The Shape of Space (Pure and Applied Mathematics)

Book Description

Maintaining the standard of excellence set by the previous edition, this textbook covers the basic geometry of two- and three-dimensional spaces Written by a master expositor, leading researcher in the field, and MacArthur Fellow, it includes experiments to determine the true shape of the universe and contains illustrated examples and engaging exercises that teach mind-expanding ideas in an intuitive and informal way. Bridging the gap from geometry to the latest work in observational cosmology, the book illustrates the connection between geometry and the behavior of the physical universe and explains how radiation remaining from the big bang may reveal the actual shape of the universe.

Customer Reviews:

Magic book on Topology for educated commons.......2007-08-05

This is a great book for anyone who is interest in Mathematical Topology and Cosmology Topology. This book does not require a reader to have strong mathematics knowledge. It only requires a reader to have patience to think and solve some problems in the book. The most brilliant point in this book is using diagrams to illustrate the Topology concepts, such as Manifold. This help the reader to get a "feeling" of some really difficult concepts in Topology. This book should be a classic like "Flatland".

chris tam
hong kong

The joy of math.......2007-08-02

I have a bachelors degree in Math.

As Feynman said, what we really mean by math is careful reasoning. This book brings you the joy of careful reasoning, guided by an expert.

Perhaps what turns some people off math in school is that the supreme example of careful reasoning is the mathematical PROOF. (Or perhaps it's just that most math teachers are so poor.) A proof tends to look dull and ponderous on the outside, and a student can easily miss the beauty of the underlying ideas. On the other hand, for your own amusement you can figure something out to your own satisfaction, without necessarily constructing a watertight proof. This book helps you do just that.

Many newspapers contain Sudoku problems, often with the reassuring claim that no math is required! People who hated math in school can be seen working happily on Sudoku puzzles, for the sheer joy of exercising their ability to reason carefully. The same ability would bring them far more joy while reading this book and answering the puzzles/exercises spinkled throughout.

Excellent Introduction, No Assumptions.......2007-07-05

This text is non-intimidating as an introduction to topology. Weeks carefully guides the reader through the building blocks of torii, Moebius strips, projective planes, and other surfaces. After working appropriate exercises, the reader gets a chance to visualize 3-manifolds and connected sums. Some aspects of these two topics can be difficult to explain, but analogies are applied to make understanding attainable. Further, figures and illustrations exist throughout the text, and these are definitely helpful for visualizing connected sums and non-orientable surfaces (both one-sided and two-sided).

(I especially like the approach to the Gauss-Bonet theorem using double lunes. It is a carefully crafted derivation with plenty of illustrations to avoid confusion.)

Some may think this text is too simple, but it is a "must read" for anyone who has not encountered topology and who wants to do individual research on the topic. Many texts claim to be introductory texts, but they are actually designed for those who already have a degree in math and who have seen similar subject matter. However, this one is definitely for "newbies." So don't worry.

Interesting book.......2006-11-26

This is a painless way to learn some advanced topology--or at least to gain insight. It's almost a picture book. Most problems include solutions and require only a few minutes of thought. They are also worth solving.

Now that I understand what is meant be a certain topology of the cosmos, I'm astounded that anybody actually considers it possible. Fascinating.

Easy Reading.......2006-02-20

This is a very good book for people whom have a light background in math. It is a readable book and great introduction into manifolds and torus. As a mathematican I am amazed with the quality of material, examples, and thus provide one with the ability to understand the topics. I plan to use this book and some of its topics in future teachings. Thus I recommend this book for anyone especially for people who struggle with math.

History: Fiction or Science? (Chronology, No. 1)

Average customer rating:

Calculations are only as good as your numbers
Pants on fire?
Accepted History & Chronology Must Be Changed.
Very Interesting
History as Science Fiction

History: Fiction or Science? (Chronology, No. 1)
Anatoly Fomenko
Manufacturer: Mithec
ProductGroup: Book
Binding: Paperback

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Similar Items:

History: Fiction or Science? Chronology 2 (Chronology)
History: Fiction or Science? Astronomical methods as applied to chronology. Ptolemy's Almagest. Chronology III
Discovering the Mysteries of Ancient America: Lost History And Legends, Unearthed And Explored
Before the Pharaohs: Egypt's Mysterious Prehistory
They Cast No Shadows: A Collection of Essays on the Illuminati, Revisionist History, and Suppressed Technologies

ASIN: 2913621058

Book Description

Recorded history is a finely-woven magic fabric of intricate lies about events predating the sixteenth century. There is not a single piece of evidence that can be reliably and independently traced back earlier than the eleventh century. This book details events that are substantiated by hard facts and logic, and validated by new astronomical research and statistical analysis of ancient sources.

Customer Reviews:

Calculations are only as good as your numbers.......2007-08-03

Yes, we can all agree that mainstream history is nearly 100% BS due to politics, economics, ego, problems with dating techniques, and various conspiracies. Agreed. But, I've been researching the distinct possibility that human history (in terms of civilizations) are much more ancient than we've been told, so coming across this book was very interesting to me. I wondered how Fomenko could be wrong (if at all) because he is very persuasive in his presentations. Then it dawned on me. If at previous times in prehistory, due to the various catastrophies that are well documented (comets, asteroids, planetary disruptions, plasma discharge, pole reversals, etc) the Earth was in a different position in relation to the sun, different tilt on its axis, different orbit, different rotation (in terms of velocity and DIRECTION), and the continents were in different positions, then would this not cause the ancients to see the sky (constellations) differently? In other words, is Fomenko making erronious assumptions about the physics of the Earth in pre-history, which then corrupt his data with regards to dating the relevant astrology? The last event to seriously disrupt our planet occured roughly 3500 years ago, according to other good researchers, so is it possible Fomenko has been confused by this? The vastly different physics of our planet in the not so distant past may explain this confusion, which is not to say the "mainstream" version of history is correct; on the contrary. I am not an expert in these fields, but wanted to see if this idea could spark discussion.

Pants on fire?.......2007-07-19

Will people ever read before spamming? Yes, Jesuits could not rewrite world history alone, they had help. Anyway, Dr Prof Acad A.Fomenko does not point to jesuits as the driving force of world wide history manipulation in published volumes 1,2,3;, actually he barely mentions the poor devils. Check it with 'Search inside' feature, please. China is rarely mentioned either, in fact, Dr Fomenko is completely eurocentric. Right, his theory contradicts all mainstream schools of history, because in their actual state they are all built on blatantly erroneus chronology. You don't need a mysterious cabal (conspiracy) to falsify history, the falsification is its modus operandi. It is inherent to history(ians) to falsify (distort) events, as it is inherent to humans to boast as it is inherent to power (authority) to legimize itself by referrring to glorious past made to its own order. Dr Prof Fomenko and team have identified scores of instances of such manipulation in Russian, European, etc.. history, and delivered valid statistical proof thereof. His own 'reconstruction' is completely another story. Forget c14 as a valid method of dating. W.Libby has initially discovered a brilliant method of INDEPENDENT dating. Too bad, c14 method has become a joke after a forced marrige with dendrochronology with consensual chronological scale inbuilt. Radiocarbon method can't stand blind tests, but is so very productive as a rubberstamp.

Accepted History & Chronology Must Be Changed. .......2007-04-09

There is no doubt that history as most know it is a sham, & institution's version of History both University & Church is fradulent & inaccurate. Everything was established with an agenda, The real "Dark Ages" are now when we have access to incredible amounts of information past authorities & more important 'common folk' didn't have but our institutions & educators are slow to evolve because of what has ignorantly & arrogantly been taught for too long. This is on many subjects not just Chronology.

For anyone to question "Why would a Mathematician have anything credible to say of History?" The answer is from Dr. Fomenko's preface in the book: "It would be worthwhile to remind the reader that in the XVI-XVII century Chronology was considered to be a subdivision of Mathematics." These volumes could possibly be some of the most important works to date & should be read by everyone with an interest in History, especially professors & educators who have a duty to the public. I have read both books & must say that 'Chronology 1' has some very eye opening & revolutionary information. Even if these volumes are part true the implications are profound & opens the doors to further investigations & questions which must be done. I speak several different lanquages & must say the logic Dr. Fomenko uses with "inflection" of words & words being read from left to right in one region & right to left in another then written backwards, the removal of vowels & get down to basics of words, or different cities & locations having the same name etc. is correct. Vowel usage has always been optional & varied, actually complicating linquistics & study. The first thing one has to understand is that words never had a fixed spelling in history like we do now, the spelling of words was mutable & regional, as well as names & titles of people were vast, varied & changed, NOTHING WAS FIXED or understood linear. Matters of Life & Death as well as financial profiteering yesterday & today were & are made with ignorant, illogical & conspiratorial views of history & reality, it's time people get closer to the Truth & society collectively grow up.

Very Interesting.......2007-03-07

It is a good proposal and I believe it will mature into something even better in the future. I think it deserves to be read.

History as Science Fiction.......2007-01-10

Anatoly Fomenko has written a very intriguing book, full of pictures, charts, and computer 'proof' of his thesis: backwards of AD900 we don't really know what happened or when. Between AD900 and AD1600 there is more certainty, but there is still a lot of fuzzy ground, and things don't get reliable until we get past the 1600's where the printing press made it very difficult for the perpetrators of this timeline manipulation to change anything that had been committed to print. The Dark Ages did not happen. Books were burned for a reason. One organization has doubled the actual length of its existence by expanding the real chronology. Read why.

I had always wondered why Christ died about AD33 and yet men waited until the 11th century to form the Knights Templar, the Cathars, etc and go after the Holy Land by force. Why the 1000 year gap? Turns out there wasn't more than a 10-12 year gap and he proves it using astronomy. This also implies that the planet is not as old as we have been told, and current Christian and other creationist scientists are already championing that idea without being aware of Fomenko's book. The two groups, creationist scientists and the Russian mathematical analysts corroborate each other. Fascinating.

Of course, all this flies in the face of what we have been told traditionally is the 'proper' chronology of western civilization, and most readers will experience 'cognitive dissonance' in reading this book. It means that our history going backwards from AD1600 becomes progressively more incorrect and unreliable until it cannot be trusted at all... in the space of 700-800 years.

Naturally, the curious, open-minded reader will want to know WHO did this, WHY, and did any of the events we think of as really ancient ever happen?
Dr. Fomenko is a respected scientist/mathematician at Moscow State University who has already answered these questions to the satisfaction of his initially skeptical colleagues. Most of them are now believers, a few still refuse to believe (the usual diehards), and of course the western press has ignored Fomenko's work -- for obvious reasons when you read the book. The ones who perpetrated this chronology ruse have a lot to answer for. They are still with us. That's why this book is a well-kept secret.

I gave the book a 4-star rating because I was unable to check out some of his claims; those I checked were as he said. But if even 1/3 of his claims are true, this punches a big hole in what we think is our history, the meaning of western civilization, our educational process (for repeating the ruse as gospel), and the trustworthiness of the organization that perpetrated this ruse, well-intentioned or not.

This book relates to current research into a Young Earth paradigm, to John Keel's discoveries about our planet, and Fr Malachi Martin's insights (in his now out-of-print books). We are indeed sheep who are manipulated and kept ignorant -- for a reason. While knowing what these men have to say may be the "booby prize" (as in: 'what can you do with this knowledge?'), it will provide interesting reading. Didn't someone say: "...and the Truth will set you free."?? For you to judge if this book contains the truth.

Differential Geometry of Curves and Surfaces

Average customer rating:

Good book.
Best DG book out there
There is a reason why it is a classic.
engineers should get another book
Very Difficult

Differential Geometry of Curves and Surfaces
Manfredo Do Carmo
Manufacturer: Prentice Hall
ProductGroup: Book
Binding: Hardcover

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Similar Items:

Riemannian Geometry
Elementary Differential Geometry
A Comprehensive Introduction to Differential Geometry, Volume 1, 3rd Edition
Schaum's Outline of Differential Geometry (Schaum's)
Calculus on Manifolds: A Modern Approach to Classical Theorems of Advanced Calculus

ASIN: 0132125897

Customer Reviews:

Good book........2006-08-18

Most popular textbook on Differential geometry. Feynman once said the most popular one may not be the best, which is not completely true here. If you want another view of differential geometry, Su Buqing's Lectures on Differential Geometry is a great little book.

Best DG book out there.......2005-04-21

This book is rather expensive, but when compared to the other books available, it is not a waste of your money. It has plenty of exercises, many of them with answer or hints in the back of the book, and its exposition is broad, very clear and concise.

It is hard to tell being a math student, but I think anyone with a solid knowledge in multi-variable calculus (Apostol's book would be perfect) or, better yet, who has taken multi-variable analysis course would find this book accessible. One of the advantages of this book is that it is self-contained, so even though it uses, for example, the inverse function theorem (which is something unavoidable for a DG book), it has an appendix on differentiability and continuity which covers this.

The exercises range from easy to very hard, but because of the exposition and of the way the exercises are stated (the tougher ones are many times itemized so that they drive you to the answer) it is rare to find a problem that the reader will not be able to solve upon a little thinking.

The greatest advantage of this book is its clear and well-written exposition. It has very few errors, mostly typographical. It covers a lot of topics and its notation is extremely simple and suggestive, which, believe me, is of great help in a DG book. In short, if you want or have to learn differential geometry, save your time and get this book. As another reader very intelligently put it, there is a reason why this is a classic.

There is a reason why it is a classic........2005-04-03

Before talking about the book itself, let me tell you that I am a mathematician, and when I took a differential geometry course and used do Carmo's book, I already knew I wanted to be a mathematician. So, is this a book for mathematicians? Well, yes, but not exclusively. It is certainly written from a mathematician's point-of-view, and it assumes some maturity on the part of the reader. For instance, the exercises contain very little in the way of drill, and are used to enhance the theory (as pointed out by another reviewer). It seems to me that the author believes that mature readers can provide their own `drill' exercises. So, you won't find many exercises asking for you to find pricipal curvatures for this or that surface, and that other as well; exercises in this book have a theoretical flavor to them. This, of course, makes for some hard exercises, and I do remember spending a lot of time over them, often working together with other students taking the same course. The upside is that we learned the material, and thoroughly. Also, the author provided plenty, plenty of examples. The figures are very well drawn and really allow you to see what is going on - even though these days, with powerful computer packages like Maple, Mathematica, Matlab, and others, any student can provide his/her own pictures. But just because now we can use computers, I wouldn't say the text shows signs of age. It is jus as clear now in its exposition of topics and concepts as it was many years ago. So, even though there are many good alternatives in the market, if I had to teach a course now on this subject, or even better, if I were a student now taking this subject, I would certainly have this book at the top of my list of possible textbooks.

engineers should get another book.......2005-03-16

If you are a mathematician this book probably suits your purposes, BUT if you are an engineer (interested in shell structures for instance) I would recommend "Elementary Differential Geometry" by Pressley.
This book focuses on many sub-topics that are not of interest to an engineer and many of the exercises are abstract and of very little practical value. Also "Elementary Differential Geometry" focuses more on real 3-D shapes and their properties, and thus it is more readable.

Very Difficult.......2004-01-22

Although some claim it is classic, don't expect it to be readable. The book's definitions cna be quite confusing, and it is often difficult to understand many of the definitions or problems without a great deal of effort. If you are using this book for a class, I would reccomend getting a more readable text for reference.

Schaum's Outline of Differential Geometry (Schaum's)

Average customer rating:

Differential Geometry review
Good as a basic textbook and a source of solve problems
Differential Geometry - A Schaum's Outline Series

Schaum's Outline of Differential Geometry (Schaum's)
Martin M. Lipschutz
Manufacturer: McGraw-Hill
ProductGroup: Book
Binding: Paperback

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Schaum's Outline of Tensor Calculus (Schaum's)
Schaum's Outline of General Topology
Schaum's Outline of Vector Analysis
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Differential Geometry

ASIN: 0070379858

Book Description

Students will find all the information covered in the standard textbooks--and more--explained clearly and concisely in this powerful study tool. Unusually detailed, it elucidates all the most difficult-to-grasp concepts that class studies and texts sometimes gloss over. The hundreds of problems with fully explained solutions illuminate important points and teach students sound problem-solving skills. Ideal, also, for independent study.

Customer Reviews:

Differential Geometry review.......2007-01-04

I have found this to be an excellent addition to my library.

Good as a basic textbook and a source of solve problems.......2006-06-05

This book is intended to assist upper level undergraduate and graduate students in their understanding of differential geometry, which is the study of geometry using calculus. Usually students study differential geometry in reference to its use in relativity. I personally have a rather oddball application for the subject - modeling of curved geometry for computer graphics applications. The fundamental concepts are presented for curves and surfaces in three-dimensional Euclidean space to add to the intuitive nature of the material.
The book presumes very little in the way of background and thus starts out with the basic theory of vectors and vector calculus of a single variable in the first two chapters. The following three chapters discuss the concept and theory of curves in three dimensions including selected topics in the theory of contact.
Great care is given to the definition of a surface so that the reader has a firm foundation in preparation for further study in modern differential geometry. Thus, there is some background material in analysis and in point set topology in Euclidean spaces presented in chapters 6 and 7. The definition of a surface is detailed in chapter eight. Chapters 9 and 10 are devoted to the theory of the non-intrinsic geometry of a surface. This includes an introduction to tensor methods and selected topics in the global geometry of surfaces. The last chapter of the outline presents the basic theory of the intrinsic geometry of surfaces in three-dimensional Euclidean space.
Exercises are primarily in the form of proofs, and there are plenty of worked examples. Since the examples are kept to no more than three dimensions, the outline contains plenty of good instructive diagrams that illustrate key concepts. This Schaum's outline has quite a bit of instruction in it past the bare required minimum, but you might still want a good primary textbook. My personal favorite is Pressley's "Elementary Differential Geometry". Overall I find this to be a very good outline and source of solved problems on the subject and I highly recommend it.

Differential Geometry - A Schaum's Outline Series.......2000-06-25

As with all of the Schaum's Outline Series, this book is particularly useful if the readers intent is to gain a working knowledge of the subject. The subject of Differential Geometry is no exception. Dr. Lipschultz has done an excellent job of communicating the essential aspects of differential geometry to the reader. The book assumes a fairly low level of mathematical ability having calculus as the primary prerequisite. From this humble beginning, Dr. Lipschultz takes the reader through the necessary discussions of vector functions, curvature, fundamental forms, and tensor analysis. Given the theoretical nature of the subject, Dr. Lipschultz has included most of the theorems and associated proofs necessary for a general understanding of the subject. However, this book is not a substitute for a serious study of differential geometry. In addition most of the problems are limited to two dimensional surfaces and this reader would have enjoyed a more adventurous investigation of higher dimensional spaces. Like all Schaum's series, the text is chock full of problems and their solution. I recommend this book for anyone interested in quickly gaining a working knowledge of the subject.

Average customer rating:

Good reference maybe

Bezier and B-Spline Techniques
Hartmut Prautzsch , Wolfgang Boehm , and Marco Paluszny
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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Similar Items:

A Practical Guide to Splines
The NURBS Book (Monographs in Visual Communication)

Accessories:

Web Designer's Reference
Introduction to Scientific Visualization
Mobile 3D Graphics

ASIN: 3540437614

Book Description

This book provides a solid and uniform derivation of the various properties Bézier and B-spline representations have, and shows the beauty of the underlying rich mathematical structure. The book focuses on the core concepts of Computer Aided Geometric Design with the intension to give a clear and illustrative presentation of the basic principles, as well as a treatment of advanced material including multivariate splines, some subdivision techniques and constructions of free form surfaces with arbitrary smoothness.
The text is beautifully illustrated with many excellent figures to emphasize the geometric constructive approach of this book.

Customer Reviews:

Good reference maybe.......2006-08-09

I'm not sure what sort of person would find this book useful. If you want to LEARN about Bezier or B-Spline curves, then I don't think this book is for you. The authors' stated goal was to "provide a solid and uniform derivation" of Bezier and B-Spline properties. I believe that they have succeeded, almost every factoid I've seen in other books is included and proved rigorously. What is NOT included is any sort of meaningful explanation of the concepts. The material is presented at a breakneck pace, with everything presented exactly once, and most often in mathematical notation rather than in English. This is a good way to pack a lot of material into a few pages, but it makes for pretty difficult reading. I really don't see how a person could possibly follow the exposition in this book unless they basically already knew the material.

If you already are familiar with Bezier and B-Spline techniques, or perhaps you are an expert in a related field like approximation theory, then you might find this useful.

So if the Authors acheived their stated goal, then why only the 3-star rating? I've recently bought quite a few of these books on splines, in preperation to write a chapter in my own (introductory) 3d math book. Most of the material in this book can be found in other books. Of course, all of the books have significant overlap, since they are covering the same subject. But if you could have a book that covers most of the same material AND also has more exposition, I'd go for the one with the more exposition. I don't think there's enough unique material in this book to trade off the loss of the much more graceful exposition in the other books.

In particular, if you're interested in *learning* about Bezier curves or B-Splines, I found these two books much more accessible:

An Introduction to Splines for use Computer Graphics and Geometric Modeling by Bartels et al. has a much slower pace - paradoxially this means that if you're learning the material, you will be able to read it FASTER since you can maintain a constant pace. It focuses on B-Splines and only stops breifly to mention Bezier curves as a general case.

The other book is Curves and Surfaces for COmputer Aided Geometric Design by Farin. He introduces Bezier curves and fully develops them, at a reasonable pace, before discussing B-splines. I personally found this approach to be better from a teaching perspective, since B-Splines are more abstract and Bezier curves are easier to understand. (Be warned that I have a rather old editition, the 2nd, I believe he's on the 5th now. I don't know what all has changed since then.)

CRC Standard Curves and Surfaces with Mathematica, Second Edition (Chapman & Hall/Crc Applied Mathematics and Nonlinear Science)

Average customer rating:

A great updated book on expressing surfaces in Mathematica
A New Edition After 14 Years

CRC Standard Curves and Surfaces with Mathematica, Second Edition (Chapman & Hall/Crc Applied Mathematics and Nonlinear Science)
David H. von Seggern
Manufacturer: Chapman & Hall/CRC
ProductGroup: Book
Binding: Hardcover

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ASIN: 1584885998

Book Description

Since the publication of the first edition, Mathematica has matured considerably and the computing power of desktop computers has increased greatly. This enables the presentation of more complex curves and surfaces as well as the efficient computation of formerly prohibitive graphical plots. Incorporating both of these aspects, CRC Standard Curves and Surfaces with Mathematica, Second Edition is a virtual encyclopedia of curves and functions that depicts nearly all of the standard mathematical functions rendered using Mathematica. While the easy-to-use format remains unchanged from the previous edition, many chapters have been reorganized and better graphical representations of numerous curves and surfaces have been produced. An introductory chapter describes the basic properties of curves and surfaces, includes two handy tables of 2-D and 3-D curve and surface transformations, and provides a quick understanding of the basic nature of mathematical functions. To facilitate more efficient and more thorough use of the material, the whole gamut of curves and surfaces is divided into sixteen individual chapters. The accompanying CD-ROM includes Mathematica notebooks of code to construct plots of all the functions presented in the book. New to the Second Edition · Chapters on minimal surfaces and Green's functions that involve Poisson, wave, diffusion, and Helmholtz equations · Knots and links in the 3-D curves chapter · Archimedean solids, duals of Platonic solids, and stellated forms in the regular polyhedra chapter · Additional curves and surfaces in almost every chapter · Expanded index for quick access to curves or surfaces of interest and to find definitions of common mathematical terms · Upgraded Mathematica notebooks with more uniform formatting, more complete documentation on particular curves and surfaces, an explanation of the plotting algorithms, and more explicit designations of variable parameters to easily adjust curve or surface plots

Customer Reviews:

A great updated book on expressing surfaces in Mathematica.......2007-01-20

This book is a virtual encyclopedia of curves and functions, and depicts nearly all of the standard mathematical functions rendered using the software package Mathematica. Along with lots of examples, historical notes, and citations, this expanded second edition features four new chapters: Green's Functions, Regular Surfaces, Irregular and Miscellaneous Surfaces, and Minimal Surfaces. It includes coverage on Riemann's continuous but nowhere differentiable function. The book also updates the Mathematica code, called "notebooks," to the latest version (5.0), which allows much more detailed illustrations, and makes these notebooks available on an enclosed CD-ROM, usable on any platform, so that you can easily render and manipulate the functions presented in the book. The book does not provide a tutorial on Mathematica, nor does it delve deeply into the pure mathematics of it all, so you should already be familiar with both. Chapter one is the closest thing to a tutorial in the book. The rest of the chapters read more like a catalog. Highly recommended for anyone involved in scientific visualization who has access to Mathematica, which is a very expensive program. The following is the table of contents:

Chapter 1 - Introduction
1.1. Concept of a Curve
1.2. Concept of a Surface
1.3. Coordinate Systems
1.3.1. Cartesian Coordinates
1.3.2. Polar Coordinates
1.3.3. Cylindrical Coordinates
1.3.4. Spherical Coordinates
1.4. Qualitative Properties of Curves and Surfaces
1.4.1. Derivative
1.4.2. Symmetry
1.4.3. Extent
1.4.4. Asymptotes
1.4.5. Periodicity
1.4.6. Continuity
1.4.7. Singular Points
1.4.8. Critical Points
1.4.9. Zeroes
1.4.10. Integrability
1.4.11. Multiple Values
1.4.12. Curvature
1.5. Classification of Curves and Surfaces
1.5.1. Algebraic Curves
1.5.2. Transcendental Curves
1.5.3. Integral Curves
1.5.4. Piecewise Continuous Functions
1.5.5. Classification of Surfaces
1.6. Basic Curve and Surface Operations
1.6.1. Translation
1.6.2. Rotation
1.6.3. Linear Scaling
1.6.4. Reflection
1.6.5. Rotational Scaling
1.6.6. Radial Translation
1.6.7. Weighting
1.6.8. Nonlinear Scaling
1.6.9. Shear
1.6.10. Matrix Method for Transformation
1.7. Method of Presentation
1.7.1 Equations
1.7.2 Plots

Chapter 2 - Algebraic Functions
2.1 Functions with xn/m
2.2 Functions with xn and (a + bx)m
2.3 Functions with a2 + x2 and xm
2.4 Functions with a2 - x2 and xm
2.5 Functions with a3 + x3 and xm
2.6 Functions with a3 - x3 and xm
2.7 Functions with a4 + x4 and xm
2.8 Functions with a4 - x4 and xm
2.9 Functions with (a + bx)1/2 and xm
2.10 Functions with (a2 - x2)1/2 and xm
2.11 Functions with (x2 - a2)1/2 and xm
2.12 Functions with (a2 + x2)1/2 and xm
2.13 Miscellaneous Functions
2.14 Functions Expressible in Polar Coordinates
2.15 Functions Expressed Parametrically

Chapter 3 - Transcendental Functions
3.1 Functions with sinn(ax) and cosm(bx) (n,m integers)
3.2 Functions with 1 ± a sinn(cx) and 1 ± b cosm(cx)
3.3 Functions with a sinn(cx) + b cosm(cx)
3.4 Functions of More Complicated Arguments
3.5 Inverse Trigonometric Functions
3.6 Logarithmic Functions
3.7 Exponential Functions
3.8 Hyperbolic Functions
3.9 Inverse Hyperbolic Functions
3.10 Trigonometric and Exponential Functions Combined
3.11 Trigonometric Functions Combined with Powers of x
3.12 Logarithmic Functions Combined with Powers of x
3.13 Exponential Functions Combined with Powers of x
3.14 Hyperbolic Functions Combined with Powers of x
3.15 Combinations of Trigonometric Functions, Exponential Functions, and Powers of x
3.16 Miscellaneous Functions
3.17 Functions Expressible in Polar Coordinates
3.18 Functions Expressed Parametrically

Chapter 4 - Polynomial Sets
4.1 Orthogonal Polynomials
4.2 Non-orthogonal Polynomials

Chapter 5 - Special Functions in Mathematical Physics
5.1 Exponential and Related Integrals
5.2 Sine and Cosine Integrals
5.3 Gamma and Related Functions
5.4 Error Functions
5.5 Fresnel Integrals
5.6 Legendre Functions
5.7 Bessel Functions
5.8 Modified Bessel Functions
5.9 Kelvin Functions
5.10 Spherical Bessel Functions
5.11 Modified Spherical Bessel Functions
5.12 Airy Functions
5.13 Riemann Functions
5.14 Parabolic Cylinder Functions
5.15 Elliptic Integrals
5.16 Jacobi Elliptic Functions

Chapter 6 - Green's Functions
6.1 Green's Function for the Poisson Equation
6.2 Green's Function for the Wave Equation
6.3 Green's Function for the Diffusion Equation
6.4 Green's Function for the Helmholtz Equation
6.5 Miscellaneous Green's Functions
6.6 Harmonic Functions - Solutions to Laplace's Equation

Chapter 7 - Special Functions in Probability and Statistics
7.1 Discrete Probability Densities
7.2 Continuous Probability Densities
7.3 Sampling Distributions

Chapter 8 - Nondifferentiable and Discontinuous Functions
8.1 Functions with a Finite Number of Discontinuities
8.2 Functions with an Infinite Number of Discontinuities
8.3 Functions with a Finite Number of Discontinuities in First Derivative
8.4 Functions with an Infinite Number of Discontinuities in First Derivative

Chapter 9 - Random Processes
9.1 Elementary Random Processes
9.2 General Linear Processes
9.3 Integrated Processes
9.4 Fractal Processes
9.5 Poisson Processes

Chapter 10 - Polygons
10.1 Regular Polygons
10.2 Star Polygons
10.3 Irregular Triangles
10.4 Irregular Quadrilaterals
10.5 Polyiamonds
10.6 Polyominoes
10.7 Polyhexes
10.8 Miscellaneous Polygons

Chapter 11 - Three-Dimensional Curves
11.1 Helical Curves
11.2 Sine Waves in Three Dimensions
11.3 Miscellaneous 3-D Curves
11.4 Knots
11.5 Links

Chapter 12 - Algebraic Surfaces
12.1 Functions with ax + by
12.2 Functions with x2/a2 ± y2/b2
12.3 Functions with (x2/a2 + y2/b2 ± c2)1/2
12.4 Functions with x3/a3 ± y3/b3
12.5 Functions with x4/a4 ± y4/b4
12.6 Miscellaneous Functions
12.7 Miscellaneous Functions Expressed Parametrically

Chapter 13 - Transcendental Surfaces
13.1 Trigonometric Functions
13.2 Logarithmic Functions
13.3 Exponential Functions
13.4 Trigonometric and Exponential Functions Combined
13.5 Surface Spherical Harmonics

Chapter 14 - Complex Variable Surfaces
14.1 Algebraic Functions
14.2 Transcendental Functions

Chapter 15 - Minimal Surfaces
15.1 Elementary Minimal Surfaces
15.2 Complex Minimal Surfaces

Chapter 16 - Regular and Semi-Regular Solids with Edges
16.1 Platonic Solids
16.2 Archimedean Solids
16.3 Duals of Platonic Solids
16.4 Stellated (Star) Polyhedra

Chapter 17 - Irregular and Miscellaneous Solids
17.1 Irregular Polyhedra
17.2 Miscellaneous Closed Surfaces with Edges

A New Edition After 14 Years.......2007-01-18

In the 14 years since the previous edition of this book was published:

Mathematica has matured, expanded and improved tremendously The power of the desktop PC has increased many-fold in both processing speed and in memory capacity Several useful but complex curves and surfaces were deliberately left out of the earlier edition because of the first two points.

Taken together, this has almost required this offering of a new edition. Virtually every chapter has been re-written. Even the older curves and surfaces have been re-coded to take advantages of new capabilities within Mathematica. Several new chapters have been writteh to cover:

Green's functions
Minimal Surfaces
Knots and Links added to 3-D curves
the chapter on regular polyhedra has been greatly expanded.

The CD supplied with the books contains Mathematica notebooks of code to construct plots of all the functions presented in the book.

Average customer rating:

Dissapointing
(Most) College students will love this book
A quick introduction to differential geometry

Elementary Differential Geometry
Andrew Pressley
Manufacturer: Springer
ProductGroup: Book
Binding: Paperback

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Similar Items:

Schaum's Outline of Differential Geometry (Schaum's)
Differential Geometry of Curves and Surfaces
Differential Geometry
Essential Topology (Springer Undergraduate Mathematics Series)
A Geometric Approach to Differential Forms

Accessories:

Metric Structures for Riemannian and Non-Riemannian Spaces (Modern Birkhäuser Classics)
Riemannian Geometry (Graduate Texts in Mathematics)

ASIN: 1852331526

Book Description

Curves and surfaces are objects that everyone can see, and many of the questions that can be asked about them are natural and easily understood. Differential geometry is concerned with the precise mathematical formulation of some of these questions, and with trying to answer them using calculus techniques. It is a subject that contains some of the most beautiful and profound results in mathematics, yet many of them are accessible to higher level undergraduates.
Elementary Differential Geometry presents the main results in the differential geometry of curves and surfaces while keeping the prerequisites to an absolute minimum. Nothing more than first courses in linear algebra and multivariate calculus are required, and the most direct and straightforward approach is used at all times. Numerous diagrams illustrate both the ideas in the text and the examples of curves and surfaces discussed there.

Customer Reviews:

Dissapointing.......2007-06-20

The book starts ok, but very quickly deteriorates into the classical boring math style of theorem-proof. There are a million books on the subject matter, and I don't see the need of another one which is pretty much identical. It is not a bad book, but has absolutely no added value - just pick any of the differential geometry books out there, and they will be the exact same thing. Why do they bother writing the same book over and over??

(Most) College students will love this book.......2002-11-16

I am using this book for a 2 semester Differential Geometry course at my university. The school used to use Do Carmo, but apparently the book was too advanced for the undergraduate level, so this semester they decided to switch over to give this one a test and see how it worked out. This book is not bad. It is basically Do Carmo rehashed for the not so mathematically mature. In all seriousness, the book even follows almost the exact same flow as Do Carmo, the topics are just presented with less rigor. The exercises are rather tedious at the end of each chapter, and in my opinion they don't really help to enhance the subject matter.

On the other hand, if you fall in the category that most of the math majors at my university fall in (i.e. the category of people who really don't care, they just want to get an A and graduate, and don't care about mathematics), then you'll love this book. Why? Because the solution to every single problem is at the end of the book. In my opinion this is a huge flaw. It would be great if everyone were honest and everybody was genuinely interested in the learning Differential Geometry, but that isn't the case. So 90% of my class simply copies the answers out of the back of the book and hands it in to get a 100 on the homework assignments. Pretty sad if you ask me. The book is almost there. Without full solutions to every problem, this book would get 5 stars. But those students who simply turn to the back of the book 15 seconds after looking at the problem statement will learn nothing from this book, so I have to knock it down 2 stars. After all, what good is a book if it doesn't serve it's intended purpose. Perhaps some people would rate a book by "how easy is it to get an A in the class if this is the textbook", in which case they would probably rate this book 5 stars.

Differential Geometry is a hard subject. It's _supposed_ to be hard. We're not talking about taking the reciprocal of a fraction here, it's Differential Geometry. You're _supposed_ to think about these problems for a long time. So if you're a professor considering this book for a course I would recommend against it. The text is good, but the students won't learn anything from it. I've suggested to my professor that perhaps it would be good to not assign problems from the text, but rather get problems from other textbooks where students can't look at the answers.

In my opinion that is the only flaw with this book. Otherwise I think it's a great introduction, and about as elementary as you can really make the subject. If another book was too hard, then this is the one for you.

Also, if you're interested in this book for self study it's a good choice since obviously you're genuinely interested in the subject matter and won't be tempted to look at the answer at the first opportunity.

A quick introduction to differential geometry.......2001-10-27

Pressley's gives you a very comprehensible and down to earth introduction to differential geometry.
By avoiding the more modern and abstract generalizations of differential geometry to more than three dimensions you really feel that you grasp what the theorems and methods are about. In this way you are able to work your way quickly through the book and avoid getting stuck and loosing interest. Another plus is that the book contains lots of examples and fully worked answers to all exercises, which makes it perfect for self-study.
The downside is that the book is not as exhuastive as you perhaps would like, when you have looked at books like O'Neills and DoCarmos ... on the other hand, you only need to spend a fraction of the time to get through Pressleys.
I definitely think that this is a much better book that Struiks classical work (by being more structured and goal oriented) and an excellent introduction to further studies in differential and Riemann geometry.

Differential Geometry: Curves - Surfaces - Manifolds, Second Edition

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Fast moving
A excellent introduction for the 21st century
A beautiful geometry
Attractive book on differential geometry

Differential Geometry: Curves - Surfaces - Manifolds, Second Edition
Wolfgang Kuhnel
Manufacturer: American Mathematical Society
ProductGroup: Book
Binding: Paperback

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A Geometric Approach to Differential Forms
Lie Groups, Lie Algebras, and Some of Their Applications
Riemannian Geometry
Introduction to Lie Algebras (Springer Undergraduate Mathematics Series)
Differential Topology: First Steps

ASIN: 0821839888

Product Description

Our first knowledge of differential geometry usually comes from the study of the curves and surfaces in $I\!\!R^3$ that arise in calculus. Here we learn about line and surface integrals, divergence and curl, and the various forms of Stokes' Theorem. If we are fortunate, we may encounter curvature and such things as the Serret-Frenet formulas. With just the basic tools from multivariable calculus, plus a little knowledge of linear algebra, it is possible to begin a much richer and rewarding study of differential geometry, which is what is presented in this book. It starts with an introduction to the classical differential geometry of curves and surfaces in Euclidean space, then leads to an introduction to the Riemannian geometry of more general manifolds, including a look at Einstein spaces. An important bridge from the low-dimensional theory to the general case is provided by a chapter on the intrinsic geometry of surfaces. The first half of the book, covering the geometry of curves and surfaces, would be suitable for a one-semester undergraduate course. The local and global theories of curves and surfaces are presented, including detailed discussions of surfaces of rotation, ruled surfaces, and minimal surfaces. The second half of the book, which could be used for a more advanced course, begins with an introduction to differentiable manifolds, Riemannian structures, and the curvature tensor. Two special topics are treated in detail: spaces of constant curvature and Einstein spaces. The main goal of the book is to get started in a fairly elementary way, then to guide the reader toward more sophisticated concepts and more advanced topics. There are many examples and exercises to help along the way. Numerous figures help the reader visualize key concepts and examples, especially in lower dimensions. For the second edition, a number of errors were corrected and some text and a number of figures have been added.

Customer Reviews:

Fast moving.......2006-11-25

This is a very fast moving book, covering a huge amount of material at a fairly sophisticated level in under 380 pages. For example, differential forms are introduced in about 2 pages so that the Maurer-Cartan structural equations can be defined. The first 4 chapters makes up a very concise course in curves and surfaces, while the last 4 chapters cover Riemannian geometry. In comparison, do Carmo's two books take 500 pages for the former and 320 pages for the latter.

For this reason I think the claim that this could be used as an undergraduate text is overly optimistic. For that I would use a more self-contained text like Millman & Parker (ISBN: 0132641437). But it would make an excellent text for a graduate survey, or as a second text for someone wanting to make the transition from classical theory (learned from, say, one of the Dover books like Struik, ISBN: 0486656098) to more modern methods. Also, you'll probably want to supplement with a gentler introduction to differential forms.

Of interest to students of physics, the book covers curves and surfaces in Minkowski space, as well as Einstein spaces.

A excellent introduction for the 21st century.......2006-03-23

While there is exist many classic texts on differential geometry, I have particularly appreciated this book for its up-to-date treatment, numerous well-done figures, broad coverage, elegant type-setting, and clear expositions. The book covers all the basics expected from an introduction to differential geometry, including curves and 2-D surfaces, but with a look towards the more advanced material in the second half of the book. It alternates between Ricci style notation and Koszul style notation, often carefully explaining the relation between the two and giving examples (I found this particularly helpful). There are, however, some sections where the english is a bit rough (perhaps the fault of the translator). It is also quite brisk throughout, often mentioning advanced topics before they are treated in detail. For example, it already mentions submanifolds, tangent spaces, and tangent bundles in the first chapter on "Notations and Prerequisites from Analysis." It will require serious attention, especially if one has not encountered a good dose of abstract mathematics before. Nonetheless, I have found myself returning to it over several years as an excellent reference and source of many additional topics that I skipped on a first reading. For example, the final chapter on Einstein spaces is a valuable, though demanding, bonus. Thanks to the AMS for publishing a fine edition of a top-notch German author's work.

A beautiful geometry.......2005-10-12

This book is very useful for students who are interested in geometry. The book is organized from elementary facts to advanced geometry very well. This book provides to students the reason why they study the geometry. This book explains very easily that the geometry of curves and surfaces can be generalized to high dimensional Riemannian manifolds naturally.
Moreover, the edition of this book is very beautiful and helpful for readers. For example, the important results are placed in boxes.

Attractive book on differential geometry.......2003-09-22

Differential geomety is perhaps the most beautiful part of higher mathematics. It combines geometry, analysis and intuition in a wonderful way. This attractive book is a concise and modern book that manages to be both pedagogical and accurate in a pleasant way. In only 350 pages most of the differential geometry that a non-expert will ever need is outlined. Illustrations and notation seem optimal for their purpose. The book is a worthy successor of classics like Struik, Stoker, and Kreyzig.

Curves and Surfaces (Graduate Studies in Mathematics)

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Curves and Surfaces (Graduate Studies in Mathematics)
Antonio Ros
Manufacturer: American Mathematical Society, Real Sociedad Matem\'{a}tica Espa\~{n}ola (RSME)
ProductGroup: Book
Binding: Hardcover

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Similar Items:

A Course in Differential Geometry (Graduate Studies in Mathematics)

ASIN: 0821838156

Book Description

This introductory textbook puts forth a clear and focused point of view on the differential geometry of curves and surfaces, emphasizing the global aspects. The excellent collection of examples and exercises (with hints) will help students in learning the material. Advanced undergraduates and graduate students will find this a nice entry point to differential geometry.

In order to study the global properties of curves and surfaces, it is necessary to have more sophisticated tools than are usually found in textbooks on the topic. In particular, students must have a firm grasp on certain topological theories. Indeed, this monograph treats the Gauss-Bonnet theorem and discusses the Euler characteristic. The authors also cover Alexandrov's theorem on embedded compact surfaces in $\mathbb{R}^3$ with constant mean curvature. The last chapter addresses the global geometry of curves, including periodic space curves and the four-vertices theorem for plane curves that are not necessarily convex.

This volume is suitable for advanced undergraduates, graduate students, and researchers interested in the differential geometry of curves and surfaces. It can also be used as an introduction to a more general study of differential geometry.

Product Description

In this book, Miranda takes the approach that algebraic curves are best encountered for the first time over the complex numbers, where the reader's classical intuition about surfaces, integration, and other concepts can be brought into play. Therefore, many examples of algebraic curves are presented in the first chapters. In this way, the book begins as a primer on Riemann surfaces, with complex charts and meromorphic functions taking center stage. But the main examples come from projective curves, and slowly but surely the text moves toward the algebraic category. Proofs of the Riemann-Roch and Serre Duality Theorems are presented in an algebraic manner, via an adaptation of the adelic proof, expressed completely in terms of solving a Mittag-Leffler problem. Sheaves and cohomology are introduced as a unifying device in the latter chapters, so that their utility and naturalness are immediately obvious. Requiring a background of a one semester of complex variable! theory and a year of abstract algebra, this is an excellent graduate textbook for a second-semester course in complex variables or a year-long course in algebraic geometry.

Customer Reviews:

An excellent Introduction.......2005-09-03

This book gives a very readable account of Riemann Surfaces-- a good course in Complex Analysis is all that's required as a prereq. The proofs are very clear, the material is presented beautifully, and (most of) the exercises are fairly straight forward and supplement the book very well. The notion of divisors, proof of the Riemann Roch theorem and Abel's theorem are explained very nicely. It serves as the perfect transition into more advanced books in algebraic geometry and on complex manifolds.

An incredible book for any mathematician !! .......2004-08-23

If you want to learn the basic properties of compact Riemann surfaces this is the book to read. If you want to know the "motivations" of modern Algebraic geometry this is again a book to read.

First of all the pace and the style are very casual. You really don't feel overwhelm by a mountain of definitions. The author always favor simplicity and concreteness instead of abstractions and generality. This is really a book that I should have read before taking a class on Schemes. For exemple in the context of Riemann surfaces an "very ample divisor" is simply a linear system without fixed base point that gives rise to an holomorphic embedding. This definition (at least for me) is much much more satisfactory and illuminating than the definition of a very ample sheaf that you can find in Hartshorne (even though his definition is much more general).

There is a very nice chapter on meromorphic differentials which explains how those object can be used to define line integral on any riemann surface. Topics like divisors, Riemann-Roch and curves are treated with a lot of depth. There are not a lot of pictures but having pictures supported by an unclear text is quite useless. Here the writing is so clear (not to say flawless) that on the first reading you really get the idea of what's going on.
There are very few mistakes in this book which is another reason why I like it. I'm really pissed off by those mathematicians
that are rushing to publish their books crowded by mistakes.
But don't get me wrong, I don't have anything against mathematicians that are writing books (this is a learning experience) but don't feel force to publish them unless they are very polished and "innovative".

Finally the last chapters treat of Abel's theorem ( which tells us exactly when a divisor is principal), Sheaves, Cech cohomologies and line bundles. Again the exposition is very well
motivated with a good supply of interesting exemples.

This is the best book that I read on subject and honestly if professor Miranda is writing another book related to my field of research you can be sure that I will have it my collection.

Hugo Chapdelaine,
McGill

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