Product Description
Spacetime and Geometry: An Introduction to General Relativity provides a lucid and thoroughly modern introduction to general relativity. With an accessible and lively writing style, it introduces modern techniques to what can often be a formal and intimidating subject.Readers are led from the physics of flat spacetime (special relativity), through the intricacies of differential geometry and Einstein's equations, and on to exciting applications such as black holes, gravitational radiation, and cosmology.For advanced undergraduates and graduate students, or anyone interested in astronomy, cosmology, physics, or general relativity. ... Read more

Customer Reviews (12)

Great GR book to learn GR from
I'm using this book as a supplement to Wald to teach myself and a few friends in my department GR. Apparently (according to my professor who was with Carroll at Harvard), thats how the book came into existance in the first place. As far as I can tell, the book is excellent. I highly recommend it. Basically it's Wald in English. Many things in Wald are explained in more detail (don't confuse detail with clarity, Wald posesses the supreme clarity of Math). Therefore, this text is best used in conjunction with Wald.

Wordy and Wonderful
This is an advanced text, but all the same it is not particularly rigorous or dense, so it is in principle accessible to the beginner.With an easy authority, Carroll leads us on a wandering journey through the mystical lands of general relativity.This is very different from, and compliments nicely, the clarity and directness of Wald.As a student of GR, I use Wald for the bottom line on any subject, and Carroll for the random physical or computational insights that I invariably find in any section of the book.Carroll's prose is like music to the ear and I always enjoy myself when I decide to open up this book.

Be warned that there are lots of mistakes in this first edition--you might want to wait for the second one.

Also, his chapter on cosmology is better than any I've seen.

BY FAR the best book on GR
I am currently on the 4th chapter of Carroll's "Spacetime and Geometry" and thus far I am amazed at how clear it is.Sure there is a lot of math in it however that also is very clearly explained.In fact, I think that Carroll explains the differential geometry material better than any mathematician has in any book on the subject.If you want to learn general relativity, there is no getting around the math; sooner or later you'll have to learn it.I'd suggest, especially if you are self-studying the subject, to rather pick up this book and go through it than pick up a more "elementary" text and a book on Riemannian geometry to look at later.

(Although I do also highly recommend Kay's (Schaum outline) "Tensor Calculus" for self study.The prima donnas don't like Kay's book because it "doesn't have enough theory."I suppose if a freshman calculus book does not have the Lebesgue integral defined in ti they'll complain about that too.)

Because, you can always skip through certain sections if the math is too heavy and go back through it later.And like I wrote earlier, you won't find a better introduction to the mathematical material than here.

Carroll should be given the Nobel prize for this book.If not in Physics, then in literature.I'd give this textbook 10 stars if I could.

A nice blend of the ideas of physics with mathematics
Kudos to Carroll.

This book is an excellent INTRODUCTION to SR and GR for the graduate physics student as well as the graduate mathematics students.

Pure mathematics often loses sight of the ideas which motivated it and physics often loses the mathematical foundations from which it is built.

This book offers some level of mathematical formalism to the physics student while exposing the ideas motivating the mathematical concepts.

I particularly like how he builds up the mathematical machinery of GR by introducing sets then topology on this set giving a topological space. Now he adds in the ideas of a manifold which make this topological space look like Rn locally with the patches sewn together smoothly. The manifold comes equipped with tangent space, cotangent spaces and their product spaces giving tensor spaces. These are defined nicely with reference to component formalism as well as the multilinear algebra approach as maps from products spaces to the reals, etc. He delves into forms and tantalized the reader with deRham cohomology although doesnt go into it. He shows how these can be differentiated ( exterior derivative ) and integrated.

Now the metric is introduced giving a geometry. To this is added a connection which is independent of the metric and leads to notions of parallel transport and differentiation of tensors ( covariant derivative ). One sees that in a special case one can derive a unique connection from the metric ( Levi-Cevita ) which is used in GR.

Fibre bundles, Lie derivatives, pullbacks etc are introduced as needed.

He then presents some introductory GR material by applying the mathematics.

Great Book But Won't Get You To The Promised Land
My comments come with a few caveats.

1. This is my fourth GR book.
2. I'm not hardcore into physics.I'm not a physic grad and I'm reading GR for fun.I have a decent graduate math background but I've been corrupted with 10+ years in working in various roles software engineering, electronics engineering and marketing.
3. I assume that since you're considering buying this book, you're goal is to get at the "real" GR, not the watered down discover channel version.

With these caveats in mind, here are my comments.

First, on a scale of 1-5, I rank Carroll at level 3 in terms of math/physics maturity and thoroughness.Here is my full ranking of authors from my limited reading:1. schutz2. hartle3. penrose3. carroll 4. wald5. physics journal articles

Second, using the rankings above, I recommend Carroll as the second port of entry.If you're comfortable with multivariable calculus, start with schutz (#1). You'll get warm fuzzies doing the toy exercises. But Schutz is tensor/math-lite.If you've had advanced calculus and geometry already, jump in with carroll (#3).But you'll be hard-pressed to find anyone else as polite to the reader.He won't prepare you for 80 percent of what's published.If you're ready to throw off the training wheels and jump dive into mainstream GR go with Wald (#4).

Note that Hartle (#2) is a good "tweener" book with feel-good exercises and some of the full-on GR equations at the end.I bet most instructors teaching a first year grad course would go with Hartle along with a dose of supplementary material.

Third, don't expect Carroll to be your last GR book purchase if you want to reach the promised land (see caveat #4).Living and breathing GR is found in physics journals and for that you'll need Wald or another advanced GR book. ... Read more

Product Description
Exposition of fourth dimension, concepts of relativity as Flatland characters continue adventures. Popular, easily followed yet accurate, profound. Topics include curved space time as a higher dimension, special relativity and shape of space-time. Accessible to layman but also of interest to specialist. 141 illustrations.
... Read more

Customer Reviews (22)

geometry, relativity and the fourth dimemsion
too abstract. Didn't touch on relativity until the 4th chapter and had trouble following the book til then.

Well Written Introduction to the Fourth Dimension
A great mathematical read! Fascinating diagrams. Begins with accessible concepts for all who love geometry. Gets into spacetime later in the book. Considers some philosophical/spiritual elements too, but mostly geared toward math and physics. A classic read. Highly recommend!

Good intro to related topics to Special Relativity
I found this work to be quite readable and something I can introduce to people with less math background.However, reading the book raises more questions than answers in my mind regarding the history of mathematics.For example, non-Euclidean geometry has been around for a long time and is the basis for ancient systems of navigation.

Similarly, for those who have studied the history of astrology (and its initimate relationship in the ancient world to navigation and agriculture), a great number of things (for example, the divisions of the houses) are all based on spherical geometry and many go back nearly two thousand years.For anyone who has ever known that the earth was a sphere, many of these problems were largely taken for granted.The only real problem with disproving Euclid's 5th postulate has been defining parallel lines on a sphere.I am not entirely sure that Rucker answers this in looking at the flattened sphere because the sphere could be rotated to make any two lines parallel.

Otherwise, I think this is a decent beginner book relating to the subjects in question.It is a useful work and I would generally highly recommend it as an introduction.

Instructive, and interesting
I found the book to be both educational, in that I learned great deal about geomtery and the history of diemsions from this book, as well as being fun to read. Both interesting and intellectually stimulating--I find this combination rare. I recommend ths book to anyone interested in the field.

With few exceptions, it is a readable, stepwise explanation of how the universe is structured
To understand relativity, it is necessary to understand geometry, specifically how a straight line can be curved. For nearly everyone, any attempt to understand four-dimensional space begins with understanding how a three-dimensional creature would appear to a two-dimensional one. One of the earliest and still the greatest of all introductions to going up a dimension is "Flatland" by Edwin A. Abbott. Quite naturally and sensibly, Rucker starts with Abbott's rendition of the properties of Flatland.
Rucker then moves on to the idea of curved space, where the shortest distance between two points is a "straight line", which is curved by the properties of the space. The space that we occupy is curved by the presence of matter, as Einstein claimed in his relativity theories. Furthermore, movement causes shrinkage in the direction of the movement and the slowing of time, which causes time to become just another dimension of space. As counterintuitive as this may appear, Einstein's relativity theory has been verified over and over again to a large number of significant figures.
One of the best things about this book is that Rucker has included problems at the end of each chapter. These problems reinforce the concepts of the chapter; it is unfortunate that no solutions were included.
In this book, Rucker steps the reader through all of the background material necessary to understand relativity and four-dimensional space. With few exceptions, the accounts are understandable to anyone with an understanding of college algebra.
... Read more

Product Description

Hermann Minkowski recast special relativity as essentially a new geometric structure for spacetime. This book looks at the ideas of both Einstein and Minkowski, and then introduces the theory of frames, surfaces and intrinsic geometry, developing the main implications of Einstein's general relativity theory.

Customer Reviews (11)

Excellent and will never find better !
This book is a terasure in its own right !
everything is explained using diagrams, figures with simplicity and rigor.
you will never feel you got lost anywhere. Although the introduction to tensors is limited, the application of Fermi coordinates is great although I would have expected to see the actual derivation of vacuum equations as einstein first wrote it .
The proofs are excellent. The application, though limited but clearly exposed.

A great intermediate level book.
We all get an initial taste of relativity in Freshman/Sophomore physics. But where to go next can be a problem.If you like the math accompanying your physics a bit more rigorous than "hand waving", this is a great book.I tried Schutz's book but didn't find the math self contained or rigorous, while trying to jump into Wald's graduate level text on General relativity was way too much to soon.This book strikes a good balance between the physics and the math. Nice coverage of the Lorentz transformation and the invariance of Maxwell's equations under it. Minkowski space time and "hyperbolic" geometry (nice review of hyperbolic functions in analogy with trigonometric functions). And a self contained introduction to differential geometry (as applied to general relativity).I'm finding this great for self study.

Great for learning how to actually use the math behind GR
This book is great for teaching the math behind GR using excellent examples from Math and Physics problems (for another great problem solver see also Schaum's Outline of Tensor Calculus, but this has less Physics). It is a bit long winded, spending alot of time on SR and in some place just over the top (for Physicists!), but once through it there should be no problem going to the more advanced texts which deal with more of the uses of GR. At the same level I would also recommend Schutz's First Course in GR, however, Callahan's book goes through and explains the use of the math better, whereas Schutz's is better for uses in GR, surprisingly this is the strength of Callahan's book: you can't really do the Physics properly unless you can do the math! After this it's on to more Physics orientated books like Carroll's excellent Introduction to GR, as a stepping stone to MTW's Gravitation and Wald's GR.

One of the best.
This is one of the best introduction to General Relativity. It is the most accessible introduction to differential geometry. Naturally you have to know calculus, linear algebra, and the basics of special relativity. I bought many books on the subject, and this one belengs to the set I suggest for self-learning.

Disappointing
I've only read the first third in detail, but so far this book is frankly disappointing. The treatment is lightweight and padded out with verbiage, some of it oddly off-key. What math or physics student at this level needs (for example) an elementary account of the properties of hyperbolic functions? Spacetime diagrams are drawn with the time axis horizontal, which is something I've never seen in any other relativity text. Okay, it's a minor point, but I found this and similar nonstandard usages a constant irritant. More seriously, the development of relativistic momentum and covariance in chap.3 is quite incoherent, and the definition of 4-velocity is WRONG (at least, by everyone else's standards - it isn't even a 4-vector). There are plenty of exercises, which is good, but no solutions at all - not even outlines - which is not so good.

The book takes over three hundred pages to get to general relativity (where there seems to be no mention of the equivalence principle!), and I doubt if it's worth the effort. You would do better to work through Foster & Nightingale's 'Short Course in General Relativity', which is a first-rate and accessible introduction if you have a little background in special relativity. And it's two-thirds the price.

Conclusion: There may be a good book waiting to be written on these lines, but I'm sorry to say this isn't it. I wouldn't recommend it to anyone as a first course in relativity. ... 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

Product Description
The book has no illustrations or index. Purchasers are entitled to a free trial membership in the General Books Club where they can select from more than a million books without charge. Subjects: Mathematics; Geometry; ... Read more

Product Description

"Geometry and Physics" addresses mathematicians wanting to understand modern physics, and physicists wanting to learn geometry. It gives an introduction to modern quantum field theory and related areas of theoretical high-energy physics from the perspective of Riemannian geometry, and an introduction to modern geometry as needed and utilized in modern physics. Jürgen Jost, a well-known research mathematician and advanced textbook author, also develops important geometric concepts and methods that can be used for the structures of physics. In particular, he discusses the Lagrangians of the standard model and its supersymmetric extensions from a geometric perspective.

Product Description
Very clean inside, normal cover wear ... Read more

Customer Reviews (1)

Discovering Geometry
The book was in very good condition and was delivered on time. I have ordred several books from amazon and, have always been very pleased. ... Read more

Product Description
This fully revised and updated Second Edition of an incomparable reference text bridges the gap between modern differential geometry and the mathematical physics of general relativity by providing an invariant treatment of Lorentzian geometry -- reflecting the more complete understanding of Lorentzian geometry achieved since the publication of the previous edition. ... Read more

Customer Reviews (1)

Essential for an advanced student of relativity
My review is based on a previous edition of this text.I have seen the new (2nd) edition and it appears that several chapters have been added but the old chapters are essentially the same.

As of the time of this writing, I have only made it to the 2nd chapter (again, of the 1st edition).Nevertheless, I've read the introductory material in the introductory (1st) chapter several times, because it is so rich.

This text is perhaps most useful to a student who knows a few things about differential, to be more precise, Riemannian geometry (and is interested in general relativity).There are many differences between a Riemannian manifold and a Lorentzian manifold, where the latter metric is not positive definite in that the metric gives one negative eigenvalue.This text is quick to point out the differences, which is a great aid in understanding the new material.

I have some background in general relativity and from my experience in the subject there were many questions I had unanswered.This book is a blessing to me in that it has uncovered for me some of the mystery of Lorentzian manifolds, in particular space-times.There are still many things I do not understand but I am confident this text will aid me in getting a clearer picture.

I highly recommend this text to student of relativity theory who has an understanding of mathematical reasoning, and yearns for a stronger mathematical understanding of the Lorentzian manifold.The current edition is a bit expensive but even if you do not think it is worth it there are still some 1st editions floating around (#67 in the Dekker Pure & Applied Math Series) which are much cheaper.I may eventually buy the 2nd edition if I find the additional chapters make the book worth the price. ... Read more

Product Description
Three million high school students and 172, 000 college students enroll in geometry classes every year. Schaum's Outline of Geometry, Third Edition, is fully updated to reflect the many changes in geometry curriculum, including new terminology and notation and a new chapter on how to use the graphing calculator. ... Read more

Customer Reviews (12)

Good review of concepts - Poor Editing!
I am using this book as a refresher while studying for an upcoming qualification exam. In just the opening chapters covering Algebra review, I was appalled at the number of errors made. These are not typographical errors as is the case where the book says that something weighs "11 km", but flagrant syntactical errors that produce a muddled understanding of the underlying concepts.

Luckily, I am still fresh enough with Algebra to catch these errors, however, I have to question their ability to clearly convey geometry material without confusion.

This is not to say that the text is a total wash, but I do expect a certain level of accuracy from outline materials such as this.

Geometry review on schaum's outline
For the most part this book is great as a tutorial with ample exercises that provide critical thinking pertaining to proving triangles congruent and reasoing in general. Thats the way geometry should be taught critical thinking unlike most books that regurgitate and are watered down. Even though this book is modern, its not as great as plane geometry munro 1959, theres not ample exercises on tedious proofs. My favorite sections are proving quadrilaterals are parallelograms and areas of polygons because these problems force the individual (student) to think outside the box. For example, there are problems where circles are inscribed in circles, sectors inscribed in equilateral triangles, right triangles part of circles, etc.

The weakness is the fact that this book does not provide surface area of hexagonal prisms, polygonal pyramids involve apothems, radii, surface area of cones, no composite figures, just surface area of rectangular prisms and cubes, its the same like schaums outline for algebra in regards to this section and the same regarding reflections and translations. I therefore give this 3 stars because of some redundancies.

Not horrible, not great...
I got this book as review of basic geometry.Mostly because they never made a Forgotten Geometry text.It's really not bad.It covers quite a bit of ground, from simple geometry to a taste of analytical and transformational geometry.

Conversely, this book didn't wow me either.It covers some basic algebra in the beginning, which is fine for the easier formulas like area and perimeter, but not nearly enough for a comprehensive study of geometry.One should study Schaum's outline of Intermediate Algebra or College Algebra, or a text of their choosing, before tackling any geometry.Especially if your preparing for a Calculus/Analytical Geometry Course.

I haven't found a good intro geometry book yet(I haven't even looked!), but when I do, I'll be sure to update this review.As always, good luck!

Good for basic refresher
I bought this book as a recommended book for a masters Geometry class I was taking.While the concepts of my class were far more advanced than this book, the content of the book made remembering about the geometry and basics (probably good through hs geometry) more clear.I good book to take you through high school geometry.

Caution - There are Mistakes
I bought this book to use with my daughter for added drill and review of Geometry and was shocked to find an inaccurate mathematical statement after the Commutative Law of Multiplication (3a X 5 = 5 X 2a = 10a) and three errors in the solutions provided to practice questions in the first eight pages.I haven't ventured further, but based on my experience thus far, I will need to review every example and problem for accuracy, something I hadn't planned to do and shouldn't need to do. ... Read more

Product Description

Discrete differential geometry is an active mathematical terrain where differential geometry and discrete geometry meet and interact. It provides discrete equivalents of the geometric notions and methods of differential geometry, such as notions of curvature and integrability for polyhedral surfaces. Current progress in this field is to a large extent stimulated by its relevance for computer graphics and mathematical physics. This collection of essays, which documents the main lectures of the 2004 Oberwolfach Seminar on the topic, as well as a number of additional contributions by key participants, gives a lively, multi-facetted introduction to this emerging field.

Product Description
This new title in the Homework Helpers series will reinforce mathematical foundations and bolster students' confidence in geometry. The concepts are explained in everyday language before the examples are worked. Good habits, such as checking your answers after every problem, are reinforced. There are practice problems throughout the book, and the answers to all of the practice problems are included. The problems are solved clearly and systematically, with step-by-step instructions provided.

Particular attention is placed on topics that students traditionally struggle with the most. While this book could be used to supplement standard geometry textbooks, it could also be used by college students or adult learners to refresh long-forgotten concepts and skills.

Homework Helpers: Geometry includes all the topics that are traditionally covered in a high school geometry course, including:
-Parallel lines
-Congruent lines
-Quadrilaterals and other polygons
-Similarity and special triangles
-Right triangle trigonometry
-Circles
-Area volume and solids
... Read more

Customer Reviews (2)

Not up to the Homework Helper standard!
We usually love books from this series, especially algebra and chemistry, but we gave up on this due to the typos and the poor examples.Too many odd analogies and overly wordy explanations.We gave up and bought something else.

HOMEWORK HELPERS:GEOMETRY
THIS IS VERY ORGANIZED BOOK. SIMPLE AND CLEAR IN CONCEPTS. IT HELPED MY SON IN HIS STUDY.
... Read more

Product Description
This introduction to computational geometry focuses on algorithms. Motivation is provided from the application areas as all techniques are related to particular applications in robotics, graphics, CAD/CAM, and geographic information systems. Modern insights in computational geometry are used to provide solutions that are both efficient and easy to understand and implement. ... Read more

Customer Reviews (16)

let my money back assp
I didn't order this book...

furthermore i don't saw this book.

How it can be happen?

Now I can't believe ordering system of amazon...

Let my money back asap!!!

Concise reference for computational geometry
This book covers the concepts and algorithms concisely and hence forms a very handy reference to Computational Geometry. You could use this as the starting point for any Comp Geom application and build on that. I am pretty happy with this buy!

Good book, not for a primer
The subject is not easy, so the book is surely not for a primer on graphical programming, even more for a primer on computation and algorithms.
But if you need some very advanced algorithms to solve any computational geometry problem, you'll find it here. Maybe the very latest advances on subject are not present here (a new revision of this book is available, not much news on that, look for the difference on the web).
Thanks to the author, whom I asked a clarification on an algorithm present in the book, and responded in less than 3 hours.

The definitive guide to computational geometry.
When studying computer science, one will encounter a number of books."The Dinosaur Book", Operating System Concepts (7th Edition), "The White Book", Introduction to Algorithms, "The Green Book", Artificial Intelligence: A Modern Approach (2nd Edition) (Prentice Hall Series in Artificial Intelligence), and a select few more.The best way to articulate my satisfaction with this material is to refer to it as "The Blue and Yellow Book."

Each chapter is introduced with a problem.For example, "How would one install cameras on the inside of an art gallery (represented by a polygon) such that each wall can be observed with as few cameras as possible."The chapter then presents the material in a clear, concise fashion, and applies this newfound information to solve said problem.

It could be argued that the book is math heavy; certainly those with a strong grip on linear algebra and geometry will have an easier time, but those without can still grasp the material enough to benefit.For those interested in proofs, there's no shortage in the book, either.

Strongly recommended and a great deal of fun to read.

Excellent Background
This book is extremely well written, easy to understand, and actually is the standard text for Computational Geometry classes, as far as I know.The only thing I didn't like about it was that there seemed to be a few errors in some of the pseudocode.But, it's to be expected when publishing a textbook, and I think it'll probably be cleared up in future editions.

Overall, great book.I'd recommend it to anyone taking graphics or a computational geometry class. ... Read more

Product Description
Geometry Textbook Ideal for reaching the greatest number of students and assuring their success in learning Geometry,including Resource Classes, ESL Classes and Remedial/ Struggling Learners ... Read more

Customer Reviews (1)

AGS Geometry
The AGS Geometry book I purchased is in the shape I requested and meets the needs of my classroom.Amazon.com is a great resource to get materials that are quality copies but also at a substantial reduction of price!! ... Read more

Product Description
Stimulating collection of unusual problems dealing with congruence and parallelism, the Pythagorean theorem, circles, area relationships, Ptolemy and the cyclic quadrilateral, collinearity and concurrency and many other topics. Arranged in order of difficulty. Detailed solutions.
... Read more

Customer Reviews (8)

Intuitive Guide
This book is suitable for anyone who want to learn advanced high school geometry or want to participate in any mathematical contest and have to learn much though not really new on it. The problems are set from the quite easy to advanced, with many of them are quite simple so you don't get frustrated because you can't do any of the problems. It covers the basic and common problems in math contest.

Unfortunately, it don't have good set of theorems. Sure, it's written on the back but they're not easy to navigate. Also, many of them are not really basic even for contest geometry. Like its title, 'Challenging' is sure quite challenging, since many of the problems, though not really hard, need deeper thinking and you need to draw the 'help line' to solve the problem. The hints written on the back is not really helpful.

Overall, for those who want to improve skills, participate in contest, or teacher who wants to make a surprise test, this book is a really good source of information.

Really, - Challenging Geometry
This books presents a lot of problems to solve. One challenge after another, you can find several problems and better still if you get stuck, you have hints that really help in solving the problems, and one, sometime two or even three different ways of solving it.
As written at Plato's academy, for geometers only, you have to be willing to spend sometime doing geometry.

Learning geometry from the principles
I liked this book very much. I solved every single problem in the book with two students that I tutor for International Math Olympiads and carefully read the hints and solutions proposed at the end of the book. They really teach how to "attack" geometry problems using simple stuff like angle chasing, drawing parallel lines etc. I cannot recommend this book more to the readers with some mathematical sophistication. I even have a suggestion for parents that have some sort of mathematical background (engineers, bankers, doctors, etc.): If you want to spend quality time with your children, get this book and enjoy solving the problems together. I cannot imagine a more amusing pastime. I am looking forward to seeing new titles from the authors.

Very good after the basics
This is a great book! But, don't buy it if you don't know the basics well. You'll get frustrated easily and leave geometry. For beginning this is what I recommend: [...]

Firstly, don't try a problem for 10 minutes and then just look at the solution. This way, you'll gain nothing from the book. You HAVE to try these problems for at least an hour (some may even take up to 2-3 hours)if you can't solve them. You can, however, break this up into pieces. For example, sit for about 15-25 minutes with one line of attack and then if couldn't solve it, then come back when you have time and give a try with another line of attack. And, let me tell you, when you do solve a problem after trying it for 1-2 hours, it'll be motivation enough to move on to the next problem.

I especially like this book because I can hide it under my desk at school :)

Also recommended is Geometry Revisited (buy it with this if you can).

Problems and solutions
Posamentiers' book is a little bit unbalanced. It contains around 200 problems with solutions. The easy problems are just what you would expect in the exercises sections of an introduction to Euclidean geometry like Kiselev's Geometry / Book I. Planimetry. The the harder problems you will find as classical theorems and examples in more advanced texts like Altshiller Courts' College Geometry: An Introduction to the Modern Geometry of the Triangle and the Circle (Dover Books on Mathematics). A more balanced text would have contained more intermediate problems and the harder ones would have been more "original".

The methods used are purely synthetic, no analytic geometry. The book is aimed at an advanced high school level audience. Prerequisite is the stuff you find in a book like kiselev I mentioned above.

If you need a book to train your geometric problem solving abilities I think that Altshiller Courts' book is a better choice although there are no solutions to the exercises in that book. Butwhat use are the solutions? Problems should be solved and not looked up!

For many problems, especially the hard ones, several solutions are provided. To me this is what makes the book attractive. ... Read more

Product Description

This book offers a unique opportunity to understand the essence of one of the great thinkers of western civilization. A guided reading of Euclid's Elements leads to a critical discussion and rigorous modern treatment of Euclid's geometry and its more recent descendants, with complete proofs. Topics include the introduction of coordinates, the theory of area, history of the parallel postulate, the various non-Euclidean geometries, and the regular and semi-regular polyhedra.

Customer Reviews (11)

Good introduction to the relationship between algebra and geometry
The book begins with a quotation from Gauss that suggests the elegance of treating Geometry in the "pure spirit of geometry" i.e. without using real numbers. And Hartshorne follows this principle by developing Euclidean geometry at first from the Elements of Euclid and then (after remarking their weaknesses) by using Hilbert's axioms. However the book is not about the foundations of geometry and much attention is given to the meaning of these axioms in the context of ruler and compass constructions and how this topic is related to analytical methods which lead directly to the theory of field extensions and Galois groups.

I think one of the main purposes of this book is to show how the abstract structure of a Field arise naturally both in Euclidean and Non-euclidean geometry and in this way prove that their typical algebraic models are categorical (that is, they are unique up to isomorphism) which is interesting for its own sake.

So this is not the usual approach to Geometry based on groups of transformations which can be found on other books, but a more "classical" one. But even if the approach is classical, the study of classical problems is always connected with modern algebraic facts, the most striking of them (for me) is the use of algebraic invariants to solve Hilbert's third problem which can be perfectly formulated (but not solved) in elementary terms.

Geometry - anything else you need?
So this book answers one of the questions I always had. Call me an ignorant if you please, but I had never had a complete reference of the axiomatization of geometry in my hands before.

I had read Proffessor Hartshorne's book "Agebraic Geometry" before andI thought he was one of those algebrists that hide themselves inside the name of "Algebraic Geometers". Note that I like Algebraic Geometry myself, but I see it more as an "algebraic" branch of mathematics than a "geometric" one. Anyway, this book proved me wrong yet again. After reading it, I found out that Proffessor Hartshorne is really good explaining geometry.

Since I was told some years ago that Geometry could be Axiomatized, I had always hoped to see the structure being constructed. This book finally fulfilled my curiosity. I am indeed grateful with professor Hartshorne just for writting this book.

Where was this book when I was a student?
This is a great book, a mature and lively treatment of a familiar subject made new again.If I'd had a text like this as an undergraduate I'd likely still be in math.Most of the serious advances in pre-20th century geometry get subsumed in the typically more topological, or algebraic, but in either case more abstract, treatment one finds today in a typical undergraduate course.Lost in this approach is the intuitive grounding which makes more modern approaches meaningful and not just mere formalism. This book, which would lend itself to self-study as well as to classroom use, goes a long way to restoring that lost grounding.Very highly recommended.

Bring your copy of Elements!
I'm still working through this text but I should warn prospective buyers of one thing: The book's early chapters makes heavy references to Euclid's propositions in his books The Elements. I don't just mean references like "Remember that Proposition 43 from Book 2 that says...". No, would that it were so. He'll just give the number and assume you've got your copy of Elements handy.

In that way, it's not really a complete survey of geometry from the start. You'll want to order a copy of Elements with this book. Dover publishes eleven of the books in two volumes.

a wonderful book by a world famous geometer
This book reveals the love professor Hartshorne has for geometry and euclid.I became excited about the subject just reading the introduction.The book assumes the student knows high school geometry. which unfortunately eliminates many college students, but I am going to try to use it at least for the second part of my college course.

This is a really well written, expert, wonderfully enthusiastic book, about a great, absolutely classic topic, by a powerful world famous authority in geometry.

The organization assumes the student is reading euclid concurrently.then prof hartshorne explains the difficullties with euclids treatment and shows how to remedy them. e.g. he observes euclids proof of SAS uses a principle of superposition without stating it, then although he adopts the Hilbert option of making this an axiom, he also presents an alternative treatment in which the principle of superposition is an axiom, and SAS is then proved exactly as euclid does.this sort of thing shows very clearly that euclids proofs become correct, merely by clarifying his implicit assumptions.

i love this and think it enhances the subject enormously.

the exercises are so ambitious and far reaching I at first dismissed them as unrealistic, but soon became infected with dr hartshornes enthusiasm for putting the students in touch with their best abilities, and challenging them to reach as deeply as they can.

This book is a remarkable work of scholarship, with far more content than one course can use.The student has here a work that will repay years of study.again the price makes it a bargain compared to far inferior works at double the price. ... Read more

Product Description

This book, based on a graduate course on Riemannian geometry and analysis on manifolds, held in Paris, covers the topics of differential manifolds, Riemannian metrics, connections, geodesics and curvature, with special emphasis on the intrinsic features of the subject. Classical results on the relations between curvature and topology are treated in detail. The book is quite self-contained, assuming of the reader only differential calculus in Euclidean space. It contains numerous exercises with full solutions and a series of detailed examples which are picked up repeatedly to illustrate each new definition or property introduced.

Customer Reviews (1)

Hard to say
This was the official 100% recommended, guaranteed text for my Riemannian Geometry class.Supplementing this book with do Carmo's text, I was able to get something out of the class, but I think rereading both of them now would be much better.The condensed one chapter course on manifolds at the beginning of GHL wasn't sufficient to learn/relearn everything I needed to know in order to read it for the first time. ... Read more

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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
Geometry is probably the most accessible branch of mathematics, and can provide an easy route to understanding some of the more complex ideas that mathematics can present. This book is intended to introduce readers to the major geometrical topics taught at undergraduate level, in a manner that is both accessible and rigorous. The author uses world measurement as a synonym for geometry - hence the importance of numbers, coordinates and their manipulation - and has included over 300 exercises, with answers to most of them. The text includes such topics as: - Coordinates - Euclidean plane geometry - Complex numbers - Solid geometry - Conics and quadratic surfaces - Spherical geometry - Quaternions It is suitable for all undergraduate geometry courses, but it is also a useful resource for advanced sixth formers, research mathematicians, and those taking courses in physics, introductory astronomy and other science subjects. ... Read more

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Excellent
The best geometry book available for someone who has a working knowledge algebra.Well written and moves from the basic to the intermediate at a measured pace.HIGHLY recommended. ... Read more

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The geometry of the hyperbolic plane has been an active and fascinating field of mathematical inquiry for most of the past two centuries. This second edition of Hyperbolic Geometry has been thoroughly rewritten and updated. Chapter 4 focuses on planar models of hyperbolic plane that arise from complex analysis and looks at the connections between planar hyperbolic geometry and complex analysis.

Customer Reviews (3)

Excellent book
This is an excellent introduction to hyperbolic geometry. It assumes knowledge of euclidean geometry, trigonometry, basic complex analysis, basic abstract algebra, and basic point set topology. That material is very well presented, and the exercises shed more light on what is being discussed. Plus, solutions to all the exercises are at the end of the book.

Very good introduction
I used this text along with Tristan Needham's "Visual Complex Analysis" to get a full dose of the geometric beauty inherent in studying complex variables. I found it to be a nice complement to the second year course in geometry at Cambridge University. Anderson does a wonderful job of working out in detail lots of examples so that you can get the algorithmic practice of solving problems. However this is not merely a cookbook. Rather, core elements of the theory are presented from the ground up, with plenty of time spent on understanding the group structure of Mobius transformations in various settings. Disc and upper-half plane models are treated as well as more general models. I recommend you buy both this book and Needham's if you want to appreciate the world of complex numbers.

great book
this is a really great introduction to hyperbolic geometry.especially if you want to study gammas acting on the upper half plane.it starts at a much lower level then any other text. ... Read more