Customer Reviews

Algebra and Trigonometry with Analytic Geometry (with CD)

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I teach a high school class for advanced mathematics in preparation for college maths, and I honestly have to say that this is the worst book from which to teach. Yes, I can understand it perfectly, but a student will be lost the moment he or she lays eyes on the first page. The only good thing about this book is the number of exercises it has in each section.

I'm a little torn on what to say about this book. On one hand, I have a huge amount of respect for this book. On the other hand, it's not an easy book to learn from.

I have no doubt that if people work through this book, they will be very knowledgable and skilled in the areas covered. It is, however, a slow, tedious, sometimes frustrating process. The authors are clearly proficient at math, but their style is pretty dry. It's a "just the facts, ma'am" approach to instruction. It would be nice to have perspective, interpretation, and helpful guidance in addition to straight math. It's kind of like reading a technical manual. I prefer a more engaging presentation.

This book is required by my college and dealing with it was the most unpleasant period of my life. Prior to using this book I used the Saxon Math Program in which each lesson contains enough information to learn the material without the help of an instructor. There is no way that you can teach yourself from this book if you don't all ready know the material, and many math professors are lazy and tell you to get the knowledge out of the book. The lesson material is too brief and the explanations are almost cryptic. The solutions manual that comes with it is supposed to have the answers to all the odd problems, but the author decided to leave out a couple of these problems in which the answer would take up a little more paper than the others, these are often the ones you need the solutions to, the book just leaves you stranded. If you have to use this book, I pity you, you better hope that you have a darn good math professor. If you don't have to use it, steer clear of it.

Frankly, I found this text way too brief in its coverage of topics prior to being bombarded with questions. There isn't much good to say about this book other than providing lots of problems to work. Save yourself the money and buy a "10000 problem" text instead.

Precalculus is hard enough without having to use a book like this. I thought that the prose was unreadable, the graphics confusing, and many of the exercises supercomplicated (our professor thought so too). In my opinion *Algebra and Trignometry* is a triumph of marketing over pedagogical competence. My advice? Not only should you not buy this book; you should avoid a class in which it is assigned.

The text only introduces the basics of a concept before introducing much more complicated problems in the chapter practices. Very little detailed information to help understand concepts. I had to use other texts and online resources to supplement this POS testbook.

It was well-organized without being too formatted and nit-picky. The explanations made sense and it was great for note-taking. The problems were challenging, but not so hard that it was no fun. I strongly recommend this book for use in the classroom and out of it for private use and/or review.

I taught out of this book for a college algebra class consisting mainly of college freshman who are not math majors but some of whose majors will eventually require calculus. I was very disappointed with the overall quality and presentation of this book. Below are the main flaws I found with it:

1. Lack of sound organizational structure and wasted connection-making opportunities:

This book, like many other widely used college textbooks, is written in a very haphazard way. Here are the chapters that the course I taught covered:

Chapter 1- Fundamental Concepts of Algebra

Chapter 2- Equations and Inequalities

Chapter 3- Functions and Graphs

Chapter 4- Polynomial and Rational Functions (only sections 1 and 6)

Chapter 9- Systems of Equations and Inequalities (only sections 1 and 2)

Chapter 5- Inverse, Exponential and Logarithmic Functions

The absolute worst problem with the order of this presentation is the lack of introduction of functions until the 3rd chapter. Functions are the MOST important concept in a college algebra/precalculus class; not only are they the building blocks for learning calculus and higher-level mathematics, but they are a central component in the process of connection making. Functions connect ALL of the concepts in the first three chapters together, but by deferring them until the third chapter, the authors miss a critical pedagogical bridge in the process of learning how mathematics works.

I understand that a typical college algebra class usually contains many students who need the first two chapters to review their algebraic manipulation skills; what I don't understand is why the authors couldn't have integrated these topics side-by-side with functions. Ignoring this process leads to two basic flaws:

A. Spreading out material that could be covered in one section or chapter

B. Making said similar material appear unrelated and distant due to chapter-size gaps between different pieces of the material.

Much of the material in Chapters 1-3 is repeated across several sections due to putting off the introduction of functions. An example of this is Section 2.3 which talks about quadratic equations and how to solve them, but these are introduced again as quadratic functions in Section 3.6. This creates a huge distance between the two topics which are dealt with in the EXACT SAME WAY. Solving a quadratic equation is intimately related to the process of operating with a quadratic function (for example, finding zeros of a quadratic is the same thing as finding the x-intercepts). Because these topics are treated separately, students miss this crucial connection and oftentimes think that solving a quadratic equation and finding the x-intercepts are totally unrealted processes. In a book written for a class of non-math majors, this totally inhibits the CONNECTION-MAKING process that is crucial to understanding math. Non-math majors usually have a difficult time with math because they are unable to see these connections. Also, separating quadratics in this way creates an unnecessary gap between Sections 3.5 (graphs) and 3.7 (operations and graph shifting). Graphs and shifts of functions are intimately related, and adding quadratics in between them makes the two topics seem more distant than they really are.

A second organizational flaw comes in Chapter 9. The class I taught covered Sections 9.1 and 9.2. The ordering of these two sections is haphazard at best. The first section deals with systems of equations, mostly systems that are nonlinear and involve the graphs of lines and parabolas intersecting with circles, parabolas, ellipses and hyperbolas. These are generally more difficult for students to solve since their equations usually contain either more than 1 solution, or present systems with zero solutions that may be difficult to graph without a graphing utility. Then for some strange reason, the authors introduce systems of linear equations in two variables in Section 9.2. This makes very little sense to me; systems of linear equations are inherently MUCH simpler than general systems of equations that are not necessairly linear. Linear equations in two variables have three cases that can occur (no solution, one solution or infinitely many solutions). If you compare this to the difficulty of the previous section, it is far easier; so WHY introduce the more difficult topic first (especially dealing with students whose strong suit is not math)? Why not start with the easiest case and then build it up more slowly?

The last organizational flaw that I will mention comes in Chapter 5. The topic of exponential functions is broken up into two sections: one on general exponential functions and the second on the natural exponential function. Why the authors did this is a mystery to me; the natural exponential function arises quite naturally from the general exponential functions and behaves in exactly the same way as the others. So why introduce it separately? This makes students believe that the natural exponential function is somehow disconnected from the other exponentials when really it is not.

2. Poorly written exercises:

The second largest flaw with this book is with the exercises. Many of the word problems are written in such a way that it makes the student (and sometimes the instructors) misinterpret the question due to poor wording and or setup. An example of this is Problem 49 in Section 3.7. The problem asks for the altitude of a balloon as a function of time. The basic idea in this problem is to set up a composition of two functions by relating them in a special way. This is a great setup to the realted rates problems that occur frequently in calculus. However, the books does not tell the student where the altitude of the balloon is in the picture, so for many it is unclear that they are solving for one of the legs of the right triangle formed instead of the hypotenuse. The book never before defines an altitude and it is unlikely that non-math major students will know which side of the triangle to solve for. This can easliy lead to frustration. All the authors had to do was label the side of the triangle that represented h; for non-visual, non-intuitive learners, this problem can be a bane.

3. Examples that fail to promote multiple approaches to problem solving:

Little to no emphasis is given on using multiple approaches to solving a problem (graphs vs. algebraic vs. calculator, etc.). This is usually because an equation that could easily be solved graphically will appear in a section before graphs are introduced, leading to students not seeing the CONNECTIONS between the topics of solving graphically and solving algebraically. Again, connection making is the central process in mathematics and is usually what distinguishes meidocre math students from strong ones; good students who have been well-trained from a good instructor and a better-written text will almost always have more than one approach to solve a problem which will lead to greater efficency and good mathematical judgement when choosing the easiest approach to a problem.

Compare this fecal matter to Larson, Edwards and Hostetler's "Precalculus with Limits: A Graphing Approach" (2001). Nearly EVERY example in Larson's text includes an algebraic, graphical and numeric approach and clearly explains the advantages and disadvantages of each (mainly this helps you decide when to use which approach). I understand that this "Classic Edition" of Swokowski/Cole is trying to steer clear of the use of a graphing utilty, but it still fails to mention numerical approaches to solutions of equations and rarely incoporates graphs due to the lack of introduction of functions and graphs until the 3rd chapter.

4. Lack of a "Library of Funcions" and other connection-making features:

This text fails to include any kind of a library of functions (a reference page listing the most common functions and their properties). Larson's text includes one of these in the front and back covers of the book, but Swokowski's text does not include it anywhere. In fact, Swokowski devotes the front and back covers to formulas instead, when he could have just put all of the formulas in an appendix. Depriving students of the ability to see the most common functions and their properties (domain/range, a quick sketch, etc.) side-by-side again inhibits the CONNECTION MAKING ABILITY that is so crucial to understanding HOW and WHY math works.

5. The price:

Like most other college textbooks, this book is extremely overpriced. Buy used, or else you'll be expected to fork over around $150 for this garbage when you could just buy Larson's text off of eBay or Amazon for a much cheaper price.

In short, this book fails pedagogically on multiple levels, but most profoundly on its lack of connection-making opportunities that are so crucial to the understanding and interpolation of higher-level mathematics. In a book that's designed to show non-math majors the way to calculus, this book falls completely short. You'd be much better off buying Larson's text (I own the 3rd edition from 2001 along with the Instructor's Solutions Manual); in my opinion, Larson is more useful for self-study and for people seeking a book from which they can actually learn instead of just repeating seemingly isolated (but actually connected) processes over and over again like they will with Swokowski.