Euclidean-Geometry Books

This is a potentially quite useful book that with minimal additional material would be outstanding. However, in this edition, its value is significantly diminished by its minimum set of solved examples, and its failure to include exercise solutions.

In each Chapter the author presents a brief discussion of various mathematical concepts followed by short presentations on how to use Maple to solve related problems. These discussions and presentations are quickly followed by "Your Turn" and other groups of exercises. Solutions are not provided, so readers are unable to confirm they have understood the concepts, or know how to obtain correct answers using Maple.

This might be appropriate in a classroom or computer laboratory environment where the instructor provides solutions to the exercises, however, not as a choice for self-study.

Each Chapter begins with a list of well-structured learning objectives, and the discussions preceding the exercises are short and well-written Thus, this book could serve as the basis for a set of lecture notes, updated to the latest version of Maple, with accompanying student laboratory exercises.

However, owing to the lack of a larger selection of solved in-text examples or exercise solutions, I would not recommended this book either as a course supplement or for self-study.

First of all, there are numerous minor errors in the printing; they get to be annoying at best, and extremely confusing at their worst.

The book also is too much of an overview--it makes a good introduction but a poor reference text. It is also very poorly indexed, which can make it hard to find things. The exercises are also poor--many new concepts are introduced in the exercises at the end of the chapters.

The writing is actually pretty good, for the most part. I think that the stuff that is explained in the book is explained well in most places, and the author does a very good job of tieing things together and bringing in historical background and significance of the topics being discussed.

I lastly might add that the name is very misleading--the geometries described in this book were mostly discovered over 100 years ago--there is nothing drastically "modern" about them.

Overall, this book was not prepared for being published--it needs a new edition to correct errors and tie up loose ends.

In Einstein's day this might have been a very good read! It is very well written. It is like reading a Spanish concurrent to Russell. A little reading finds it is a translation of a 1912 text. With general Relativity being a product of the understanding of the velocity based non Euclidean geometry of Lorentz who based his work on Poincare who based his work on Klein who based his work on... you see that history is important in an axiomatic development like this has been! But for a modern student of geometry, this book is much like buying a copy of Euclid's book on geometry: a reference that might help with understanding, but is so far out of date that it can be very little help in current problem!

This book should not be used in a honors-level class. But this book is good for high school students.

Galilean geometry is the study of the x-t plane under the motions that correspond to changes in time origin and change of uniform motion coordinate system. Although we introduce this geometry on physical grounds, we quickly move on to study this geometry in its own right without any physical motivation. Distance in Galilean geometry should mean distance in space and not in time so the distance between two points is the distance between their projections on the x-axis. Therefore circles in Galilean geometry are pairs of lines t=constant. The angle between two lines can be defined in terms of the section they cut out of a circle centred at their intersection, so in this way we have angles in Galilean geometry. But circles can also be defined in terms of angles: a moving point on a circle makes a constant angle with any two fixed points of the circle (half the central angle). Applying this definition in Galilean geometry gives a new type of curve which we call cycles. Circles and cycles together are in many ways the natural analog of Euclidean circles. We see this in particular when we study circle inversion. Euclidean circle inversion can be understood in terms of stereographic projection: put the plane tangent to the south pole and the eye at the north pole and project up on the sphere, then interchange the plane and the eye and project back. In Galilean geometry the sphere must be replaced by a cylinder (since, e.g., the center of the circle t=-c, t=+c is the line t=0 and thus maps to a line at infinity). In the chapter called "Conclusion" we look at how our ideas carry over to the geometry of space-time in special relativity, again without much concern for physics. As before, we use physics only to derive the motions of our geometry, in this case the Lorentz transformations, and then quickly go on to consider things of purely geometric interest. For instance, we see that the difference in signs between space and time components of a Lorentz transformation implies that a circle will be a hyperbola x^2-t^2=0 and the analog of stereographic projection requires a hyperboloid.

This book has pros and cons galore.

Pro: It is filled with an abundance of information relating to trigonometry and border-line physics. Con: There is no real emphasis on method used or relationalism. Pro: There are plenty of practice exercises and problems to help the diligent reader gain experience and ability. Con: Only the odd-numbered questions are answered and with very little detail and no method. Pro: Reference section and appendix for Trig. Tables, geometric facts, and metric system. Con: Language and vocabulary used is quite advanced and complicated. Final result: Unless you're a dedicated mathematician who enjoys mystery and deciphering, I would recommend you begin with a lighter introduction to trigonometry.

I've seen lots and lots of Precalculus textbooks, and this one is just about the bottom of the barrel. Faires and DeFranza have put together a book that's dull, poorly-organized, badly-written, and overpriced. The page layout is hazy and unfocused (look sharp for the tiny, tiny symbol that marks the end of one example and the start of another), and good luck spotting where one subject ends and the next one starts. They insist on using several lines of unfathomable symbology where a simple English sentence would explain things much more clearly. This would be fine for a Calc III book, but come on...

And unforgivably, there are dozens of incorrect answers in the back. My guess is that some questions were modified slightly to justify publishing the Fourth Edition, but the publisher was too cheap to hire a few grad students to make sure that the answers matched the new questions. And for my own personal gripe, I'll add that it's very irritating that some of the answers are given in simplified form and others aren't, seemingly at random.

This book is useless even if you're using it in a math class. The only positive thing I can say about it is that it weighs less than most of the other math textbooks I've had to carry around campus.

This book fails in teaching calculus.
It is simply a guide of problems without answers. Worthless for anyone looking to be learn calculus. It assumes a student has a good teacher who will explain everything. Very few classroom instructors spend enough time with students to make up for the deficiencies of this book....

I've taken up to college level Calculus I before I bought this book for my boyfriend who was taking Pre-Calculus. Since I took Pre-Cal a few years ago (and actually enjoyed it), whenever my boyfriend asked me if I could help him on his Pre-Cal homework, I turned to this book, which he bought as required text for his class, to refresh my memory on how to do some problems.

But instead of reminding me how to do the problems, this book confused me even more! Examples from the book that were supposed to help seemed to skip more than 2 steps at a time and provided no explanation on why some steps were taken. I ended up just looking at some other books and going to the Internet to re-learn concepts I've already been taught.

All in all, buy this book if you have to (ie, is required for class), but personally, I wouldn't recommend trying to teach yourself (or even re-teach) from this book.

This review is about two books: Precalculus, by Faires and DeFranza, and the Study Guide for the same book.

The reviews above seem to be about the text itself (which is, at the moment, not what is being offered for sale; the ISBN is that of the Study Guide).

While the comments from other readers may be valid relative to the uses to which they have put the book, I have found the book an admirable aid for teaching out of. It is compact, has good exercises and examples, is well laid-out and well planned.

Books which are good for self-teaching are not often useful for an instructor who can teach with competence. The text is not a substitute for the professor; it forms the third member of the trio who comprise the learning team: teacher, student, and text.

The book is not encyclopedic, which is a plus In my opinion. It leaves space for the instructor to supplement it with other topics. The approaches taken in the introduction of various topics are appropriate in the majority of cases; these are experts, who see the subject in perspective, and know how each topic fits into the bigger picture which is applied mathematics. A sophomore writing a book to help his freshman friends will write a very different book--possibly more immediately useful to them in some ways, but ultimately less useful! The reviewers seem not to realize that the book being offered for sale is the very Study Guide which could be of great help to those who want a self-teaching book.

I purchased this text as it is required for my precalc class. The review that follows this review talks about how this book is not a self teaching guide but is to supplement the classroom experience. I can't say that I agree wit that. The book is very difficult to read even after attending the classroom session on the topic. The author does a poor job of introducing topics and drawing out points. Symbols are used in a confusing manner without explanation. The author will introduce a topic, explain it in just a few sentences and follow with "therefore" followed by a conclusion that is not explained. The authors seem more interested in proving how smart they are and less interested in teaching. Not really a good book but the graphs are good and odd answers are in the back.

We found this book rather dull and also annoying in that it leaves out many proofs ("it turns out that...", "Gauss showed that...", etc.). We would not have bothered writing a review had we not been provoked by a sweeping statement regarding the history of mathematics on page 127: "if we assume Descartes's theorem [on exterior solid angles of polyhedra], we can prove that for any convex polyhedron V-E+F=2. As Malkevich points out in his article [in Shaping Space: A Polyhedral Approach, Senechal & Fleck (eds.)], this has led to the erroneous impression that Descartes could easily have discovered Euler's formula. But that would have required Descartes to think of a polyhedron as a combinatorial object, rather than a geometric object, a major intellectual leap at the time." This is complete nonsense. In fact, Descartes did think of polyhedra as combinatorial objects but choose not to publish since he did not get very far. A surviving manuscript has now been published: Descartes on Polyhedra: A Study of the "De solidorum elementis", Federico, Springer, 1982. Here Descartes gives several Euler-style identities, but none involving edges. Clearly, then, there was no "major intellectual leap" required to discover Euler's formula, just luck and persistence. The reason why Descartes and his contemporaries did not develop the combinatorial approach further was not some mysterious conceptual wall but simply the fact that this approach did not seem very fruitful.

While some of these complaints may be due to the course that used this book, I do believe that this is one of the worst math books I've ever read.

The book has several problems. The most glaring problem is its vagueness. None of the (117) figures are labeled. None of the questions are numbered, or given any other identifying mark. Some questions refer to figures on different pages, but simply say "look at [the figure]," only to leave the reader with the thought "what figure." Or to suggest one figure, though to use a different figure all together. Coupled with the fact that many theorems are not stated, or are not identified and are rarely proven. Stylistically, this book is just a mess.

If that weren't bad enough, many of the figures look like clipart images from 1991. The book is copyright 1998, suggesting to me that if he spent 7 (or more) years writing this book, maybe he should have redone some of the figures so they're not such an eyesore. Maybe this is a minor point, but if you're going to advertise the fact that you have 117 images, maybe you should make those images look nice.

As for the books good points, the information presented is in a logical fashion, and is correct. The text is easy to read (in that the font is not too small, or strange), and the pages are sturdy enough to write on them if you need to play with the figures.

For any teachers/professors reading this, I would not recommend using this book as a primary source for your course. Maybe it would be ok as a supplementary source.

Finally, if you were considering using this book for the topic on graph theory, then I would suggest instead using "Introduction to Graph Theory" by Robin J. Wilson (ISBN: 0-582-24993-7)

My son is using this textbook at school in a 10th grade pre-calculus course. As a microwave antenna engineer I take a strong interest in my son's science and maths education, and try to help with supplementary material where I think it is needed. When I read the first sentence in the book, which states that "a real number is any number that can be written as a decimal", my heart sank. The language usage is as poor as the accuracy of the statement, and it did not bode well for what the rest of the book may offer. It then proceeds to explain that the set of real numbers contains several important subsets, and calls out the natural numbers, whole numbers and the integers out in 3 clearly separated paragraphs. But this is followed by a discussion on the use of brackets, before the rational numbers and later, the irrational numbers are described - you have to read the text carefully before it is clear that these are two more subsets of the real numbers. Clearly marked paragraphs for these subsets would have worked better.

While skimming though the rest of the textbook, my initial misgivings were confirmed by the general lack of rigour, and the over-emphasis on terms, formulas and nomenclature without consistently explaining and/or proving how these are derived. A good example of this is the formulas given in Chapter 3, pp. 334-341 for annuities and mortgages without any proof or explanation. These are presented as examples of exponential functions, but in doing so the mathematics is reduced to a subject more akin to the learning of facts rather than learning the art of deduction. It would have been better to present the section on finance after the section on geometric series, since you need that to explain the formulas. Indeed, the book admits to this "loose end" in Chapter 9, where it belatedly derives one of these formulas, i.e. the future value of an annuity, p. 743.

The text is well illustrated, with attractive and colourful tables, graphs and pictures. But the content should be better organized with more attention to rigour, thus I would not recommend this book.

The topics in this text have enough breadth to cover
Functions (algebraic, transcendentals, etc) and their Graphs.

One typical feature that is extremely disturbing is the fact that the authors decided to throw in mathematical terms without
defining them first. For instance, as early as Chapter 1.2,
the term "lim f(x) as x approaches ***" is introduced so that
the graphical concept "continuity" can be taught.
There is much more to
limits than just "plotting the graph, seeing where the curve goes". The purpose of PreCalc as suggested by its name is to prepare the students to take Calculus. And if we do not want to
cover some concepts correctly (algebraically and graphically - the motto of this text!) but only to do it in a touchy-feely sense, then please do NOT cover it in PreCalc. Do it in Calculus!

The only reason I ever used this is because someone else chose it for our multiple sections course!

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.

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.

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.

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.

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.