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The fundamental goal in Tussy and Gustafson's INTRODUCTORY ALGEBRA, Third Edition is to teach students to read, write, and think about mathematics through building a conceptual foundation in the language of mathematics. The book blends instructional approaches that include vocabulary, practice, and well-defined pedagogy, along with an emphasis on reasoning, modeling, communication, and technology skills to develop students' fluency in the "language of algebra". Tussy and Gustafson understand the challenges of teaching developmental students and this book reflects a holistic approach to teaching mathematics that includes developing study skills, problem solving and critical thinking alongside mathematical concepts. New features in this edition include a pretest for students to gauge their understanding of prerequisite concepts, problems that make correlations between student life and the mathematical concepts and study skills information designed to give students the best chance to succeed in the course. Additionally, the texts widely acclaimed Study Sets at the end of every section are tailored to improve students' ability to read, write and communicate mathematical ideas.
1. AN INTRODUCTION TO ALGEBRA. Describing Numerical Relationships. Fractions and Decimals. The Real Numbers. Adding and Subtracting Real Numbers. Multiplying and Dividing Real Numbers. Exponents and Order of Operations. Algebraic Expressions. Key Concept: Variables. 2. EQUATIONS, INEQUALITIES, AND PROBLEM SOLVING. Solving Equations. Problem Solving. Simplifying Algebraic Expressions. Simplifying Algebraic Expressions. More About Solving Equations. Formulas. More Problem Solving. Inequalities. Key Concept: Simplify and Solve. 3. GRAPHS, LINEAR EQUATIONS, AND FUNCTIONS. Graphing Using the Rectangular Coordinate System. Equations Containing Two Variables. Graphing Linear Equations. Rate of Change and the Slope of a Line. Describing Linear Relationships. Writing Linear Equations. Functions. Key Concept: Describing Linear Relationships. 4. EXPONENTS AND POLYNOMIALS. Natural-Number Exponents. Zero and Negative Integer Exponents. Scientific Notation. Polynomials. Adding and Subtracting Polynomials. Multiplying Polynomials. Dividing Polynomials by Monomials. Dividing Polynomials by Polynomials. Key Concept: Polynomials. 5. FACTORING AND QUADRATIC EQUATIONS. Factoring Out the Greatest Common Factor and Factoring by Grouping. Factoring Trinomials of the Form x2 + bx + c. Factoring Trinomials of the Form ax2 + bx + c. Special Factorizations and a Factoring Strategy. Quadratic Equations. Key Concept: Factoring. 6. RATIONAL EXPRESSIONS AND EQUATIONS. Simplifying Rational Expressions. Multiplying and Dividing Rational Expressions. Adding and Subtracting Rational Expressions. Complex Fractions. Rational Equations and Problem Solving. Proportions and Similar Triangles. Variation. Key Concept: Expressions and Equations. 7. SOLVING SYSTEMS OF EQUATIONS AND INEQUALITIES. Solving Systems of Equations by Graphing. Solving Systems of Equations by Substitution. Solving Systems by Addition. Applications of Systems of Equations. Graphing Linear Inequalities. Solving Systems of Linear Equations. Key Concept: Systems of Equations and Inequalities. 8. ROOTS AND RADICALS. Square Roots. Higher Order Roots and Radicands That Contain Variables. Simplifying Radical Expressions. Adding and Subtracting Radical Expressions. Multiplying and Dividing Radical Expressions. Solving Radical Equations: The Distance Formula. Rational Exponents. Key Concept: Inverse Operations. 9. QUADRATIC EQUATIONS. Completing the Square. The Quadratic Formula. Graphing Quadratic Functions. Key Concept: Quadratic Equations. Appendix I: Statistics. Appendix II: Roots and Powers.