# Precalculus

Carl Stitz, Lakeland Community College

Jeff Zeager, Lorain County Community College

Copyright Year: 2013

Publisher: Stitz Zeager Open Source Mathematics

Language: English

## Conditions of Use

Attribution-NonCommercial-ShareAlike

CC BY-NC-SA

## Reviews

The book is thorough in its treatment of topics. It assumes some algebra skills, the first five chapters will go too quickly for a student that needs a comprehensive college algebra course, but the pace is appropriate for a two semester course... read more

<p> The book is thorough in its treatment of topics. It assumes some algebra skills, the first five chapters will go too quickly for a student that needs a comprehensive college algebra course, but the pace is appropriate for a two semester course designed to get students ready for calculus. Had this been a hard copy text, students would complain about its length (over 1000 pages). That's the beauty of open-source .pdf file texts, and the authors made use of it, including deep topics like 'rotated conics'. It contains a discussion of matrices in the chapter on solving equations and dot products (but not cross products).</p>

<p> I haven't used the text yet myself, and therefore can't verify that the solution to the problems are correct, but it is in its 3rd edition, so it is likely that lots of these kinks have been worked out. The presentation of the mathematics seems fairly standard.</p>

<p> The text has almost no color and is lacking in graphics by today's standards. For example, it is noted that the integers, rationals, reals ... are 'nested' like Matryoshka dolls, but there is no picture, nor even a Venn diagram to illustrate the nesting. Other will contend I am wrong on this, but the degree-minute-second method of measuring angles is a thing of the past. This is one example of where the authors could have examined the standard ways we have taught things for decades and brought them up-to-date. Many of the graphics use a TI-8x series calculator. I am finding that a majority of my students use an online graphing utility (wolframalpha or desmos).</p>

<p> The authors attempt to let their personality show in their writing with their humor, but it often comes off as an inside joke. If you have either of the authors as your professor, it probably seems like natural conversation, but I could see it as a bit distracting for most students. The mathematical content is very formal, (ordered pairs as defined as 'abscissa and ordinate') but presented in a very standard way. The graphs support the mathematics clearly.</p>

<p> The format is similar to most formal mathematical texts. The authors have done a good job providing links to references. For example, when a theorem from a previous chapter is referenced, you can click on the link to go back and see the theorem. Unfortunately, you may not be able to get back. Problems are linked in a similar way. It is handy be alerted to a future problem that uses the current material, but if you take the link to look at the problem, you may not be able get back.</p>

<p> Since the chapters and problem sections are numbered, it's not clear how the links could be reorganized. Otherwise, the material is subdivided in a fairly standard chapter/section/subsection hierarchy. Those that prefer to do trigonometry early could easily move chapter 10 ahead four chapters.</p>

<p> Very standard for a math text, with one exception: The solutions to the exercises are given at the end of the section, not at the end of the book. Again, a great feature of open-source material is that if you prefer to have the answers at the end of the book, or in a separate volume all-together, it could be easily done.</p>

<p> There are many links within the text, taking the reader to statements of previous theorems, previous examples, particular exercises which is a handy feature. Unfortunately, when you follow the link, you may not be able to get back. It seems to work back-and-forth in Firefox, but not in GoogleChrome. There are also links to more detailed work if necessary. The main text works out problems at a standard and appropriately small number of steps. For those whose algebra skills are weaker, there are links to more detailed work, which is handy.</p>

<p> At times, sentences run on, with the sentence looking more like a paragraph and having multiple commas. Otherwise, the writing looks clean, although at quite a high level.</p>

<p> The authors use standard wording to problems and don't try to personalize the material. For example, they say that 'a car is travelling at ...' rather than trying to name the person driving the car in a shallow attempt to include diversity. The book is neutral in this sense.</p>

<p> Overall, the book is very formal in its definitions, which may be good for advanced high school students who will pursue degrees in math and science, but is likely beyond the level of college students taking precalculus. Composition of functions and one-to-one function are dealt with in a very formal algebraic way, and supported with brief graphical representations. The derivation of formulas is quite formal, leading to the formula being highlighted in a box, leaving the reader to believe that the result is an important formula to be memorized, and thus works well if you believe in memorization. If you want your students to pay attention to the process of creating the formula and the underlying concept, the layout of the book will be a hindrance.</p>

## Table of Contents

- 1 Relations and Functions
- 2 Linear and Quadratic Functions
- 3 Polynomial Functions
- 4 Rational Functions
- 5 Further Topics in Functions
- 6 Exponential and Logarithmic Functions
- 7 Hooked on Conics
- 8 Systems of Equations and Matrices
- 9 Sequences and the Binomial Theorem
- 10 Foundations of Trigonometry
- 11 Applications of Trigonometry

## Ancillary Material

## About the Book

A casual glance through the Table of Contents of most of the major publishers' College Algebra books reveals nearly isomorphic content in both order and depth. Our Table of Contents shows a different approach, one that might be labeled “Functions First.” To truly use The Rule of Four, that is, in order to discuss each new concept algebraically, graphically, numerically and verbally, it seems completely obvious to us that one would need to introduce functions first. (Take a moment and compare our ordering to the classic “equations first, then the Cartesian Plane and THEN functions” approach seen in most of the major players.) We then introduce a class of functions and discuss the equations, inequalities (with a heavy emphasis on sign diagrams) and applications which involve functions in that class.

The material is presented at a level that definitely prepares a student for Calculus while giving them relevant Mathematics which can be used in other classes as well. Graphing calculators are used sparingly and only as a tool to enhance the Mathematics, not to replace it. The answers to nearly all of the computational homework exercises are given in thetext and we have gone to great lengths to write some very thought provoking discussion questions whose answers are not given. One will notice that our exercise sets are much shorter than the traditional sets of nearly 100 “drill and kill” questions which build skill devoid of understanding. Our experience has been that students can do about 15-20 homework exercises a night so we very carefully chose smaller sets of questions which cover all of the necessary skills and get the students thinking more deeply about the Mathematics involved.

## About the Contributors

### Authors

**Carl Stitz**, Professor of Mathematics at Lakeland Community College. Kent State University, PhD, Mathematics (Low Dimensional Topology).

**Jeff Zeager**, Professor at Lorain County Community College, Science and Mathematics Division. Kent State University, BS, MS, PhD, Pure Mathematics.