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Customer Reviews (4)

Fun and informative
This book is a great introduction into geometry. Fun story plus my kids and I enjoyed searching for all of the shapes hidden within each illustration.

Mummy Math
Illustrations are done well, the story line is engaging for children.It keeps them involved in the mystery.

Lesson Kickoff!
I used this book for two separate lesson plans.I made a game board and added game cards based on the book.This quickly became an engaging way to count faces, vertices, and edges.I also used it in 7th grade social studies to add questions about history.BONUS: my 13 yr. old and 10 yr. old thought it was an engaging book!

math fun
This is a picture book about the Zills family.The family is off on an adventure to hiddenburial site of an ancient pharaoh.The twin brothers in the family get stuck inside a pyramid with their dog.They must use math to figure out a way to escape the pyramid. They must use skills to figure out the riddles written on the wall and locate the hidden burial chamber. Will they ever figure it out?Read Mummy Math to find out!

It's one of those special books which children will read without realizing they are learning a mathematical concept.

This is a recommended book for those teacher or parents that want to make math a little more exciting for children. ... Read more

Product Description
Geometry & Trigonometry for Calculus By Peter H. Selby If you need geometry and trigonometry as a tool for technical work … as a refresher course … or as a prerequisite for calculus, here’s a quick, efficient way for you to learn it! With this book, you can teach yourself the fundamentals of plane geometry, trigonometry, and analytic geometry … and learn how these topics relate to what you already know about algebra and what you’d like to know about calculus. You’ll work your way through geometry, numerical trigonometry, methods of trigonometric analysis, analytics, and limits—all the way up to the "front door" of calculus. Geometry and Trigonometry for Calculus is one of the Wiley Self-Teaching Guides. It’s been tested, rewritten, and retested until we’re sure you can teach yourself the concepts of geometry and trigonometry. And it’s programmed—so you work at your own pace. No prerequisites are needed. Objectives and self-tests tell you how you’re doing and allow you to skip ahead or find extra help if you need it. Frequent reviews and practice exercises reinforce what you learn. Wiley Self-Teaching Guides Astronomy, Moche Basic Physics, Kuhn Chemistry: Concepts and Problems, Houk How to Succeed in Organic Chemistry, Gordon Basic Electricity, Ryan Electronics, Kybett Ecology, Sutton Energy for Life, Allamong Plant Anatomy, Stevenson Quick Medical Terminology, Smith Human Anatomy, Ashley Dental Anatomy and Terminology, Ashley Math Skills for the Sciences, Pearson Thinking Metric, 2nd ed., Gilbert Using Graphs and Tables, Selby Geometry and Trigonometry for Calculus, Selby Quick Calculus, Kleppner BASIC, 2nd ed., Albrecht BASIC for Home Computers, Albrecht ANS COBOL, 2nd ed., Ashley Structured COBOL, Ashley Fortran IV, Friedmann, Greenberg & Hoffberg ATARI BASIC, Albrecht TRS-80 BASIC, Albrecht Job Control Language, Ashley Flowcharting, Stern Introduction to Data Processing, 2nd ed., Harris Background Math for a Computer World, Ashley Probability, Koosis Statistics, 2nd ed., Koosis Finite Mathematics, Rothenberg Practical Algebra, Selby Quick Arithmetic, Carman Math Shortcuts, Locke Study Skills: A Student’s Guide for Survival, Carman Psychological Research: How to Do It, Quirk Psychology of Learning, Royer Choosing Success: TA on the Job, Jongeward Successful Time Management, Ferner Communication for Problem Solving, Curtis Skills for Effective Communication, Becvar Clear Writing, Gilbert Punctuation, Markgraf Vocabulary for Adults, Romine Spelling for Adults, Ryan Reading Skills, Adams Art: As You See It, Bell Your Library —What’s in It for You? Lolley Quickhand, Grossman Quick Typing, Grossman Consumer Math, Locke ... Read more

Customer Reviews (14)

Great book!
I bought this book as a `running start'and refresher for college level math classes. The book was very easy to follow and, as a person who is NOT math savvy in any way, was never fustrated or confused.Thiswas a great book and recommend it to anyone. I would have bought the book new Vs used had I known there were so many opportunities to work the problems in the book. With the problems already worked out the challenge wasn't there BUT was found helpful when I was stuck.

Calculus prep - or Precalc review
This particular calculus study guide is clearly oriented for those whom are considering engineering or science related fields as business calculus will have less of a need of geometry and trigonometry. For those whom are interested in engineering/science fields and struggled a bit in geometry or trig, then this text can be a great support to have by your side during your precalc class OR for self-study/review after precalc and before calculus.

Indeed, there are several circumstances in which this self-study text can be used.

1) If you are in precalculus and struggling and wondering what parts are really important for calculus next year/semester.

2) If you took precalculus last year/semester and want a study guide (besides your old textbook) to get ready for Calculus.Indeed, for high school students this may be a great summer book to work through after precalc to assure you're ready for Calculus.

3) If you took precalc many years ago and want a refresher, or even if you took Calculus 1 many years ago and want to review the prerequisites prior to refreshing your calculus.

There is a final chapter on Limits which will be covered in the start of Calculus 1 and which can probably be skipped. There is a stronger emphasis on "focus" and "foci" than in many precalc books so this may make some students think, "Why didn't my teacher cover this?" Also, there's a trig table... just remember the book was originally published in 1975 and so a couple of emphases are now slightly different but overall the value of the text remains high as a supplement.

READ HERE FOR DETAILS
This book is excellent. I don't believe that I can find anything wrong with this book.

Some readers are saying that this book has too small of a font, or that the binding is loose, or that the book offers little in explanations to the awnsers for the practice problems. These are simply false. The font is a size twelve by most computer's standard font, if you can't see that small get glasses. If some books are falling apart stop throwing them or bending the spine. The explanation part is true in that the book doesn'tsay things like "the reason this is the awnser is..." However, I feel that the explanation of how geometry works and what it's rules are, is sufficient for the reader to analyse why the awnser is what it is. If you cannot do this it may be adviseable to bring the problem in question to a friend or teacher knowledgeable in geometry (I mean this in the kindest of manners).

Over all the book is clear and quick to the point. Some people may find it a bit dry in that there is no humor really or any stories, strictly instructional. Some may find it difficult to remember things this way or to read a book written in such a manner.

This book is written so that a reader who has no knowledge about geometry can understand it.

Overall a five star book and worth the price and then some.

(Please forgive anything mispelled I didn't have time to check this review.)

good as a companion only
If you want to test your knowledge of geometry and trig after reading another text book, this is good.However, this is not a standalone book.It offers problems and answers, but very little in examples and explanations of why.

Unless you want a refresher, I'd go somwhere else, maybe a dummies or idiots guide instead.

There aren't enough exercises..
The best and most enjoyable way to learn math is through practice, and although Peter H. Selby articulately explains the concepts presented in this book, there just aren't enough exercises for you to "teach yourself" the subject.A given section on plane geometry will give you about 15 abstract principles followed by 5 easy practice exercises.I have learned from this book, but in order to do so, I've had to make flashcards and do lots and lots of rereading to help me memorize the vocabulary and rules.This book would be okay for someone who just needs a quick refresher, but if you really want to learn the material, I would suggest buying separate 350-400 page books for each subject. ... Read more

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Customer Reviews (18)

Excellent examples
Finally, an understandable upper-level math text! Greenberg walks you step-by-step through the proofs of the foundation ideas for each chapter (with selected exceptions left as examples. However, these proceed predictably from other examples that do have full proofs). There are numerous exercises at the end of each chapter, typically professors will choose a handful that they find interesting or amusing and assign those. No answers are at the back of the book. The problems require proofs and I have yet to see a text that provides answers to proofs problems in the back. Anyhow, many problems have multiple approaches. I actually found this book easier to understand than the professor.

an excellent and really untertaining book
There are already 16 reviews of this excellent and exciting book so i will only add that some people complained about the great number of results of the core text the reader is asked to search proofs as exercises. For a mathematically inclined reader this is not such a big trouble because most of these exercises have extended indications which math-inclined people can easily transform in a complete and sound proof. For myself i had almost no trouble with them (there is one exception with the section on axioms of beetwenness in chapter 3, i took the strategy of admitting the propositions of this section i could not prove as complementary axioms (these propositions are visualy obvious and easy to accept) so i proceeded further for the really interesting matters).
So the difficulty is only for people who did not have a mathematical training as college junior. Even in this casethey can learn a lot about the nature and purpose of pure mathematics and, if they are persistent and enduring, how to read and write mathematical proofs.
As a Frenchman i wonder why such a good book has not been translated in French, it really deserves it because books in French on geometry are so often unexciting and boring.

Quintessential Work on Non-Euclidean Geometry
I had the pleasure of reading and studying the Second Edition of this text while in college.This course with this text was my favorite course during all of my undergraduate math courses.

Being a fan of the subject, I was eager to see the new Fourth Edition of the text.The Fourth Edition is quite expanded from earlier editions, going past the wonderful main story of the Parallel Postulate - told better by Greenberg than any other author, IMHO - and diving into the different non-Euclidean geometries that "open one's eyes" by setting aside the "obvious axiom of a unique parallel". The last chapters are greatly enhanced, with a superb presentation of the issue of straightedge and compass constructions in the Hyperbolic plane.

This presentation of Non-Euclidean geometry is more serious than the "popularized" books on advanced mathematical topics.If you're looking for a "light, fun" reading of this topic, this is not the book for you.

I feel that the real power of the story of the maturing of intellectual thought, so brilliantly portrayed in the story of the Parallel Postulate, must be experienced, through the effort (and often hard work) of actually **doing** geometry, rather than just reading lightly about it. If you want to dive in and actual experience geometry (and the consequent rewards), then this is the book for you.The explanations are magnificent, the problems are wonderful (and, at times, very challenging), all culminating in the "wow!" of modifying the Euclidean way of thinking to a new and beautiful alternate geometrical universe.

As other reviewers have noted, this text reads like a great novel - a drama involving geometry.If PBS/Nova ever make a "What does Parallel mean anyway?" show, this text will be the basis for that show.

I believe this Fourth Edition can be considered the quintessential text on this topic, on which all future discussion of the topics can be based, including both the introductory materials, as well as moving to the forefront of research on many topics in Hyperbolic geometry.

For a university course, weaker students will find this text quite challenging, and possibly too hard.For average students, this text will provide sufficient challenge and interest, and ample areas in the text that will not overwhelm.For advanced students, this text will certainly challenge in many different directions and interests, both in the later chapter discussions, and various problems throughout.

Greenberg's writing is meticulous - you will never find an error, a comma out of place, nor a sentence that is not perfect.

Euclidean and Non-Euclidean Geometries, Fourth Edition, by Marvin Jay Greenberg
The Fourth Edition of M.J. Greenberg's textbook is a wonderful addition to the geometry textbook literature. No praise could be higher than to say that it is even better--indeed, a good deal better--than the highly regarded earlier editions. There are important revisions to each of the chapters and appendices, some of them extensive. As Greenberg aptly notes: "this book is a resource for a wide variety of students, from the naive to the sophisticated, from the non-mathematical-but-educated to the mathematical wizards."In this reviewer's opinion, Greenberg's fourth edition along with the Robin Hartshorne's mathematically more technical Geometry: Euclid and Beyond (2000)--a text to which Greenberg repeatedly makes reference--are far and away the most informed, up-to-date, and historically and philosophically sensitive geometry texts on the market today. No one with an interest in the foundations of geometry can afford to be without copies of these two great works.

A very good book about Geometry
This is a very good book about Euclidean and Non-Euclidean Geometries.
Well written, this book introduces to the lector in the historical context of the development of the Geometry.
I enjoyed very much.

Why is it so cheap, now (April, 2008) ?Because, this is the 3rd edition and exists a new 4th edition since September 28, 2007. ... Read more

Product Description
This title will soon be available in kindle. Geometry is lots of fun and applies to so many things in the real world. Now is an excellent time to learn all about geometry the easy way! This is a new title by America's math teacher and author, Richard W. Fisher. This book will provide students with all the essential geometry skills. Vocabulary, points, lines, planes, perimeter, area, volume, and the Pythagorean theorem are just some of the topics that are covered. Each lesson contains built-in review and easy-to-understand instruction that introduces new material with lots of examples. There is plenty of real-life problem solving that shows students the importance of geometry in the real world. An excellent summer review prior to taking high school geometry. CHECK OUT THE REST OF OUR MASTERING ESSENTIAL MATH SKILLS BOOKS AND DVD'S! ... Read more

Customer Reviews (3)

A bit overpriced, but still worth it.
It's a good basic book which will serve someone well for that extra bit of study.

Hole-Free Math Skills
In his customary succinct and painless way, Richard Fisher has written a series of skill specific math workbooks. Like an efficient patch kit, each book seals any holes that might exist in your student's math skills. I had the opportunity to look over these six, streamlined, no-fluff workbooks (just the way I like them). Fractions, Geometry, Percents and Decimals, Problem Solving, Whole Numbers and Integers, and Pre-algebra Concepts are individually and precisely targeted. Each subject is given a thorough yet simple treatment (a rare combination). First, by laying a firm foundation with the basics, building precept upon precept, and finally topping off the skills we have gained with final reviews to ensure hole-free mastery. With my limited understanding of math, I was able to easily comprehend the short lessons in the Helpful Hints section with examples. I could have used a little more explanation for the more complex concepts to nudge my brain to its grasping point; still, I was able to ascertain a concept by looking at the answer and figuring out how it was arrived at (I call it creative learning). I used Pre-Algebra Concepts with companion DVD for a review of Pre-Algebra and would unquestionably have used it as my son's primary text had I discovered this series sooner (the other books in this series do not come with a companion DVD). I recommend these books and will be using them for reinforcing any weak areas that crop up in my son's math comprehension.

Everything your student needs to know about geometry
I reviewed all six of the new Mastering Essentials Math Skills titles at the 2008 NCTM Math conference.As a math consultant, I have always been a big fan of Fisher's book. It is amazing how much geometry is covered in just 80 pages.Each lesson is short and self-contained.All of Fisher's books have built-in review, a helpful hints section for each new topic, and lots of real-life applications. An excellent book that will provide students with mastery of the essential geometry skills.Also, lots of real-life applications.Highly recommended. ... Read more

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Kids most frequent geometry questions answered by expert math teachers
This easy-to-follow resource is a must for any student who has questions about geometry basics. With an entertaining tone and lots of illustrations, the experts at the Math Forum help students gain the knowledge they'll need to tackle the topics in a beginning geometry curriculum, from definitions of two- and three-dimensional figures to the Pythagorean theorem and finding the volume of a cylinder. The Math Doctors also provide clear explanations, real-world examples, and helpful tips for solving the problems beginning geometry students find most challenging.

The Math Forum at Drexel University (Philadelphia, PA) is an award-winning Web site and the most popular online math resource for parents, teachers, and students in elementary and secondary math courses. Previous books in this series include Dr. Math Gets You Ready for Algebra (0-471-22556-8) and Dr. Math Explains Algebra (0-471-22555-X). ... Read more

Customer Reviews (2)

For learning math, this is a great start
Dr. Math is a website that answered homework questions.Thousands upon thousands of real questions from real students, who would write for more info if their question wasn't answered sufficiently."Dr. Math" wasn't a single person, but a whole team of professors, teachers, other students, and volunteers.

The text starts with a square.Just a square, and some details about that square.Then it goes into what a point is, and what a segment is, all using questions that Dr. Math answered.

The formatting is excellent.

If you have basic questions involving geometry, and you want to actually see that question in the text, and then have that question answered, this is the book for you.

very informal pedagogy
Drexel University has been putting out a series of Dr Math books, with this being one of the latest. It has that trademark cheerful, breezy style that is meant to engage a recalcitrant primary school student. Or perhaps even a high school student. Though the material seems rather basic for high school.

Students who are already into maths won't need a book like this. But the forced informality and cartoony aspect is thought to be more likely to attract students with little interest or ability in maths.

The material here is Euclidean geometry, in 2 and 3 dimensions. Needless to say, the level of rigour in the proofs in minimal. But enough is given to provide a logical framework. ... Read more

Product Description
Textbook presents a modern view of calculus enhanced by the use of technology. Revised and updated edition includes examples and discussions that encourage students to think visually and numerically. DLC: Calculus. ... Read more

Customer Reviews (36)

calculus and analytic geometry 7th edition
The book came in on time and was very quick arriving at my door.The book was in excellent condition. Inside there was blemishes but maybe it was my fault.
I felt in love with this book; that is why I bought it to replace the very old one.The mathematics was very elegant and the way they are conceived so impressed me.That is why I decided to buy it again.Overall, a beautiful book on mathematics.

Great Customer Service
The purchasing experience exeeded my expectations.The Sellers followed up to ensure that we were happy with the conditon of the purchase.Overall good experience.

satisfactory
The book I got was the correct one, but I didn't get it until about a week after the estimated ship date.The description said that the book was in like new condition, but when I got it the corners were slightly beat up, the pages were in good condition but I would classify it as either good or very good condition not like new

Excellent book (5th ed), I still own it and use it ...
I used this book for a University Honors Calculus class that I took as a senior in High School.As a math enthusiast (my dad was a Math Professor), and compared to other math books, I would say that the exposition in this book is very very good.The authors were from MIT and U-Illinois, respectively (the latter is where I took the honor calculus class), and at the time it was being used at both schools.

Some people have criticized this book as 'repetitive' and 'obvious' but I HEAVILY disagree.Calculus is a set of tools for approaching geometric problems.There are hundreds of tools in this book.My honors calculus professor had us working one sub-section of the book EVERY NIGHT, FOR AN ENTIRE YEAR.In that time, we finished the entire book.I worked 4 problems EVERY NIGHT, FOR AN ENTIRE YEAR.Later on, I attended MIT, and I was helping the freshmen in their calculus homeworks 5 years later FROM MEMORY!Meanwhile, the MIT students, who had less practice (one problem set per week) quickly forgot what they had learned!So I was helping the upperclassmen to remember their calculus, too !!

Calculus is the very last "bag of tricks" subject that is taught in most math curriculums.The theory behind integration and differentiation and other techniques are all there, in the Thomas and Finney book.The burden is on the reader to understand the theory, before they jump to the practicum.It's true that Thomas and Finney do not ask you to derive new theorems, but there is too much material to allow this in a 2-semester or 3-semester textbook.

I wonder how far people have gone after complaining that there was too much rote practice in this book.In my case, I enjoyed the book and completed a PhD in theoretical computer science.

---> Better Than Nothing <---
I am on the brink of completing Calc II. Between this book and 2 other calc textbooks that I have, Larson 7e, and Stewart 5e - ET, I finally made it through calculus. (Damn public school system.) There are topics in this book that my other 2 calc books have provided a much better explanation for. If the three authors were to collaborate they could possibly produce a rather fine Calculus textbook. ---- Ultimately, there is NO perfect textbook.

If you find that you are having difficulty understanding concepts in one textbook try finding an equal counterpart by a different author. It has helped me.

Read and learn all you can. Don't be a participant in the dumbing down process. ... Read more

Product Description
Intended for upper undergraduate or beginning graduate students, this book introduces students to the modern theory of manifolds. Assuming a basic knowledge of the differential geometry of curves and surfaces the focus is on differentiable manifolds and the study of Riemannian manifolds. The book concludes with applications of manifolds to physics. Exercises at the end of each section and appendices on topology and linear algebra make this book ideal for self-study or as a textbook. ... Read more

Customer Reviews (1)

Nice! Very clear, concise, rigorous reader-friendly introduction to differential manifolds
Lovett provides a very nice introduction to the differential geometry of manifolds useful for self-study.It is very clearly written, rigorous, concise yet reader-friendly.The difficulty level is midway between O'Neill's Elementary Differential Geometry, Revised 2nd Edition, Second Edition and Tu's An Introduction to Manifolds (Universitext) (Volume 0).

The pace is nice.As you can see in more detail from the "search inside this book" function: Ch. 1 Analysis of Multivariable Functions [pp. 1-36] provides some background math; Ch. 2 [pp. 37-78] Coordinates, Frames, and Tensor Notation discusses some more applied topics needed for physics applications; Ch. 3 Differential Manifolds [pp. 79-124] and Ch. 4 Analysis on Manifolds [pp. 125-184] discuss essential standard topics including differential maps; immersions, submersions and submanifolds; vector bundles; differential forms; integration and Stokes' Theorem;Ch. 5 [pp. 185-248] provides an introduction to Riemannian Geometry, including vector fields, geodesics and the curvature tensor; and finally Ch. 6 [pp. 249-294] provides very brief discussions of some applications to physics including Hamiltonian mechanics, electromagnetism, string theory and general relativity.

My main gripe is that there are no answers to problems, which detracts from its value for self-study (but to fill that gap, cf. Analysis and Algebra on Differentiable Manifolds: A Workbook for Students and Teachers). This is especially annoying because Lovett refers to answers to some problems in his mathematical exposition, e.g., on p. 234 (section 5.4.1), he refers to problem 5.2.17 on page 217 in his discussion of connections that are not symmetric; moreover answers to some exercises depend on material in other problems, e.g., the answer to problem 5.2.17 refers to problem 5.2.14.This is a common practice I dislike because it seriously degrades from a book's value for self-study. It could well be that one star should be deducted for this despicable practice.Nevertheless, I have given it 5 stars because I like the fact that it covers Riemannian Geometry (including an exposition of Pseudo-Riemannian metrics in section 5.1.4 and 5.3.3) and in section 6.4, a short introduction to general relativity but mostly because it's the only book I know that can help one make the leap from very elementary books like O'Neill's Elementary Differential Geometry, Revised 2nd Edition, Second Edition, Pressley's Elementary Differential Geometry (Springer Undergraduate Mathematics Series) or Banchof and Lovett's Differential Geometry of Curves and Surfaces to graduate level books like Tu's An Introduction to Manifolds (Universitext) (Volume 0), John Lee's Introduction to Smooth Manifoldsor Jeffrey Lee's massive [[ASIN:0821848151 Manifolds and Differential Geometry (Graduate Studies in Mathematics), all of which I also recommend after Lovett.

All in all, this text is a welcome addition to the many books on differential geometry because of its refreshing, "no nonsense" clarity, rigor and conciseness as well as the various topics covered. ... Read more

Product Description
The great work that founded analytical geometry. Included here is the original French text, Descartes’ own diagrams, together with the definitive Smith-Latham translation. "The greatest single step ever made in the progress of the exact sciences."— John Stuart Mill.
... Read more

Customer Reviews (5)

Enormously important in the history of mathematics
Descartes' Geometrie, published in 1637, is possibly the second most influential book in the history of mathematics, after Euclid's Elements.In it, Descartes introduces analytic geometry, that is, the connection between geometry and algebra, in order to use algebra to solve geometric locus problems.The book's influence is reflected in the fact that Descartes' notation is far closer to the notation used today than anyone else's from that period (for example, Fermat or Viete).But it is not a book for someone who is not already knowledgeable.As Descartes himself wrote, (as translated and quoted in a footnote on page 10), "In my previous writings I have tried to make my meaning clear to everybody; but I doubt if this treatise will be read by anyone not familiar with the books on geometry, so I have thought it superfluous to repeat demonstrations contained in them."The 17th century mathematicians who read La Geometrie found it difficult, both because it was in French and because of its uncompromising exposition.Thus the book only became understood after the publication in 1649 of a Latin translation with commentaries by Frans van Schooten.

For the modern reader the book is a fascinating record of the state of mathematics in the early 17th century, and the format, with Descartes' 17th century French (readily readable to someone with some knowledge of modern French) opposite the reliable English translation, is very helpful for understanding what Descartes does in the book. How can it not have five stars?

Fabulous
This is a cheaply printed book with unquestionable value for any mathematician or liberal arts major.It has facing-page French with an English translation (which is fairly strict and literal), with great diagrams.It's difficult to read, and that's okay, because when other mathematicians at the time read it they thought it was impossible and that Descartes was insane.

Descartes, apart from this edition, is brilliant and worth the time to study.

This book is a bad choice for anyone not familiar with Euclidian and Apollonian geometry.Period.If you're not, you should find some commentary on Cartesian geometry instead of tackling this monster head-on.

has only limited historical value
The problems discussed in this book are very remote from our
present day geometry. The English translation uses a smaller font
than the French original, which makes the book even harder to read.

Great book to work through
This book contains a facsimile of the original version which runs nearly page for page with the English version.This is a true mathematical masterpiece.This was the supposed beginning of analytical Geometry(although it is now known that this was not true).It's a great book to work through that should be accessable to a high school student with some Geometry background. A Fantastic Book!

Enter Modern Mathematics
Using the locii problems investigated by Apollonius, Descartes employs the rules of his "method" in this treatise on geometry. By approaching geometrical problems with algebraic processes and vice versa, he manages to create point coordinate geometry. This work drastically changed the way in which we view conic sections as well as the very process of analytic inquiry. The math is mostly straightforward and more familiar to the reader than the works of the ancient mathematicians. It is not neccesary to have studied much previous mathematical works to gain a basic comprehension of Descartes' solutions. Attempting at most times to maintain the simple and straighforward presentation advocated by his method, Descartes will give you most of the basics that you need to understand the rest of the work. However, close concentration must be paid for the math to mean anything. It is easy to skip a step in a proof and find yourself completely lost. Given the proper patience, this work is invaluable for anyone who wants to see the origins of our method of thought today. Fascinating both as a mathematical treatise and as a perfect trial run for anyone wanting to follow the cartesian method of learning. ... Read more

Product Description
The effects of geometry and linear algebra on each other receive close attention in this examination of geometry’s correlation with other branches of math and science. In-depth discussions include a review of systematic geometric motivations in vector space theory and matrix theory; the use of the center of mass in geometry, with an introduction to barycentric coordinates; axiomatic development of determinants in a chapter dealing with area and volume; and a careful consideration of the particle problem. 1965 edition.
... Read more

Customer Reviews (7)

Geometric Overview of Core Math and Physics +++
This book presents a wonderful geometric overview of core math and physics. It is equally great for a preview or review of core math and physics. This work is done with attention to learning such core topics via a unifying and clarifying approach. Via this approach someone learns about a vector space approach to geometry via great cross-magnification of the illustrative sub-topics. I finally feel I clearly see the various sub-topics via the illumination of vector space geometry. But there is more -- physics methods, such as center-of-mass, are used directly [as primary mathematics] to magnify vector space geometry from the start. The notation is also clear and sharp as well as the mathematics presentation and the order of the chapters and topics. This is quite a unique timeless work +++

A bit longwinded
I didn't find this book to read like a novel.I got it hoping to learn about projective transformations for computer graphics, but was disappointed because of the method of presentation was too long to get through.I believe the text would appeal to those whose interest was strongly in geometry and had a college level background in math. I gave it three stars for the seemingly interminable proofs of geometric theorems that I had little use for.

Must have if on the road to Linear Algebra
This is one beautiful book. The whole book is one long thread about geometry and vectors. To make this review short, I'll say you absolutely *must* have this book if you want to set yourself on the proper track to Linear Algebra. In fact, this book could almost be considered an Analytic Geometry book 'done right.' But be careful: I said almost. By that I mean that some staple AG stuff is missing. For instance, no long discussions about a plane intersecting a sphere, no quadric surfaces. So it does lack the sort of drill exercises you need to succeed in an AG class - but such stuff is not its purported goal, anyway -but then again, your 'vector 6th sense' will increase tremendously with this book. I wish I had discovered this book while I was having my Analytic Geometry. Now I'm taking a Linear Algebra class and I'm glad I found this book.
It also is full of other interesting insights and relations to other topics, including some applications to Calculus (motion) and some topology.

A useful High School Geometry book for Computer Graphics
This is essentially a high school geometry book; but with a difference - its fully linear algebra based approach.If you are a beginner in computer graphics, and want to review elements of geometry and linear algebra, you will benefit from studying through this book.

The almost four hundred pages book is remarkably readable and is very consistent at that.There are both worked out examples and exercise problems, for each section - which are very useful for self-study or revision.

If you have never had an introduction to linear algebra before, you may have to supplement this with a linear algebra book.But if you have not had a good course in elementary geometry, and your motivation is getting started with elementary Computer Graphics/CAD and the likes, this is a good book for that.

Interspersed with the subject matter discussed at a elementary level, in a useful, stimulating style are small, interesting discussions on such useful and relatively advanced topics as function spaces, fixed point theorem in affine transformation, simplices, symmetries etc.I rarely have seen any of these topics mentioned in a book aimed at this level.

Highly recommended for freshman undergraduates and those without any mathematics experience who want to start in Graphics, CAD, CAGD and the likes.Recommended also for experienced practitioners in Graphics: it is good to review the fundamentals once in a while, and a well written bookthat is a quick read helps at that!

Perfect for first and second year, or physicists
The basics of the very deep connection between geometry and vector spaces. If you do undergrad math you will see everything in this book during first and second year. But what this book does is fit those bits together. He does this very nicely at an introductory level. If you are not in math, but need to learn some geometryfor a physics course, this will be a useful book.

It is a formal math book, with axioms, but it is strong on motivation and has some quite amusing examples.

Keywords: tangent spaces, determinants, barycentric, linear transformations. ... Read more

Product Description
Covers topics in plane and solid (space) geometry.Pictorial diagrams with thorough explanations on solving problems incongruence, parallelism, inequalities, similarities, triangles, circles,polygons, constructions, and coordinate/analytic geometry. Aninvaluable aid for students. ... Read more

Customer Reviews (3)

Enough review and you get it
I wanted to get better at organizing my mind.You knew they taught Chess at West Point.Right?Well, Geometry makes you think.It makes you think in logical steps for problem solving.This book just gives example after example and exhaustively ingrains how to solve Geometry problems.Along the way it coincidentally builds your endurance for solving other problems.This may not be the best book or the most cutting edge but it has such a huge mass of answers and ways to arrive at them that you will absorb the methods.I like it.You might say that if you stare at these pages long enough that you learn by osmosis.I think there should be a book like this in every field of endeavor.Call it canned experience. Oh, a better typeset would be nice.

Excellent resource, really does the trick.
I bought this book right after I started a class in Linear Algebra where the first chapter had us working some geometric proofs using the rules for vector addition, subtraction, and scalar multiplication.

Although this book strictly focuses on geometry and does not use vectors in its proofs, it did clearly illustrate proofs that were easy enough to think through in terms of vectors.

The book is well-written and begins with a review of Methods of Proof, Lines & Angles, Perpendicularity, and Triangles before getting into specific geometric forms.

900+ pages and 900+ problems with a summary of theorems and properties at the end of the book.Some reviews at Amazon contain complaints about REA Problems Solvers, but I have always liked them and I really like this one.They are not intended to replace a textbook, but to give lots of examples over-and-above what a textbook would include.

For example, a few years ago I was studying College Algebra and I was having trouble understanding logarithms.So I reviewed the examples in the REA Problem Solver for Algebra and Trigonometry and worked some problems along with the REA book and then I saw how simple they really were.I have purchased REA Problem Solvers for Calculus, Differential Equations, and Linear Algebra as well and have found all of them to be helpful with some being more useful or better-written than others.

One of the complaints about these books is that they are all written using a Courier-style font.This is true, but there are still Greek symbols, integral signs, exponents, etc (e.g. you do not see 10-squared written as 10^2 - they use a superscript for the exponent).Another complaint that I have seen is that they contain errors.I have not noticed any, but that does not mean there are none present.I do not review these books cover-to-cover, but take a look at those topics that I need to review, so I may not have encountered any errors but they could still be present.

Purchased new, the books may seem a bit pricey if you are on a budget (nowadays the books have a list price of $30.95 for some subjects and $25.95 for others, with discounted prices ranging between $17.95 and $30.25).I always buy them from the affiliated 3rd-party booksellers on Amazon.I got my Geometry Problem Solver extremely cheap $3.15 plus $3.99 for S&H - total of $7.14 and the book arrived in a couple of weeks and was in excellent condition (like new!).

Most of the time I have spent in the $12-$15 range (incl S&H) for these guides.Even if I only were to find help on a single topic within the book, that, to me, is still a bargain.Especially so if you consider the price relative to the cost of tuition and textbooks.If you are really price conscious, most college libraries have copies that are rarely checked out.Until my copy was shipped, I used the one in our library and saw that it had last been checked out in 2004!

p.s. I am 54 years old and went back to night school and started studying math 3 years ago with College Algebra, Trig, PreCalc, Calc 1,2,3, Diff Eq, and now Linear Alg.I have had REA guides for all of the classes and have found them useful in every case.

GREAT BOOK
A great book loaded with proofs for geometry (SAS, CPCTC, etc) and geometic problems (Pythagorean Therom). ... Read more

Product Description
Differential geometry and topology have become essential tools for many theoretical physicists. In particular, they are indispensable in theoretical studies of condensed matter physics, gravity, and particle physics. Geometry, Topology and Physics, Second Edition introduces the ideas and techniques of differential geometry and topology at a level suitable for postgraduate students and researchers in these fields.

The second edition of this popular and established text incorporates a number of changes designed to meet the needs of the reader and reflect the development of the subject. The book features a considerably expanded first chapter, reviewing aspects of path integral quantization and gauge theories. Chapter 2 introduces the mathematical concepts of maps, vector spaces, and topology. The following chapters focus on more elaborate concepts in geometry and topology and discuss the application of these concepts to liquid crystals, superfluid helium, general relativity, and bosonic string theory. Later chapters unify geometry and topology, exploring fiber bundles, characteristic classes, and index theorems. New to this second edition is the proof of the index theorem in terms of supersymmetric quantum mechanics. The final two chapters are devoted to the most fascinating applications of geometry and topology in contemporary physics, namely the study of anomalies in gauge field theories and the analysis of Polakov's bosonic string theory from the geometrical point of view.

Geometry, Topology and Physics, Second Edition is an ideal introduction to differential geometry and topology for postgraduate students and researchers in theoretical and mathematical physics. ... Read more

Customer Reviews (13)

Excellent review of math for (particle) physicists
I bought this book to supplement my knowledge of mathematics which frequently is involved in understanding Particle physics concepts. The book is terse, but peppered with examples and insights about the definitions, and so far it is really fun to read. Seems like a good investment.

Too many errors to be useful for study
Reading all the glowing reviews of this book, I wonder whether the reviewers actually tried to use the book to understand the material, or just checked the table of contents. There are so many misprints, throughout, that one wonders if the book was proofread at all. Some of the mistakes will be obvious to every physicist - for example, one of the Maxwell equations on page 56 is wrong - others are subtle, and will confuse the reader. The careful reader, who wants to really understand the material and tries to fill in the details of some of the derivations, will waste a lot of time trying to derive results that have misprints from intermediate steps which have different misprints! Some chapters are worse than others, but the average density of misprints seems to be more than one per page.
The book might be useful as a list of topics and a "road map" to the literature prior to 2003, but that hardly justifies the cost (or the paper) of a whole book.

Geometry Topology and Physics: A condesed view
This book provide a complete and useful review of geometrical instuments of mathematical physics from the beginnig to the most advanced topics of interest. It can be used by students at the beginnig of thei studies in this topics, and it's found to be a useful gallery for higher level students (or scholar).

An excellent book
This is the best book of its type, that is, a book that contains almost all if not all the advance mathematics a theoretical physicist should know. I have studied chapters 2-9 and it has the perfect balance between rigorous presentation of topics and practical uses with examples. The level is for advance graduate students. The range of topics covered is wide including Topology topics like Homotopy, Homology, Cohomology theory and others like Manifolds, Riemannian Geometry, Complex Manifolds, Fibre Bundles and Characteristics Classes. I believe this book gives you a solid base in the modern mathematics that are being used among the physicists and mathematicians that you certainly may need to know and from where you will be in a position to further extent (if you wish) into more technical advanced mathematical books on specific topics, also it is self contained but the only shortcoming is that it brings not many exercises but still my advice, get it is a superb book!

A great reference book.
No doubt, the interplay of topology and physics has stimulated phenomenal research and breakthroughs in mathematics and physics alike.

Unfortunately, there is so much mathematics to master that the average graduate physics student is left bewildered.....until now.

The text is an excellent reference book. I emphasize reference. The book presupposes an acquaintance with basic undergraduate mathematics including linear algebra and vector analysis.

The author covers a wide range of topics from tensor analysis on manifolds to topology, fundamental groups, complex manifolds, differential geometry, fibre bundles etc.

The exposition in necessarily brief but the main theorems and IDEAS of each topic are presented with specific applications to physics. For example the use of differential geometry in general relativity and the use of principal bundles in gauge theories, etc.

Unfortunately, there are very few exercises necessitating the use of supplementary texts. However, to the author's credit appropriate supplementary texts are provided. The author goes to great lengths to show which texts inspired the chapters and follows the same line of presentation.

Perhaps the greatest attribute of the text is to take disparate branches of mathematics and coallate them under one text with applications to physics. In doing so one gains a better grasp of how the fields of mathematics interact in the domain of physics. ... Read more

Product Description
This is a genuine introduction to algebraic geometry. The author makes no assumption that readers know more than can be expected of a good undergraduate. He introduces fundamental concepts in a way that enables students to move on to a more advanced book or course that relies more heavily on commutative algebra.

The language is purposefully kept on an elementary level, avoiding sheaf theory and cohomology theory. The introduction of new algebraic concepts is always motivated by a discussion of the corresponding geometric ideas. The main point of the book is to illustrate the interplay between abstract theory and specific examples. The book contains numerous problems that illustrate the general theory.

The text is suitable for advanced undergraduates and beginning graduate students. It contains sufficient material for a one-semester course. The reader should be familiar with the basic concepts of modern algebra. A course in one complex variable would be helpful, but is not necessary. It is also an excellent text for those working in neighboring fields (algebraic topology, algebra, Lie groups, etc.) who need to know the basics of algebraic geometry. ... Read more

Customer Reviews (1)

Trees, not forest
First, a calibration: I am a total neophyte to algebraic geometry, and haven't taken a university algebra course since a few decades ago when I was a physics major. This book is one of several on the subject (along with some books on commutative algebra) that I'm using to get an amateur's orientation.

As so often happens, this book looked great in the bookstore. It is thin, reasonably well-illustrated compared to other books in the field, and even helps you gets your toes wet in sheaves, category theory and some other neat topics.

That said, I believe the prerequisites in the preface (university algebra, with a complex variables course optional) are understated; e.g. it helps to know something about fibres, lifts and other topics from geometry. It might be relevant that these notes were prepared at a German university; you should consider that "undergraduates" there are heading toward the equivalent of a US M.S. degree, not B.S./B.A.

More detrimental is that the presentation slogs from one proof to another and too rarely pauses for breath to consider the "big picture" significance of what you're proving. Notwithstanding that Joe Harris's "Algebraic Geometry: A First Course" is even less of a piece of cake for me than it might be for you, his style is a breath of fresh air when it comes to enlightening you as to some geometric context and payoff for all this effort. Other supplements I found helpful include Reid and Schenck.

PS in 2008: I very belatedly found the terrific "An Invitation to Algebraic Geometry," by Karen E. Smith &al. (Springer 2000, corrected printing 2004). This is the hands-down best introduction to the subject, IMHO. ... Read more

Product Description
Written primarily for students who have completed the standard first courses in calculus and linear algebra, ELEMENTARY DIFFERENTIAL GEOMETRY, REVISED SECOND EDITION, provides an introduction to the geometry of curves and surfaces.

The Second Edition maintained the accessibility of the first, while providing an introduction to the use of computers and expanding discussion on certain topics. Further emphasis was placed on topological properties, properties of geodesics, singularities of vector fields, and the theorems of Bonnet and Hadamard.

This revision of the Second Edition provides a thorough update of commands for the symbolic computation programs Mathematica or Maple, as well as additional computer exercises. As with the Second Edition, this material supplements the content but no computer skill is necessary to take full advantage of this comprehensive text.

*Fortieth anniversary of publication! Over 36,000 copies sold worldwide
*Accessible, practical yet rigorous approach to a complex topic--also suitable for self-study
*Extensive update of appendices on Mathematica and Maple software packages
*Thorough streamlining of second edition's numbering system
*Fuller information on solutions to odd-numbered problems
*Additional exercises and hints guide students in using the latest computer modeling tools ... Read more

Customer Reviews (10)

O'Neil
I found the product in excellent condition.
The mailing was also superb.

Thanks

Introduce Some Of The Main Ideas Of Differential Geometry
"This book is an elementary account of the geometry of curves and surfaces.
It is written for students who have completed standard courses in calculus and linear algebra, and its aim is to INTRODUCE SOME OF THE MAIN IDEAS OF DIFFERENTIAL GEOMETRY....."
[from the preface to the second edition, by Barrett O'Neill]

Definitely worth checking out
I found the approach in this book on the stuff touched on in most diff. geometry books at the level I was hunting for (I'm a mech. engineering major) very nice. I liked the notation used and could follow it very well. Everything I've seen so far is in E3 which I like for intuitive grasp. I feel like this is one of those bridging books to be able to understand higher level abstract books, especially if you are trying to learn on your own. The first 50 or so pages hammer out pretty much anything I've seen at the general level in other books of this subject, and I think this book does it better than most. There are also some solutions (well, just answers) in the back.

Introductory level text with empasis on intuition examples and exercise.
If you are looking for abstraction with little in the way of intuition I suggest Conlan " differential manifolds"

If you are an applied mathematician or physicist this book is for you.

I have always beleived that to truly grasp mathematics one must be provided with a reason for WHY things are the way they are and WHAT IDEAS the expression must express. This is best done with examples and exercises.

I digress.

The book restricts is exposition to two and three dimensions. Some of the topics can readily be bootstrapped to higher dimensions.

The book starts with basic ideas of curve, directional derivative and tangent vector in Euclidean space with a sprinkling of differential forms to wet the appetite.

It then moves into the notion of frame fields along curves resulting in the Frenet formulas which express how the frame fields change along the curve. These are expressed in terms of the frame field themselves giving ideas of curvature and torsion.

The book then abstracts these concepts to show how we can talk about change of frame fields along arbritrary directions not just along the curve. The tools used to do this are the covariant derivative and connection forms which can then be used to develop connection equations ( abstracted analogue of frenet formulas ) and then the cartan structural equations.

The book talks about isometries and defines euclidean geometry as those properties preserved by isometries. It then abstracts once again to surfaces in R3 using patches and appropriate conditions on the overlap without introducing manifolds although these are briefly mentioned later.

We then see how calculus in euclidean space can be adapted to surfaces using these patches. The corresponding concepts of function, differentiability and tangent vectors on these objects is introduced. Forms on these surfaces are introduced and their application to integration theory on these surfaces is developed showing how forms on the surface are " pulled back" to euclidean space using the idea of differential of a map and integrated there. The integration gives the volume ( area ) of that surface. Stokes theorem is introduced.

We now move into the idea of shape operators on the surface and show how these describe how the normal vector on the surface move in various directions giving ideas of mean and gaussian curvature . We see a very nice interplay of algebraic analysis leading to a geometric analysis.

The book then deals with studying geometrical properties on surfaces using the Cartan methods described earlier.

We then see how to define intrinsic geometry of any surface. Namely those properties of the surface that are preserved by isometries. From the definition of isometry we see that these rely on on the concepts of tangent vector and inner products. Shape operators and mean curvature are not intrinsic.

We now study the geometry of surfaces specifically the intrinsic geometry without reference to an imbedding space ( R3). An abstract "surface" is endowed with an inner product. A different inner product gives a different geometry. We talk about gaussian curvature and covariant derivative which are intrinsic.

Geodesics are introduced as is the gauss bonnet theorem which relates a geometric property to a topological one.

The book concludes with a chapter on global properties ( 2 d surfaces ) especially how gaussian curvature influences geodesics and how the two completely determine the geometry of the surface.

Cartan's formulation of differential geometry taken up here.
My first encounter with this book was during the academic year of 2000-2001, when it was used as the main text for an upper division course on differential geometry. The class --taught by a distinguished scholar-- was only meant to be a brief excursion into the realm of continuous math, beyond analysis and topology. After finishing the term however, I decided to change direction and as time went on, I drifted more and more towards geometry as the field of further concentration. The original second edition (from 1997) contained numerous typos, but luckily, the revised 2006 issue takes care of these and also streamlines the section numbering formats which had made the referencing and following through with the material a bit cumbersome. As some of the other reviewers have mentioned, the emphasis here is on the low (= 2 and 3) dimensional geometry, formulated in the language of differnetial forms (Cartan's early 20th century approach).

Within the eight chapters of the book (seven in the 1966 edition), the reader is first introduced to some preliminaries such as tangent vectors, directional derivatives, and differential forms. In chapter two, the author presents the Frenet frame formulas, covariant derivatives, connection forms, and Cartan's structural equations, which are generalizations of the Frenet frame formulas for surfaces. In chapters three and four, there is a healthy dose of Euclidean geometry and calculus on surfaces. In chapter five, discussion is on the study of the shape operators and normal and Gaussian curvatures, where also some useful computational examples have been presented. Geometry of surfaces is the subject of chapter six, where the crucial Gauss' egregium theorem is proved, and in chapter seven students are introduced to the basics of the Riemannian geometry, culminating in the famous Gauss-Bonnet theorem. In chapter eight (which is highly topological) complete surfaces, covering spaces, Jacobi fields, and the subject of classification of surfaces are explored. The appendices include help on using popular computer algebra systems (with updates in the latest revised edition), and another appendix providing solutions to many of the odd-numbered exercises in the book.

Please note that the author leaves out a discussion of several essential tools, for example, the Schwarz-Christoffel symbols, tensors, and Lie derivatives. The exposition does not fully explore some other important topics such as the first and second fundamental forms, and parallel translation, which only show up in the exercises. Then again, perhaps to keep the level of exposition elemantary and the size limited, Dr. O'Neill has preferred to skip some topics. One remedy is to back his text up with Manfredo Do Carmo's 1976 classic, which is mathematically more rigorous, and covers more of the above-mentioned topics. Afterwards, one can certainly continue the study of the essentials by reading other advanced material such as William Boothby's "An Introduction to Differentiable Manifolds and Riemannian Geometry". There is also a somewhat obscure title by Richard W. Sharpe with the title "Differential Geometry: Cartan's Generalization of Klein's Erlangen Program", from the Springer-Verlag GTM series that's worth checking into. Finally, other elemantary-level sources to keep in mind for a beginning student are the recent texts by Andrew Pressley (2001) and Wolfgang Kuhnel (2002) both available on amazon.com's catalog.

[Review updated in May 2006] ... Read more

Product Description
This is the newly revised and expanded edition of the popular introduction to the design and implementation of geometry algorithms arising in areas such as computer graphics, robotics, and engineering design.The second edition contains material on several new topics, such as randomized algorithms for polygon triangulation, planar point location, 3D convex hull construction, intersection algorithms for ray-segment and ray-triangle, and point-in-polyhedron.A new "Sources" chapter points to supplemental literature for readers needing more information on any topic. A novel aspect is the inclusion of working C code for many of the algorithms, with discussion of practical implementation issues.The self-contained treatment presumes only an elementary knowledge of mathematics, but reaches topics on the frontier of current research, making it a useful reference for practitioners at all levels.The code in this new edition is significantly improved from the first edition, and four new routines are included.Java versions for this new edition are also available. ... Read more

Customer Reviews (7)

Excellent text, obfuscated code
I bought this book to learn about convex hulls, voronoi diagrams and delaunay triangluations, and line arrangements.So far I have made it through the chapter on 2D convex hulls, and I must say that it is an excellently written book for learning about the covered topics in computational geometry.The text is clear easy to understand; algorithms are sufficiently detailed and illustrated to allow full implementation without needing other resources.Corner cases are meticulously covered.I also like the text because it is straight to the point, i.e., it does not spoon-feed the reader. So, although relatively short book, it contains a lot of densely packed, but still enjoyably readable, information. Illustrations are simple but excellent: they are carefully designed and very helpful for understanding the described algorithms.

I give the book four stars for two reasons.

First, the coverage of floating-poing precision issues is almost non-existant: most of the algorithms are integer-only.A survey chapter over techniques for handling FP precision issues would be *VERY* welcome.(After all, geometric algorithms are most often applied to floating-point data in the real world.)Judging by the quality of existing bibliography, I think the author would make an outstanding job on this topic.(Hint for the 3rd edition :-))

Second, I have strong objections against the coding style used in this book: the presented code is an excellent demonstration of how to obfuscate C programs by using typedefs and hungarian notation (inconsistently!) applied in postfix. (NOTE: I have 10+ years of experience in C and C++ coding, so I'm not just a "little bit confused").

collates useful computational geometric algorithms
If you are perhaps a graphics or robotics programmer, then you will often have need for computing various geometric forms. And the intersections of these forms. Rather than derive algorithms from scratch, you might want to first look here. O'Rourke has collated several useful sets of methods. Germane to two and three dimenions.

Convex hulls are important enough that he devotes 2 chapters to these. While the somewhat related idea of Voronoi diagrams gets its own chapter.

The C code is a nice bonus to some readers. Though if you are experienced enough in another language, you should be able to readily code an algorithm in the book from scratch.

Nice balance of theory with code
This book was pleasantly surprising:I had expected to see code presented with minimal motivation or discussion of the underlying ideas -- something of a "Computational Geometry for Dummies" sort of book.That's not the case at all.This is a bona fide textbook on the subject, suitable for an undergraduate course.
It covers all of the the "classical" topics: convex hulls, line segment intersection, polygon triangulation, Voronoi diagrams, motion planning.

The mode of presentation -- supporting a discussion of the theories with implementable code -- is actually a bit refreshing.For comparison:Other books, when discussing the line segment intersection problem (ie: Given a set of line segments, find all of their intersection points) simply assume that computing the intersection of a pair of segments can be done in constant time.This is not an especially difficult problem, but the discussion seems more complete with a brief description of how this might be done.The same can be said about other primitive tests and operations in other algorithms.

Overall, this book can stand alone as an excellent introduction to computational geometry, but a serious student in the subject will want more: perhaps Preparata and Shamos or de Berg et. al.

Very hepful
Anyone who is involved in areas such as computer graphics, computational radiology, robot vision, or visualization software should have a copy of this book. The author has done a fine job of introducing the most important algorithms in computational geometry, choosing the C language for their implementation. The choice of C might be somewhat dated now, since C++ is now beginning to dominate computational geometry, but readers who are actually programming these algorithms using C++ can easily extend the ones in the book to C++. Not all of the algorithms in the book are implemented into C, unfortunately, but the clarity of presentation is done well enough to make this implementation a fairly straightforward task. My interest in the book came from a need to design and implement algorithms for polyhedra in VRML and toric varieties in algebraic geometry. This book, along with others, was a great help in that regard. The running time of these algorithms was not really an issue with me, so the detail the author spends on discussing the complexity of the algorithms was not a concern. Readers who need to pay attention to running-time issues will appreciate his discussion of them for the algorithms that are presented.

The ability to visualize objects in an abstract subject like algebraic geometry boils down to, in the case of toric varieties, to a consideration of how to manipulate polytopes geometrically. A major portion of the book, if not all of it, is devoted to the computational geometry of polyhedra. Because it is an introductory book, some more advanced topics, such as Bayesian methods to find similarities between polyhedra, and neural network approaches to classifying polyhedral objects are not treated. Readers who need to do such things will be well-prepared for them after a study of this book. In addition, there are good exercises assigned at the end of each chapter, so the book could be used in the classroom. Some readers will however choose to use it as a reference source, and it would be a good one, for the author gives references to topics that he only touched upon in the book.

Some particular areas that were treated especially well were: 1. The discussion on data structures for surfaces of polyhedra. Although not very general, since he choose to deal with only triangulated polytopes, readers who need to be more general will have a good start in this discussion. 2. The discussion on volume overflow and how to deal with it using robust computation. 3. The discussion, albeit short, of the randomized incremental algorithm. 4. The treatment on the minimum spanning tree and Kruskal's algorithm. Communication network performance optimization is now a major application of this algorithm and others in graph theory, including the author's later discussion of Dijkstra's algorithm.

my rewiew
i think that these website is very.it has everything that i need. all of my books are from amazan. ... Read more

Product Description
EXAMBUSTERS Study Cards printed/boxed or on CD-Rom are specifically designed for exam preparation: AP, PSAT, New SAT, SAT II, ACT, PRAXIS, PPSAT, New GRE, GED, New GMAT, New MCAT, CLEP, ASVAB, New York State Regents, HSPT, COOP, SSAT, ISEE, and classroom quizzes, tests, and finals. Each EXAMBUSTERS Study Card title provides a concise, focused review of course material. Only essential facts and formulas are presented. We cover many introductory high school and college courses, and our titles are approved by the New York City Board of Education.

Why are Study Cards the best way to learn?
Because we learn most effectively when we can:
---absorb information in small, progressive increments.
---take an active part in the process
---receive immediate feedback (the answer is shown as soon as we fill in the blank)

Who wrote the cards?
High school teachers, test prep coaches, language experts, professional interpreters and translators, and college professors, with a focus on preparing students for standardized tests such as the AP, New SAT, SAT II, PRAXIS, GRE, GED, GMAT, MCAT, ACT, CLEP, and many others. Each Course in a Box or Course on CD-Rom covers the basics of a full year introductory course. EXAMBUSTERS Study Cards focus only on essential facts, definitions, and formulas. The flash cards were designed to help students learn and review courses efficiently.

What is the advantage of flash card study over textbooks and review books?
---Parents, tutors, and teachers can work together with students. Perfect for home schooling!
---Groups of students can have fun turning a study session into a trivia game.
---Portable: Learn a few each day. A sense of accomplishment grows as your stack of I have no idea! decreases, and the stack of I know the answer! increases.

Who has benefitted from our study cards?
* high school and college students
* head start oriented grade school students
* parents and grandparents concerned about their children's education
* teachers (for classroom, small group activities)
* tutors (for one-on-one teaching)
* business travelers and tourists

What is special about EXAMBUSTERS Study Cards on CD-Rom?
Cutting edge. . . the only series of its kind. User-friendly software--simple for all ages to explore. Study cards are displayed on the screen, one at a time, and can be eliminated from the stack just like printed cards. Our Screensaver Mode displays a new question and answer every few seconds in random order. Learn subliminally! Finally, our test mode randomly selects questions to create a quiz, mid-term, or final--your choice--a new test every time. The EXAMBUSTERS software program keeps track of the test time limit and grades you at test completion. Grades are stored in a table on the help menu so you can track your progress.

What are the computer system requirements for EXAMBUSTERS Study Cards on CD-Rom?
At least 500 MHZ processor, Intel Pentium II (or equivalent), 128 MB of RAM, 400 MB of disk space. Microsoft Windows XP or VISTA operating system, 2x CD-ROM drive, 256-color SVGA monitor: minimum resolution 800 x 600. Not compatible with Macintosh. ... Read more

Customer Reviews (11)

Slips of paper
I have no complaint with the content, but just note, these are not "cards" but slips of paper.

CLASSROOM AID -- Liked the software.
My students love them. We use them in class for group study and a jeopardy/trivia game. They're good review before finals and good preview for upcoming lessons. Exambusters cover the basics in an unconfusing format. In our learning center, we use the software. It's easy to figure out. Just click around and all the functions are clear. Students can remove cards they know or don't need from a virtual stack of cards, the same as if they had index cards printed. The screensaver helped with vocabulary study especially. The computer test was different each time and no matter how many times it was taken. There are three lengths to choose from, quiz, mid-term, and final.

Good Reinforcement
Try these first to review math and/or vocabulary you haven't seen for awhile. Just the basics are presented and I found I already knew some of the answers, but other times, the cards filled in the gaps. That's what's good about flash cards, you can pull out the ones you don't need. Can't do that with a work book unless you want to rip out some pages and use a lot of white out!! The software and the cards were both helpful; the same information in two different forms. Thanks, Exambusters. You've covered it all and given me more confidence!

USED CARDS WITH ALL MY CHILDREN
Helpful to my four children in junior high and high school. They have most courses and also the tests like SAT, SSAT, AP. Easy to use and fun (which is saying a lot when your kid would rather be out with friends than studying!)

Focused studying. Photo sign language cards are helpful.
I've tried several courses: math, science, history and language. My kids especially love the Sign Language cards! I purchased all three card sets and the CD-software. The photographs are more realistic than drawings which you mostly find in ASL products. Great for younger kids too. My daughter's using them in her Brownie troupe and my three-year-old has picked up on some of the alphabet and numbers already. My older son has some mild learning disabilities and looking at a page in a book with so much information all together makes him nervous. I put one card at a time on a cleared table. It helps him focus and that gives him more confidence. People have been making or using flash cards forever, and I think they always will be no matter how fancy computers and software gets (but the Exambusters software is good too). I've recommended them to others. ... Read more

Product Description

This volume covers local as well as global differential geometry of curves and surfaces.

... Read more

Customer Reviews (21)

Highly recommend
I really like Do Carmo's style of presentation, I can just imagine what type of lecturer he was. Though there are other books on the subject that are more concise a/o cover more topics, I believe Do Carmo's treatment is excellent for beginners to the field.

Another plus is that he gives hints on how to solve some of the exercise problems, which is essential for someone like me who very often studies a subject on my own.

A must of its kind
This is an excellent book. Anyone who wants to have a global view on classical differential geometry must have it (and read it!). As an undergraduate course's textbook, I find it quite difficult for the not determined student. Nevertheless, it gives the teacher the grounds to present a rigorous course. I fully recommend it to both students and teachers.

Good content, cheaply manufactured
The content is well-presented and instructive. My main gripe with this book is the very low quality paperback edition. After just a month of (careful) reading, many pages already falling out. The cover and content look as if they have been scanned and re-printed.

Update: by the end of the semester, my copy has now completely fallen apart. I wish this hadn't been manufactured so cheaply.

classical
It's a classical book on diff. geo. But it seems that the torsion in this book is different by sign from the notion in many other books

Great Potential - If Only a 2nd Edition Were in the Works
An earlier review said this book has few errors, and even then only typographical ones. Are we talking about the same book? The text is pockmarked - nay, cratered - with scads of dire gaffes. The skeptical empiricist should go to Google and enter these keywords: bjorn carmo errata. The first hit will be a link to a 7-page pdf file a U.C. Berkeley professor and his students created a few years ago which compiles errata they turned up. Seven full pages, and they only covered a third of the text! A sample item in the list: "p. 97, definition of domain: It is not clear whether the boundary is the boundary as a subset of R^3 or the boundary as a subset of S. Either way, we run into trouble..." The Heine-Borel theorem on page 124 is so botched up it's beyond repair, and even the basic definition of what it means for a function to be continuous on a set is faulty (p. 123).

The author claims a student should be able to hack the material with"only the most basic concepts" from linear algebra and multivariable calculus. Largely but not entirely true. For example, you better be up to speed on linear mappings defined by NON-square matrices - something no undergraduate-level linear algebra book in my library discusses (though I only possess a handful). Many of those tidy little results for linear operators from R^n into R^n you might know from Linear Algebra 301 become worthless when one of those n's becomes an m. I don't really fault the author for this, but anyone thinking about acquiring this text should know it is not by any stretch "self-contained" as one previous reviewer stated.

The biggest irritant with this text is the constant abuse of notation. When you're just starting out trying to learn this stuff, it most emphatically does NOT help when the author keeps butchering or truncating the notation in the interests of "brevity". For example, entire derivations are often carried out using only the names of functions and not their arguments. Maybe I have a screw loose, but sometimes I find it really helps knowing that f is really f(x) and g is really g(y). And then in a single section the same symbol, N, is used to denote three different functions. Okay: this N really means N composed with alpha, and that N is N composed with the parametrization x, and this other N is really N all right, but when you stick q into it you really mean x inverse of q because N's domain is a plane, not three-dimensional space...yeah...oh wait...

Over the course of a semester I wasted uncounted hours unraveling DoCarmo's infuriating and uncalled-for notational "short-cuts".

So why do I give this text 3 stars? Well, in using it I still managed to master the core concepts quite nicely, so it had to be doing something right. Yes, the exercises are challenging, but I was able to crack most of the ones I attempted. Maybe a problem would take me 8 hours to do, but I could do it. I would not say this book is "dated", as one reviewer put it. In fact, I found most of the minimalist, non-computer generated figures to be refreshing and adequate. Anyone seeking cookbook methods for computing things will be sorely disappointed: this text is written largely for students of mathematics, and I have no qualms with that (being a math student myself).

Truly, if this text were given a buff and polish, it could become 5-star material (in my opinion anyway). Alas, that's probably not in the cards. ... Read more

Product Description
Each chapter devoted to single type of problem with accompanying commentary and set of practice problems. Amateur puzzlists, students of mathematics and geometry will enjoy this rare opportunity to match wits with civilization’s great mathematicians and witness the invention of modern mathematics.
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Customer Reviews (3)

Very Good for the interested reader
Although not reasonable for most high school students, this book does bring to light the background of modern geometry through its treatment of impossible and hard to solve problems.

Excellent background reading for a teacher!

Classic problems of geometry made simple
The principles of geometry are both elegant and timeless. One cannot help but understand why the Greeks considered it a pinnacle of intellectual achievement. This book sets down several of the classic problems, explaining them in such a clear way that it is easy to forget that it sometimes took centuries of work before the problem was resolved. Of course, those who first toiled on the problems did not have some of the additional machinery that we so take for granted today.
The problems covered are trisecting an angle, squaring the circle, constructing regular polygons and constructing a cube whose volume is twice that of a given cube. The background needed to understand the problems and solutions is nothing more than a solid grounding in basic algebra and trigonometry. Calculus is mentioned, but not used. Problem sets are included in all chapters and solutions to all are in the back of the book. They are well-posed, solidly reinforcing the points made in the text.
This is a book that covers several thousand years of progress in geometry in a little over one hundred pages. It is done well and it can be used as a supplement in any course in geometry, from high school to college.

Well done..
Bold has a gem of a book here.It's only a little bit over a hundred pages, but it's packed full of the great geometry problems that occupied the minds of the world's greatest thinkers for the past 2000 years.

Thetitle describes the book perfectly.These really are "Famous Problemsfrom Geometry" and he does indeed explain how to solve them.

Thebook has four major sections/chapters.He discusses in detail the threeproblems from antiquity (one section each):squaring a circle, doubling acube, and trisecting an angle.Furthermore, he spends significant timewith constructions of regular polygons (the fourth section) - which onescan be constructed and why. He also discusses which ones cannot beconstructed and why.

The reader will be expected to understand conceptsfrom Modern Algebra, particularly the concept of a Field.While Bold doesspend time explaining what a Field is, his definition is quick and isassumed to be more of a refresher for someone who has already learned aboutthem.Bold also has a section on Complex Numbers where he derives one ofthe formulas used later in the book.Again - this section is assumed to bea refresher on Complex Numbers.High School Geometry or Algebra studentswould have significant trouble understanding his explanations andproofs.

Bold provides problems for the reader to work along the way. These are problems that logically lead to the proof of the problem beingstudied.The problems are good.As a third year college student majoringin mathematics, I found the explanations/solutions to be sometimes hard tofollow.He assumes a great deal about the reader's level of proficiency inmath and in geometry.As a result, he liberally skips steps in proofs thatare assumed to be "obvious."

If you're expecting simple proofsto these problems, you're not going to find them.If they were simple,they wouldn't have taken 2000 years to solve.But they are explainedclearly here in terms that anyone with a college degree should be able tounderstand.

Overall, a superb book.A must have for anyone interestedin the famous problems from the history of Geometry. ... Read more

Product Description

For courses in Geometry or Geometry for Future Teachers.

This popular book has four main goals: 1. to help students become better problem solvers, especially in solving common application problems involving geometry; 2. to help students learn many properties of geometric figures, to verify them using proofs, and to use them to solve applied problems; 3. to expose students to the axiomatic method of synthetic Euclidean geometry at an appropriate level of sophistication; and 4. to provide students with other methods for solving problems in geometry, namely using coordinate geometry and transformation geometry. Beginning with informal experiences, the book gradually moves toward more formal proofs, and includes special topics sections.

Customer Reviews (3)

A solid introduction to geometry that emphasizes learning through problem solving
One of the problems a number of math students face is learning how to think about the problems they face.They simply never develop the necessary tool set that will allow them to understand what the problem is asking and what they should do to attack it.Once they have an answer, they are not sure if they have found the correct answer.This is a fine BASIC text for college and high school students who want to get a handle on dealing with geometry.If you have a deep mathematics background and are looking for an advanced college text on geometry, this is probably not for you.

However, if you want to learn the basics on how to think about geometry and a lot of help on how to solve a variety of geometric problems, this is a terrific text and will be a big help.I enjoy the way the text engages the student from the very beginning and asks him or her to THINK.It isn't a bunch of material to memorize.What the authors do is build the student's understanding through problem solving.If the student will take the time to work the problems and not give up on the problems he or she finds difficult, the understanding will come and will be more ingrained in his or her thought processes than would happen through memorization.

There are lots of geometric drawings, as one would hope, and there are a number of applications of geometry to real life and that should help the student, as well.Again, this is meant as a basic geometry text and can be suitable for a good high school student as well as non-majors in college that want to get an introduction to the basics of geometry.

not college level
This book is pitched at an extremely low level
quite beyond anything in the 'math for poets'
category - often dropping below even that of high
school.Indeed, the book compares unfavorably
with the canonical hs text by Jacobs.To give
just one example, it takes the authors 273 pages
to get to the ideaof cross multiplication [a staple
in the repertoire of any decent middle school
student].In particular, math majors as well
as anyone interested in the subject should
steer clear of this and consider instead books by
Pedoe, Court, Coxeter, etc.If you are looking
for a problem oriented approach to geometry, try
the relevant offering in the Schaum's series
[acknowledged masters of this approach].
In the meantime, let's not sacrifice any more trees
for products as weak as this.

An outstanding introduction to geometric thought
This is one of the few introductory level texts I have seen that gives some of the real flavor of mathematics, without being too challenging for beginning students.The initial section on problem solving is modelled on the famous book by Polya, "How to solve it," and has many simple but thought-stimulating problems.The following sections develop plane and solid geometry with many illustrated problems and interesting historical notes.The final chapters carefully introduce geometric proofs.There are also review sections on simple algebraic manipulations and basic logic, as well as a short section on the implications of alternate parallel postulates.Overall, the text has a well thought out development of basic skills and concepts, and enough interesting tidbits from more "advanced" topics to challenge the imagination of any student. ... Read more

Product Description

About the Contents:

Pretest

Helps you pinpoint where you need the most help and directs you to the corresponding sections of the book

Topic Area Reviews

• Basic geometry ideas

• Parallel lines

• Triangles

• Polygons

• Perimeter and area

• Similar figures

• Right angles

• Circles

• Solid geometry

• Coordinate geometry

Customized Full-Length Exam

Covers all subject areas

Appendix

Postulates and theorems ... Read more

Product Description
Intended to address the need for a concise overview of fundamental geometry topics. Sections 1-7 introduce such topics as angles, polygons, perimeter, area, and circles. In the second part of the text, Sections 8-11 cover congruent and similar triangles, special triangles, volume, and surface area. ... Read more

Customer Reviews (1)

basic geometry
She sent me the wrong book, I have e-mailed her twice with no response.How nice you purchase 1 item, and the sell just sends what every she feels like.She has no respect for the people that buy from her.IF I were you I would cancel any order you have with this Women and her story.Promise it will be wrong.

Christine
... Read more