Applications. Graphing Quadratic Equations.
12. GEOMETRY.
Angles. Triangles. Congruence. Similarity. Quadrilaterals. Perimeter and Area. Circles. Solid Geometry.
Appendix A: A Review of Arithmetic.
Fractions. Multiplying and Dividing Fractions. Adding and Subtracting Fractions. Decimals. Percents
Appendix B: Using a Scientific Calculator.
Appendix C: Using a Graphing Calculator.
Appendix D: Introduction to Functions
Lewis R. Hirsch and Arthur Goodman
ISBN13: 978-0534999728Hirsch and Goodman offer a mathematically sound, rigorous text to those instructors who believe students should be challenged. The text prepares students for future study in higher-level courses by gradually building students' confidence without sacrificing rigor. To help students move beyond the "how" of algebra (computational proficiency) to the "why" (conceptual understanding), the authors introduce topics at an elementary level and return to them at increasing levels of complexity. Their gradual introduction of concepts, rules, and definitions through a wealth of illustrative examples -- both numerical and algebraic--helps students compare and contrast related ideas and understand the sometimes-subtle distinctions among a variety of situations. This author team carefully prepares students to succeed in higher-level mathematics.
Table of Contents
1. THE INTEGERS.
What is Algebra? Introduction and Basic Notation. Integers. Adding Integers. Subtracting Integers. Multiplying and Dividing Integers. The Real Number System.
2. ALGEBRAIC EXPRESSIONS.
Variables and Exponents. Algebraic Substitution. The Distributive Property and Combining Like Terms. Simplifying Algebraic Expressions. Translating Phrases and Sentences Algebraically.
3. FIRST-DEGREE EQUATIONS AND INEQUALITIES.
Types of Equations. Solving First-Degree Equations in One Variable and Applications. More First-Degree Equations and Applications. Types of Inequalities and Basic Properties of Inequalities. Solving First-Degree Inequalities in One Variable and Applications.
4. RATIONAL EXPRESSIONS.
Fundamental Principle of Fractions. Multiplying and Dividing Rational Expressions. Adding and Subtracting Rational Expressions. Solving Fractional Equations and Inequalities. Ratio and Proportion. Applications.
5. GRAPHING STRAIGHT LINES.
The Rectangular (Cartesian) Coordinate System. Graphing a Linear Equation in Two Variables. The Slope. The Equation of a Line.
6. INTERPRETING GRAPHS AND SYSTEMS OF LINEAR EQUATIONS.
Interpreting Graphs. Solving Systems of Linear Equations: Graphical Method. Solving Systems of Linear Equations: Algebraic Methods. Applications.
7. EXPONENTS AND POLYNOMIALS.
Exponent Rules. Zero and Negative Exponents. Scientific Notation. Introduction to Polynomials. Multiplying Polynomials. Special Products.
8. FACTORING.
Common Factors. Factoring Trinomials. More Factoring. Solving Polynomial Equations by Factoring. Dividing Polynomials.
9. MORE RATIONAL EXPRESSIONS.
Reducing Rational Expressions. Multiplying and Dividing Rational Expressions. Adding and Subtracting Rational Expressions. Fractional Equations. Literal Equations. Applications.
10. RADICAL EXPRESSIONS AND EQUATIONS.
Definitions and Basic Notation. Properties of Radicals and Simplest Radical Form. Adding and Subtracting Radical Expressions. Multiplying and Dividing Radical Expressions. Radical Equations.
11. QUADRATIC EQUATIONS.
The Factoring and Square Root Methods. The Method of Completing the Square. The Quadratic Formula. Choosing a Method. Applications. Graphing Quadratic Equations.
12. GEOMETRY.
Angles. Triangles. Congruence. Similarity. Quadrilaterals. Perimeter and Area. Circles. Solid Geometry.
Appendix A: A Review of Arithmetic.
Fractions. Multiplying and Dividing Fractions. Adding and Subtracting Fractions. Decimals. Percents
Appendix B: Using a Scientific Calculator.
Appendix C: Using a Graphing Calculator.
Appendix D: Introduction to Functions