Intermediate Algebra, Ninth Edition

Rating:
Summary: Further adventures with algebra...
Review: This book is currently being used by the community college where I tutor as a book for the internet version of Intermediate Algebra, a course that most of our two-year degree programmes require as part of the mathematics requirement, and one of the most 'popular' courses at the tutor centre. Because this book is used by the internet course, it has to be well crafted to enable students to learn from on their own, and indeed, it seems to pass muster on that account.

The organisation of the book is fairly standard for algebra texts of this level: basic number theory is introduced (which should be a refresher or review from previous basic mathematics or algebra courses), the linear equations and inequalities are introduced, with equations of one variable, some elementary set operations, and the concept of inequalities. The third chapter introduces graphs, with the x-y coordinate axis, two-variable equations introduced. The fourth chapter looks at systems of equations, both in two and three variables, and introduces matrix methodology.

The fifth chapter develops the ideas of exponents, introducing scientific notation and polynomial multiplication and division. This is a prelude to factoring, the subject of chapter six. Trinomial factors, special cases and general approaches are discussed, including the grouping method and trial-and-error.

Chapter seven looks at rational expressions, complex fractions, and applications that build upon the factoring. Chapter eight introduces roots and radicals as a prelude to the quadratic equation in chapter nine. Graphing of functions such as parabolas is developed here.

Chapter ten looks at logarithmic, inverse and exponential functions, leading to analytic geometry topics such as conic sections, nonlinear functions and nonlinear systems in chapter eleven. This include hyperbolas, circles, and ellipses. The final chapter addresses the ideas of series (arithmetic sequences, geometric sequences) and introduces the binomial theorem.

The chapters have group activities at the end of each section that set the mathematics learned in proper 'real world' context. For example, the group activity for chapter eleven on analytic geometry topics deals with finding the paths of natural satellites; other activities include figuring out investments, the progress of disease spreading, the paths of comets, and comparing long-distance charges.

Each chapter comes with a convenient summary, a set of review exercises, and a chapter text. The summaries address key concepts, terms, new symbols introduced, and basic patterns of problems. There are also cumulative review sets after each chapter that address all the previous chapters. The first appendix is an introduction to calculators (there are many types of calculators, so this section is somewhat general, addressing those calculators which use basic algebraic logic in order of operations and other important areas.

The other appendices go into more detail about matrices and determinants (Cramer's Rule) and synthetic division for polynomials, for the ambitious students who wish to understand further.

The text is generally readable and accessible, with colourful pages, well-illustrated graphs and charts as required, and pictures thrown in for good measure and visual interest. The authors employ a six-step method for problem solving (read, assign variables, write equations, solve, state answers, check) at each step in the text. There is a student's solution manual, with detailed solutions to odd-numbered problems (plus others), available; this is where they 'show the work'; the simple answers are found in the back of the book.

This is a good book for classroom and self-study purposes.