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.
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Algebra for College Students-Mathematics
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.
NEWIntegration of AMATYC and NCTM Standards
NEWText organization reflects an emphasis
on problem solving. Chapter 1 is now Algebra and Problem Solving,
Section 3.2 includesProblem Solving and Modeling using Systems
of Equations, and Section 4.7 explores Polynomial Equations
and Problem Solving.
- 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.
NEWUsing 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.
NEWChapter 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.
NEWOptional 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.
NEWChapter Tests are included at the end
of each chapter for more review and reinforcement.
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.
(NOTE: Each chapter ends with summary and review problems
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
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
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.