Precalculus With Limits

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We use this book, `Precalculus with Limits' by Aufmann, Barker and Nation, as the two-semester sequence at our community college for College Algebra and Trigonometry. Most students at our college do not go on to Calculus, as our two-year degrees do not require that; however, they do need a solid grounding in topics such as trigonometric functions, analytic geometry, and advanced algebraic operations for the technical programmes of electronics, drafting, and other such degrees that emphasise technology and mathematical precision.

This text begins, as do algebra books at almost all levels, with a re-introduction to number theory, including absolute values, complex numbers, polynomials, factor and rational expressions. These are assumed knowledge already for students, so this is just a refresher section. The second chapter dealing with equations and inequalities, particularly linear equations and quadratic equations, are also assumed to have been covered before, but these go into new details. This section has an interesting section entitled `Can You Trust Your Calculator?' - one of the features of this text is a special interest section at the end of each chapter that ties the concepts to real-world and scientific applications, or introduces intriguing advanced mathematical concepts.

Chapters three through five address most of what is covered in our College Algebra class. This looks at two-dimensional coordinate systems and graphing. Polynomial functions, exponential functions and logarithmic functions are all discussed.

Chapters six through eight cover trigonometry. The principles of angles and arcs, how to read circles in degrees and radians, equivalences of trigonometric functions, graphing of sine and cosine curves, vectors and equations are included here.

Chapters nine through thirteen get into advanced topics of analytic geometry and advanced algebra. These include two-dimension graphing of parabolas, ellipses, hyperbolas and conic sections, and introduces the ideas of polar coordinates and axial rotation. Three-dimensional analytic geometry is introduced, including vectors in space (a key concept in physics). Work with systems of equations, advanced work with matrix algebra, and ideas of probability, series and sequences are covered.

The final chapter is a brief introduction to the idea of calculus, introducing the concept of limits and the concept of the derivative. Our courses omit this chapter, but it is interesting and seems well suited to prepare students for the next step in mathematics, should they opt to pursue this.

The book incorporates three primary features to link mathematics concepts and mathematics models. These include `Exploring Concepts with Technology', such as the calculator example above; `Topics for Discussion' prior to each exercise set, which can include group discussion elements; and `Projects', which can involve further research and narrative elements. These pieces help engage the students with mathematics beyond the simple solve-the-problem pedagogy.

This is a very useful text, easy to follow, accessible and helpful, and a solid manual for mathematics instruction.

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