Synopses & Reviews
Williams offers a refreshing and innovative approach to college algebra, motivating the topics with a variety of creative applications and thoroughly integrating the graphing calculator. Written in a clear and friendly voice that speaks to students with varying algebra skills, with a rich array of pedagogical devices to support their learning, this text teaches students to look at math from both algebraic and geometric viewpoints. Williams focuses on the underlying concepts, introducing and using the graphing calculator as an integral means, not an end. This new edition is complemented by an outstanding array of innovative supplements (including online tutorials, video lessons on CD-ROM, and powerful course management and testing resources) that facilitate teaching and enhance learning.
Review
"I really like all of the calculator work as it appears in the text, since it usually draws attention to both the drawbacks and advantages of technology." "The layout of topics was also appealing--the interplay between geometry and algebra is emphasized from the very first chapter, subject matter is reemphasized and strengthened in successive chapters, and the material on exponential and logarithmic functions is easily reached..."
Review
"The exercise sets span a wide range of rigor . . . and are more than sufficient in number. The exercises allow for more than skill and concept development." "One of the greatest strengths of Williams' COLLEGE ALGEBRA are the excellent applications from a variety of areas."
About the Author
Gareth Williams received his B. Sc. and Ph.D. from the University of Wales. He has taught at the University of Florida, the University of Denver, and most recently, at Stetson University (DeLand, FL), where he was honored with the McInery Award for Teaching Excellence. His research interests include the role of technology in mathematics education, linear algebra, relativity, applied mathematics, and mathematical modeling. He is also the author of LINEAR ALGEBRA WITH APPLICATIONS, Fourth Edition (Jones and Bartlett, 2001), computer software including THE LINEAR ALGEBRA TOOLBOX FOR MATLAB and MATHEMATICA WORKBOOK ON LINEAR ALGEBRA, and numerous articles in refereed journals. Williams is also an active member of the Mathematics Association of America.
Table of Contents
Preface. REVIEW OF BASIC ALGEBRA. Real Numbers and Their Properties. Rational Exponents, Scientific Notation, and Doses of Medicine. Polynomials. Factoring. Rational Expressions. Equations, Traffic Flow, and Fermat's Last Theorem. Chapter R Project: Space-Time Travel. Chapter R Highlights. Chapter R Review Exercises. Chapter R Test. 1. INTERPLAY BETWEEN ALGEBRA AND GEOMETRY. Equations, Graphs, and Data Analysis. Functions, Tables, and Skeleton Sizes. Lines, Least-Squares Fit, and Analysis of Tuition Costs. Linear Functions, Reservoir Monitoring, and Location Evaluation. Parabolas and Quadratic Equations. Quadratic Functions, Learning German, and Fluid Flow. Distances, Circles, and Typesetting. Chapter 1 Project: Real and Subjective Times. Chapter 1 Highlights. Chapter 1 Review Exercises. Chapter 1 Test. 2. SOLVING EQUATIONS AND INEQUALITIES. Quadratic Equations. Further Types of Equations. Equations, Variation, Architecture, Navigation, and Ecology. Inequalities, Temperature Range of a Computer, and Spread of a Disease. Equations and Inequalities with Absolute Values. Chapter 2 Project: Algorithms for Finding Roots and Solving Equations. Chapter 2 Highlights. Chapter 2 Review Exercises. Chapter 2 Test. Cumulative Test: Chapters R, 1, and 2. 3. FURTHER DEVELOPMENT OF FUNCTIONS. Polynomial Functions. Construction of Functions, Optimization, and Drug Administration. Special Functions, Symmetry, and Consumer Awareness. Shifting and Stretching Graphs, Supply and Demand for Wheat. Rational Functions, Queuing Theory. Operations on Functions and An Introduction to the Field of Chaos. Inverse Functions, One-to-One Functions, and Cryptography. Chapter 3 Project: Recalling Ability. Chapter 3 Highlights. Chapter 3 Review Exercises. Chapter 3 Test. 4. FURTHER THEORY OF POLYNOMIALS. Synthetic Division, Zeros, and Factors. Complex Numbers and the Mandelbrot Set. Complex Zeros, Complex Factors, and the Fundamental Theorem of Algebra. Computing Zeros of Polynomials. Chapter 4 Project: Julia Sets. Chapter 4 Highlights. Chapter 4 Review Exercises. Chapter 4 Test. 5. EXPONENTIAL AND LOGARITHMIC FUNCTIONS. Exponential Functions and the Growth of Escherichia Coli. The Natural Exponential Function and Color Television. Logarithmic Functions and Seismography. Logarithmic Equations, Dating of Artifacts, and the Learning Curve Effect. Exponential Regression and Intravenous Drug Administration. Chapter 5 Project: Simulating the Government Model for World Population. Chapter 5 Highlights. Chapter 5 Review Exercises. Chapter 5 Test. Cumulative Test: Chapters 3-5. 6. SYSTEMS OF EQUATIONS AND INEQUALITIES. Systems of Linear Equations in Two Variables. Systems of Linear Equations in Three Variables. Gauss-Jordan Elimination and Electrical Networks. Systems of Nonlinear Equations. Systems of Linear Inequalities. Linear Programming and Optimal Use of Resources. Chapter 6 Project: Linear Programming. Chapter 6 Highlights. Chapter 6 Review Exercises. Chapter 6 Test. 7. MATRICES. Matrices and Group Relationships in Sociology. Multiplication of Matrices and Population Movements. The Inverse of a Matrix, Color Graphics, and Interdependence of Industries. Determinants and Cramer's Rule. Symmetric Matrices and Archaeology. Chapter 7 Project: Influence Within a Group. Chapter 7 Highlights. Chapter 7 Review Exercises. Chapter 7 Test. 8. SEQUENCE AND SERIES. Sequences, Series, and the Fibonacci Sequence. Arithmetic Sequences. Geometric Sequences, Bacteria Counts, and the Flaw in the Pentium Chip. Mathematical Induction. The Binomial Theorem. Chapter 8 Project: E-mail Messages. Chapter 8 Highlights. Chapter 8 Review Exercises. Chapter 8 Test. 9. PERMUTATIONS, COMBINATIONS, AND PROBABILITY. Permutations and Combinations. Probability and Blood Groups. Chapter 9 Project: Traffic Flow. Chapter 9 Highlights. Chapter 9 Review Exercises. Chapter 9 Test. Cumulative Test: Chapters 6-9. Appendix A: Conic Sections: Parabolas, Ellipses, and Hyperbolas. Appendix B: Calculator Reference. General Calculations. TI-83 Reference. Answers to Odd-Numbered Exercises. Index of Applications. Index.