[Book Cover]

Algebra for College Students, 3/e

Robert Blitzer, Miami-Dade Community College

Published September, 1997 by Prentice Hall Engineering/Science/Mathematics

Copyright 1998, 969 pp.
Cloth
ISBN 0-13-700212-2


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Summary

Designed for a “prep” course for college algebra or an alternative course to college algebra for students seeking a terminal math course to fulfill a math requirement.
This text provides comprehensive coverage of Intermediate Algebra plus coverage of polynomial and rational functions, sequences, probability and mathematical induction to prepare students for college algebra, precalculus and other “service” math courses. The material is presented in an interesting and inviting format that utilizes “real world” data and encourages modeling, critical thinking and problem solving.

Features


NEW—Integration of AMATYC and NCTM Standards

  • Over 50 % of the applications and many of the examples have been extensively researched and rewritten to incorporate current, real-world data drawn from familiar sources such as the 1995 Statistical Abstract of the U.S. published by the Census bureau.
  • Graphing is introduced and integrated earlier, starting in Section 1.3.
  • Functions are introduced in Chapter 2 and emphasized throughout in Chapters 3, 4, 5, 7, and 8.
NEW—Text organization reflects an emphasis on problem solving. Chapter 1 is now “Algebra and Problem Solving,” Section 3.2 includes“Problem Solving and Modeling using Systems of Equations,” and Section 4.7 explores “Polynomial Equations and Problem Solving.”
NEW—Using Technology, Study Tips, and Discover for Yourself features have been added as pedagogical enrichment to encourage student success. Study Tips in particular, make mathematical content more accessible.
NEW—Chapter Projects, extended one-page applications, conclude each chapter. Some activities feature related websites (available to students via the Prentice Hall/Blitzer website) for student research and exploration.
NEW—Optional Graphing utility opportunities have been added in appropriate sections and exercise sets. These sections, examples and exercises feature explorations, many with real screen grabs from the TI-83.
NEW—Chapter Tests are included at the end of each chapter for more review and reinforcement. FEATURES
An abundance of interesting and varied exercises are included (50% have been rewritten) to appeal to the modern (often non-traditional) student. The exercises, examples and writing style has been carefully and extensively reviewed and revised to better meet the level of student taking a developmental math course.
Modeling is introduced in Chapter 1 and emphasized throughout.
Real world sourced data, interpretation of data and visualization is fully integrated.
  • The use of fine art, historical notes and interdisciplinary connections are introduced in the context and applicability of algebra.


Table of Contents
(NOTE: Each chapter ends with summary and review problems sections.)
    1. Algebra and Problem Solving.

      The Real Numbers and the Number Line. Operations with the Real Numbers and Algebraic Expressions. Graphing Equations. Properties of Integral Exponents. Scientific Notation. Solving Linear Equations. Mathematical Models. Strategies for Solving Problems.

    2. Functions, Linear Functions, and Inequalities.

      Introduction to Functions. Linear Functions and Slope. The Point-Slope Equation of a Line. Solving Linear Inequalities. Compound Inequalities. Equations and Inequalities Involving Absolute Value. Linear Inequalities Containing Two Variables.

    3. Systems of Linear Equations and Inequalities.

      Linear Systems of Equations in Two Variables. Problem Solving and Modeling Using Systems of Equations. Linear Systems of Equations in Three Variables. Matrix Solutions to Linear Systems. Solving Linear Systems of Equations Determinants and Cramer's Rule. Systems of Linear Inequalities and Linear Programming.

    4. Polynomials, Polynomial Functions, and Factoring.

      Introduction to Polynomials and Polynomial Functions. Multiplication of Polynomials. Greatest Common Factors and Factoring by Grouping. Factoring Trinomials. Factoring Special Forms. A General Factoring Strategy. Polynomial Equations, Modeling, and Problem Solving.

    5. Rational Expressions, Functions, and Equations.

      Rational Expressions and Functions: Multiplying and Dividing. Adding and Subtracting Rational Expressions. Dividing Polynomials. Rational Equations, Modeling, and Problem Solving. Modeling Using Variation.

    6. Radicals, Radical Functions, and Rational Exponents.

      Radicals and Radical Functions. Inverse Properties of nth Powers and nth Roots; Rational Exponents. Multiplying and Simplifying Radical Expressions. Dividing and Simplifying Radical Expressions. Further Operations with Radicals. Radical Equations. Imaginary and Complex Numbers.

    7. Quadratic Equations and Functions.

      Solving Quadratic Equations by the Square Root Method. Completing the Square and Graphs of Quadratic Functions. The Quadratic Formula. Problem Solving and Equations That Are Quadratic in Form. Solving Quadratic and Rational Inequalities.

    8. Exponential and Logarithmic Functions.

      Exponential Functions. Composite and Inverse Functions. Logarithmic Functions. Properties of Logarithmic Functions. Solving Exponential and Logarithmic Equations. Modeling with Exponential and Logarithmic Functions.

    9. Conic Sections and Nonlinear Systems of Equations.

      Conic Sections: Circles and Parabolas. Conic Sections: Ellipses and Hyperbolas. Nonlinear Systems of Equations.

    10. Polynomial and Rational Functions.

      Polynomial Functions and heir Graphs. Polynomial Equations Having Rational Solutions. Rational Functions.

    11. Sequences, Probability, and Mathematical Induction.

      Sequences and Series. Arithmetic Sequences and Series. Geometric Sequences and Series. The Binomial Theorem. Counting Principles, Permutations, and Combinations. An Introduction to Probability. Mathematical Induction.

    Appendix: Review Problems Covering the Entire Book.


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