Book Description

Mission Geometry; Orbit and Constellation Design and Management (OCDM) provides greatly expanded detail on many topics first introduced in the 2 of the earlier Wertz works - Spacecraft Attitude Determination and Control (SADC) and Space Mission Analysis and Design (SMAD).

If these two books got you started in mission engineering and you need more detail on the key area of Spacecraft Orbit and Attitude Systems (SOAS), then this book provides more detail in SOAS requirements definition, mission geometry, orbit and constellation design, relative motion of satellites, observation and measurement systems engineering, orbit control and management, and similar topics. ... Read more

Reviews (2)

The man was a complete loon, but in a good way.
The previous review is amazingly perceptive into Bill Burke's personality and thinking. He was not the most discplined writer or lecturer, (I had no less than 4 courses from him) but his insight and intuition could be amazing. I would recommend this book as a companion to something more traditional. If you are interested in General Relativity, which is what the book was suppose to be a precursor for, get Schutz or Misner, Thorne and Wheeler, or Wald.

Also, if you do want this book, get the errata from Burke's webpage,...is quite helpful.

I would also hearitly recommend Burke's best book: Geometry, Spacetime and Cosmology which is out of print. It is much physical and the examples are clearer. He taught english majors and theater students general relativity with that book.

It's a lot of work but I like it.
I'm not a physicist or mathematician but I play one on TV. So I am more qualified to review a book on differntial geometry than either of the above professionals. This book is a very good introduction to all the hairy squibbles that theoretical physicists are writing down these days. In particular if you are perplexed by the grand unification gang then this book will help you understand the jargon. However, having only had physics when advanced vector calculus was enough to get by, it is a bit hard going due to the frequent errors and glosses the author makes. Burke gives a very hip and entertaining introduction to some of the most beautiful ideas in physics. It is enjoyable to read if you like sinking your teeth into something more rewarding than Ann Rice. I gave it a six rating because the errors and glosses are so annoying. I suspect Burke's puckishness is responsible; the book has no actual problem sets but he does work out problems that don't always work out. So the reader really has to work at understanding by correcting the possibly(?) intentional errors. Very sly of him. I am on my second reading and suspect that several readings down the line I will probably get the message. The book deserves loving attention. ... Read more

Book Description

This book develops the differential geometrical and topological points of view in hydrodynamics. It discusses interactions of hydrodynamics with a wide variety of mathematical domains such as theory of lie groups, differential geometry, topology of knots, magnetic dynamo theory, calculus of variations and hamiltonian mechanics. The exposition contains extensive examples and figures, proofs of the main results, a survey of the recent achievements in (magneto)hydrodynamics and applications to hydrodynamic stability, dynamo theory and weather prediction. Topological methods in Hydrodynamics is the first monograph to treat topological, group-theoretic, and geometric problems of ideal hydrodynamics and magnetohydrodynamics from a unified point of view. The contents are accessible to graduate students as well as to both pure and applied mathematicians working in the fields of hydrodynamics, Lie groups, dynamical systems and differential geometry. ... Read more

Book Description

"Trudeau meets the challenge of reaching a broad audience in clever ways...(The book) is a good addition to our literature on non-Euclidean geometry and it is recommended for the undergraduate library." -CHOICE, February 1988"...the author, in this remarkable book, describes in an incomparable way the fascinating path taken by the geometry of the plane in its historical evolution from antiquity up to the discovery of non-Euclidean geometry. This 'non-Euclidean revolution', in all its aspects, is described very strikingly here...Many illustrations and some amusing sketches complement the very vividly written text." -MATHEMATICAL REVIEWS How unque and definitive is Euclidean geometry in describing the "real" space in which we live?Richard Trudeau confronts the fundamental question of truth and its representation through mathematical models in 'The Non-Euclidean Revolution.' First, the author analyzes geometry in its historical and philosophical setting; second, he examines a revolution every bit as significant as the Copernican revolution in astronomy and the Darwinian revolution in biology; third, on the most speculative level, he questions the possibility of absolute knowledge in the world.Trudeau writes in a lively, entertaining, and highly accessible style. His book provides one of the most stimulating and personal presentations of a struggle with the nature of truth in mathematics and the physical world.A portion of the book won the Pólya Prize, a distinguished award from the Mathematical Association of America. ... Read more

Reviews (1)

A nicely designed book, with accepted views of the subject
As indicated in my other reviews, my views of the subject differ from accepted ones, and I will try to explain them further in relation to this book.

The book assumes a somewhat condescending attitude, with imaginary dialogues between the author and presumably a student, possibly from the author's experience. The student asks supposedly "common sense" questions, and the author answers with lengthy explanations, sounding to me like excuses that make the teacher come out the loser.

Thus in a section about "points" (pp.23-30) the author defends the current concept of lines as composed of points, although a point is taken to have zero dimension, and zeros plus zeros are understood to add up to zero. The concept of points as the constituents of lines is indeed recent and questionable. The author like others overlooks Euclid's definition 3, "The extremities of a line are points", and points are in fact used to delimit lines, as do "breadthless" lines delimit areas, either usage not adding to dimension.

Another dialogue discusses "line" (p.170), which has caused similar confusion. Today the word is used for "straight line", while contrariwise the term is also applied to curves like great circles on a sphere. But the sticking point to me is the way it is justified to leave "primitive terms" undefined and then "interpret" them as desired (e.g. p.169).

The justification is roughly as follows. Basic logical principles are so general that one needn't specify what they are about, and then can apply them to particular cases. This is indeed true if a principle holds for anything whatsoever. But, for instance, Euclid's 5th postulate applies specifically to straight lines in a plane, which is why to reinterpret those terms as curvatures, and say the postulate then does not apply and is hence unprovable, commits the fallacy of equivocation.

What is disappointing is that undoubtedly good heads so carelessly perpetuate illogicalities while laying claim to increased rigor.
... Read more

Reviews (13)

Superb plane geometry primer for children's self-study
Easy to follow, logical, and methodical exposition of elementary classical plane geometry. Every term and concept is defined; therefore, it presupposes absolutely no prior knowledge (of either geometry or algebra). Yet, after four chapters it is possible for a child to knowledgeably explain Euclid's Fifth Postulate. The beauty of forms and patterns, the triumph of solving seemingly insoluble problems, the revelation of the power of logical thinking -- all serve to captivate my 9 year old daughter's attention. Most highly recommended for anyone who wishes to provide the means for a child to do his/her best original thinking. No cartoons, no shoot-em-up diversions, only the austere beaty of logic in an assimilable format for children. Every child in America should have the opportunity to go through this book with his/her parents. And every parent should have the oportunity of direct participation in the intellectual voyage of discovery of his/her child that this book affords.

Simplifies the subject beautifully.
Terrific tool for students of any age. My rising 9th grader is entering an advanced program which requires her to learn most of the basic theorems and postulates on her own over the summer. This book has worked beautifully for her. Even if you have one of those "I hate it if I don't understand it immediately" kind of kids, this book will work for them. I am recommending this to all of my friends with children about to take Geometry.

Geometry made easy and understandable!
This is an amazing book! It helped me personally. I had a 70 in my Geometry class (which was strange for me being a strait A student) and was studying for a quiz when my friend said i should check out her book and do some of the practice problems. The book explained the concepts in a new way and i could check my answers! I took the math quiz and got a 100%! Now im steadily on my way to become the strait A student i used to be! If you have trouble understanding geometry, or just want some back up help, then BUY THIS BOOK!

Great Geometry Tool
I am teaching myself advanced math. I read the entire book, cover to cover, and did each problem in the book. I found it extrememly useful, and I now feel I have a very good grasp on geometry. There are some minor flaws, as already explained in other reviews, but overall, I would highly recommend this book.

It's not a just easy way. It's an ultimate way !!
This book is great! You may become a master of lines, points, angles, circles, triangles, polygons ... by reading this book from the first page to the last page sequentially.
The book contains some typos but those are not major errors.
Solid geometry part is somewhat disappointing but everything else is great !
I want to add one more property of proportions, if a/b=c/d then
(a+c)/(b+d)=a/b=c/d. ... Read more

Book Description

In the past decade the systematic study of geometric algorithms has evolved to form the very active field of research known as computational geometry. Computational Geometry: An Introduction presents a comprehensive, systematic, and coherent treatment of its subject.

A fundamental task of computational geometry is identifying condepts, properties, and techniques which aid efficient algorithmic implementations from geometric problems. The approach taken here is the presentation of algorithms and the evaluation of their worst-case complexity. The particular classes of problems addressed include geometric searching and retrieval, convex hull construction and related problems, proximity, intersection, and the geometry of rectangles.

Computational Geometry: An Introduction presents its methodology through detailed case studies. The book, primarily conceived as an early graduate text, should also be essential to researchers and professionals in the fields of computer-aided design, computer graphics and robotics. ... Read more

Reviews (5)

This book is history
This book is a classic, in fact the author's PhD thesis created this field, but this book is too old for any meaningful graduate work. There are new bounds and algorithms on almost all topics, which makes this a somewhat undesirable book. Also, this book has failed to keep me interested in it, while I am reading it...

Very useful for code development. Very clear and readable.
The ideas and algorithms presented in this book are clear enough for straight implementation in code. I have long experience in developing comercial and production software for VLSI layout applications, which made extensive use of the algorithms presented in this book.
I also use some chapters of this book as a part of a graduate course in VLSI layout algorithms being tought at the Technion, Israel. The contents of this book is well understood by EE and CS students.
I personally love this book, which introduced me into the area of computational geometry and its applications.

Useful but thick
Most of the papers that I've read on computational geometry refer to this text -- and for good reason. There's many good algorithms to be found here.

The book only gets 4 stars because it's hard to read. It took me several tries to pick up the ideas in this text. I think the De Berg text is MUCH easier to read.

The book is also getting a little dated. Some of the topics have come a long way since the 80's.

This book seems to be in most University libraries if you have that option.

Still interesting after so many years ...
I have just happened to exhume this book from my library, after it spent some years gathering dust above the shelf. In spite of the long time I have not being reading it, it still retains the full meaning it showed me when I was using in calculations relating radar domain definition. May be the textbook wins by far the comparison to the current vague and inflated computer publications, may be it is not a manager-oriented issue but it is for nearly specialistic use, you find in it clearly stated, and straight, answers to the questions you meet, or at least a definite reference where a more detailed explanation can be find. It presents interesting problems, and explains you how to solve them. I think it is the best you can say about a computer science book.

A very good book, but difficult to understand !
The book is comprehensive in computational geometry, and is suitable for research. But really difficult to understand. A student is difficult to read it without teacher's teaching. But people who research in computational geometry need the book. ... Read more

Book Description

As Chaos explained the science of disorder, Nexus reveals the new science of connection and the odd logic of six degrees of separation. How can geometry explain the puzzles of human behavior? In this incisive, insightful work Mark Buchanan presents the fundamental principles of the emerging field of "small worlds" theory—the idea that a hidden pattern is the key to how networks interact and exchange information, whether that network is the information highway or the firing of neurons in the brain. Mathematicians, physicists, computer scientists, and social scientists are working to decipher this complex organizational system, for it may yield a blueprint of dynamic interactions within our physical as well as social worlds. Highlighting groundbreaking research behind network theory, Buchanan documents mounting support for the small-worlds idea and demonstrates its multiple applications to diverse problems—whether explaining the volatile global economy or the Human Genome Project, the spread of infectious disease or ecological damage. Nexus is an exciting introduction to the hidden geometry that weaves our lives so inextricably together. 20 illustrations. ... Read more

Reviews (21)

Terrific snapshot of a hot new field!
I wasn't sure I would like this book when my brother bought it for me -- but I did! It covers a truly wide range of material. Extremely impressive. Amazingly, as the book shows, strong mathematical links seem to connect the workings of biological cells with the Internet, social networks and many other complex networks, even neural networks and the human brain. The writing is extremely clear and there is little chance of misunderstanding. This is one of those areas of "hyped" research that really lives up to the hype.

From a personal point of view, I especially enjoyed the final chapters on economics and social capital. Something really seems to be emerging here -- a deep link between social patterns and natural patterns in the physical world

Six Degrees of seperation.
Actually, I bought this book with the intention of reading about genetics algorithms although I was pleasantly surprised with the out come of the book.

The book is about how our large world is small and what seems chaotic is actually an organized small network.

The author starts with how networks in nature relate to networks in technology. A very strong case for "6 degrees of separation" for our society and "19 degrees of (link) separation" for the Internet. The rest of the book explains with historical examples how scientists were able to prove the networking concepts through human decision and thought process.

I gave this book 4 star because I did not think that the conclusion had the continuity of the other chapters. I would recommend this book to all individuals who would be interested in reading and understanding the connections and influences of nature in our "connected" world.

Have fun understanding that you closer then you think to the person next door.

Good introduction to a broad subject
The author makes a strong case that many diverse phenomena can be modelled in very similar ways. This book can be summarized as a very brief introduction to network models, followed by numerous examples from the real world.

The level of mathematical sophistication needed to comprehend the matterial is minimal. I do not believe there are any equations in the entire book. There are many easily understood graphs and a few percentages.

The basic concept of the networks is very easy to explain and to understand. The applications are the interesting part. Thoughout the pages are clear and interesting examples that make you want to turn the page to see what is coming next. In my case I often found myself thinking how I would have approached the problem and more importantly what problems could this have been applied to. Any book that can do that is a good one in my book!

Like many good books, this one leaves more questions unanswered than it answers. The subject area is a generic one that allows it's self to be applied in many many different fields. The question becomes not is this model of the world valid but rather how can it be applied.

This was a quick read, certain to change my views on how the world works.

It's a small world after all.
I just finished reading Nexus right after I finished Steven Johnson's book, Emergence. Both are great, quick reads. The ideas are fascinating and build upon chaos theory that James Gleick gives a history of in Chaos, which is the last book I read that addressed topics such as complexity. It's a great thrill to receive journalistic reports on what has happened in the small-worlds theory and gaining a cursory understanding of its current and future applications. I also just started reading Harold Morowitz's The Emergence of Everything, which is interesting in its subject matter while the writing is much more austere than in Emergence and Nexus. I look forward to reading everything I can on the small-worlds, complexity theory-type popular science books.

Networks of sex partners and the Net-Are they really related
The surprising answer is yes. I picked this book up after reading Steven Strogatz's Sync which mentions a great deal about the science of networks. Buchanan explains how networks exist everywhere - the net, the web, the power grid, our circle of friends, our sex partners - and that they are in fact very similar to one another.

The phrase "six degrees of separation" comes from the fact that two randomly chosen people, A and B, will on average be connected by six social links. A knows C who knows D who knows E who knows F who knows G who finally knows B. Considering the world has over 6 billion people, an average separation of 6 seems unbelievable small, but the explanation of this incredible phenomenon lies in the makeup of our social network. Our close friends know each other but our cluster of friends has weak ties to other clusters through acquaintances, people we really don't know that well - that's why when one is looking for a job, it's better to tell an acquaintance rather than a friend so that our inquiry can jump to other clusters. Our social network is essentially highly clustered but enough links exist between these clusters to allow us to jump from ourselves to any other person through just an average of six links. Buchanan shows us how this kind of network exists everywhere as mentioned above although he distinguishes between egalitarian networks where clusters are roughly the same size and aristocratic networks such as the WWW where gigantic hubs like Amazon.com exist that link to millions of websites.

One of the most interesting chapters in the book deals with sexual networks. It turns out that in the network of sex partners, certain people have a great many more links than the average person in the network. Buchanan explains how the structure of the sexual network actually accounts for the rapid spread of HIV. The virus spread quickly because the hubs in the network spread it to their numerous partners. In fact, it turns out that a significant percentage of the inital HIV cases had a sexual relationship with one particular flight attendant.

As I wrote in my review for Strogatz's Sync, we are entering an era of science where disparate fields of study are being linked because many phenomena that we used to regard as unrelated now appear to have very similar underlying bases. It is exciting to read books like Nexus because it illustrates this point. You should definitely read this book if your are interested in the science of networks and want to know how so many different phenomena are being explained by the same underlying principles. ... Read more

Book Description

An undergraduate introduction to the fundamentals of topology — engagingly written, filled with helpful insights, complete with many stimulating and imaginative exercises to help students develop a solid grasp of the subject.
... Read more

Reviews (4)

Good Introduction to Metric Spaces and Topology
I was not a mathematics major, and only in recent years have I ventured into abstract mathematics. I was motivated to learn about topology as an aid to understanding a particular 3-D earth modeling application.

I read Introduction to Topology in three stages: as a review of set theory and metric spaces (chapters 1 and 2), then as an introduction to topology (chapter 3), and lastly as a detailed look at two important topological properties, connectedness (chapter 4) and compactness (chapter 5). I had previously read (and reviewed) another book titled Metric Spaces by Victor Bryant, but Mendelson's book was my first serious look at topology.

My reading of Mendelson's 200-page text required about 100 hours, substantially longer than the 40 to 60 hours estimated by an earlier reviewer. No solutions are provided for the section problems, which are generally of the form 'Prove that '.'.

The first chapter provides a concise overview of set theory and functions that is essential for Mendelson's subsequent set-theoretic analysis of metric spaces and topology.

The second chapter is a solid introduction to metric spaces with good discussions on continuity, open balls and neighborhoods, limits from a metric space perspective, open sets and closed sets, subspaces, and equivalence of metric spaces. Chapter 2 concludes with a brief introduction to Hilbert space in a section titled 'an infinite dimensional Euclidian space'.

The third chapter introduces topological spaces as a generalization of metric spaces, and many theorems are largely restatements of the metric space theorems derived in chapter 2. I was thankful for this approach.

Mendelson begins chapter 3 by demonstrating that 1) open sets and neighborhoods are preserved in passing from a metric space to its associated topological space and 2) the existence of a one to one correspondence between the collection of all topological spaces and the collection of all neighborhood spaces.

He then reminds us that in a metric space we can say that there are points of a subset A arbitrarily close to a point x if the metric d(x, A) = 0. In characterizing this notion of 'arbitrary closeness' in a topological space, Mendelson introduces the closure of A, the interior of A, and the boundary of A. Other topics included topological functions, continuity, homeomorphism (the equivalence relation), subspaces, and relative topology. The final sections in chapter 3 on products of topological spaces, identification topologies, and categories and functors were more difficult.

In chapter 4 the initial sections (connectedness on the real line, the intermediate value theorem, and fixed point theorems) were largely familiar. But thereafter I became bogged down with the discussions of path-connected topological spaces, especially with the longer proofs involving the concepts of homotopic paths, the fundamental group, and simple connectedness.

Chapter 5, titled Compactness, was even more abstract and difficult, with topics like coverings, finite coverings, subcoverings, compactness, compactness on the real line, products of compact spaces, compact metric spaces, the Lebesgue number, the Bolzano-Weierstrass property, and countability. I will definitely need to look at another text or two before I can handle more advanced topics.

I suspect that a reader familiar with analysis would have substantially less difficulty with the last two chapters.

In summary, Introduction to Topology quite useful for self-study. Mendelson's short text was intended for a one-semester undergraduate course, and it is thereby ideal for readers that either require a basic introduction to topology, or need a quick review of material previously studied. The last two chapters on connectedness and compactness are substantially more difficult, but are still accessible to the persistent reader.

Ideal for self-study
This book is ideal for self-study. If you have not had the luxury of taking a topology course during your undergraduate studies, but you need to know some topology and you have to study it by yourself, this is the book you need. It is very readable and it explains carefully every concept. However, it is just an introductory text and it contains only basic material. You don't have to invest a lot of time to study the material in this book: let's say 40-60 hours of study are enough to grasp everything. I reccomend it especially to those graduate students of applied mathematics, finance, statistics or economics, who need to use some basic result from topology in their work.

The best introduction to point-set topology
since, for some reason, my school didn't offer any topology course, I decided to study topology on my own. It was very fortunate that I found this book in the library. That was right after I took my first analysis course. But I could understand most of the book at that time. After reviewing basic set theory, the author discussed metric spaces, and then he motivates the definition of topological spaces. This is great, I think, becuase many of introductory topology books often give the definition of topological spaces with any motivation. However it is very important to motivate each concept in mathematics especially in introductory level. And this book does this. And as I did, this book is even good for indivisual study. However, you can get almost no geometricl flavor of topology from this book. For example, there is only one section in one chapter in which the author discusses the fumdamental group. Thus, after all this is the best introduction to "point-set topology". So if you don't know almost anything about topolosy, I strongly recommend this book. And one more thing. If you are still wondering if you should buy this one, just look at the price!

A great book, especially for the price
I know that some people don't like Dover, but I think Dover is great, and Mendelson's Introduction of Topology is an example of why.

Although the book is very short (around 150 pages), it covers the basics of topology very thoroughly and should prepare the reader for the considerably more abstruse Spanier's Algebraic Topology or other texts of such ilk.

If you are a recreational topologist, or are simply tryinging to figure out which way is up in your first topology course, this is for you. ... Read more

Book Description

This is a reissue of Professor Coxeter's classic text on non-Euclidean geometry. It begins with a historical introductory chapter, and then devotes three chapters to surveying real projective geometry, and three to elliptic geometry. After this the Euclidean and hyperbolic geometries are built up axiomatically as special cases of a more general 'descriptive geometry'. This is essential reading for anybody with an interest in geometry. ... Read more

Reviews (1)

The beauty of geometry is captured
Originally published in 1942, this book has lost none of its power in the last half century. It is a commentary on the recent demise of geometry in many curricula that 33 years elapsed between the publication of the fifth and sixth editions. Fortunately, like so many things in the world, trends in mathematics are cyclic, and one can hope that the geometric cycle is on the rise. We in mathematics owe so much to geometry. It is generally conceded that much of the origins of mathematics is due to the simple necessity of maintaining accurate plots in settlements. The only book from the ancient history of mathematics that all mathematicians have heard of is the Elements by Euclid. It is one of the most read books of all time, arguably the only book without a religious theme still in widespread use over 2000 years after the publication of the first edition. The geometry taught in high schools today is with only minor modifications found in the Euclidean classic.
There are other reasons why geometry should occupy a special place in our hearts. Most of the principles of the axiomatic method, the concept of the theorem and many of the techniques used in proofs were born and nurtured in the cradle of geometry. For many centuries, it was nearly an act of faith that all of geometry was Euclidean. That annoying fifth postulate seemed so out of place and yet it could not be made to go away. Many tried to remove it, but finally the Holmsean dictum of ,"once you have eliminated the impossible, what is left, not matter how improbable, must be true", had to be admitted. There were in fact three geometries, all of which are of equal validity. The other two, elliptic and hyperbolic, are the main topics of this wonderful book.
Coxeter is arguably the best geometer of this century but there can be no argument that he is the best explainer of geometry of this century. While fifty years is a mere spasm compared to the time since Euclid, it is certainly possible that students will be reading Coxeter far into the future with the same appreciation that we have when we read Euclid. His explanations of the non-Euclidean geometries is so clear that one cannot help but absorb the essentials. In so many ways, Euclidean geometry is but the middle way between the two other geometries. A point well made and in great detail by Coxeter.
Geometry is a jewel that was born on the banks of the Nile river and we should treasure and respect it as the seed from which so much of our basic reasoning processes sprouted. For this reason, you should buy this book and keep a copy on your shelf.

Published in Smarandache Notions Journal, reprinted with permission. ... Read more

Book Description

You, too, can understand geometry—— just ask Dr. Math ® !

Are things starting to get tougher in geometry class? Don't panic. Dr. Math—the popular online math resource—is here to help you figure out even the trickiest of your geometry problems.

Students just like you have been turning to Dr. Math for years asking questions about math problems, and the math doctors at The Math Forum have helped them find the answers with lots of clear explanations and helpful hints. Now, with Dr. Math Presents More Geometry, you'll learn just what it takes to succeed in this subject. You'll find the answers to dozens of real questions from students in a typical geometry class. You'll also find plenty of hints and shortcuts for using coordinate geometry, finding angle relationships, and working with circles. Pretty soon, everything from the Pythagorean theorem to logic and proofs will make more sense. Plus, you'll get plenty of tips for working with all kinds of real-life problems.

You won't find a better explanation of high school geometry anywhere! ... Read more

Book Description

A number of important topics in complex analysis and geometry arecovered in this excellent introductory text.Written by experts inthe subject, each chapter unfolds from the basics to the more complex.The exposition is rapid-paced and efficient, without compromisingproofs and examples that enable the reader to grasp the essentials.The most basic type of domain examined is the bounded symmetricdomain, originally described and classified by Cartan and Harish-Chandra.Two of the five parts of the text deal with these domains:one introduces the subject through the theory of semisimple Liealgebras (Koranyi), and the other through Jordan algebras and triplesystems (Roos).Larger classes of domains and spaces are furnished bythe pseudo-Hermitian symmetric spaces and related R-spaces. Theseclasses are covered via a study of their geometry and a presentationand classification of their Lie algebraic theory (Kaneyuki).In the fourth part of the book, the heat kernels of the symmetricspaces belonging to the classical Lie groups are determined (Lu).Explicit computations are made for each case, giving precise resultsand complementing the more abstract and general methods presented.Also explored are recent developments in the field, in particular, thestudy of complex semigroups which generalize complex tube domains andfunction spaces on them (Faraut).This volume will be useful as a graduate text for students of Liegroup theory with connections to complex analysis, or as a self-studyresource for newcomers to the field.Readers will reach the frontiersof the subject in a considerably shorter time than with existingtexts. ... Read more

Book Description

Knot Theory, a lively exposition of the mathematics of knotting, will appeal to a diverse audience from the undergraduate seeking experience outside the traditional range of studies to mathematicians wanting a leisurely introduction to the subject.Graduate students beginning a program of advanced study will find a worthwhile overview, and the reader will need no training beyond linear algebra to understand the mathematics presented. The interplay between topology and algebra, known as algebraic topology, arises early in the book, when tools from linear algebra and from basic group theory are introduced to study the properties of knots, including one of mathematics' most beautiful topics, symmetry. The book closes with a discussion of high-dimensional knot theory and a presentation of some of the recent advances in the subject - the Conway, Jones and Kauffman polynomials. A supplementary section presents the fundamental group, which is a centerpiece of algebraic topology. ... Read more

Reviews (3)

Excellent!
Livingston does a good job on basic knot theory in this text. While Adams seems to jump around a bit in his book, Livingston keeps a nice flow to his work. The proofs require another text and a good background in algebra to understand, but the problems are wonderful for a deeper understanding of the material.

Good for an introduction
This book is an excellent introduction to knot theory for the serious, motivated undergraduate students, beginning graduate students,mathematicains in other disciplines, or mathematically oriented scientists who want to learn some knot theory.

Prequisites are a bare minimum: some linear algebra and a course in modern algebra should suffice, though a first geometrically oriented topology course (e. g., a course out of Armstrong, or Guillemin/Pollack) would be helpful.

Many different aspects of knot theory are touched on, including some of the polynomial invariants, knot groups, Alexander polynomial and related abelian invariants, as well as some of the more geometric invariants.

This book would serve as a nice complement to C. Adams "Knot Book" in that Livingston covers fewer topics, but goes into more mathematical detail. Livingston also includes many excellent exercises. Were an undergraduate to request that I do a reading course in knot theory with him/her, this would be one of the two books I'd use (Adam's book would be the other).

This book is intentionally written at a more elementary level than, say Kaufmann (On Knots), Rolfsen (Knots and Links), Lickorish (Introduction to Knot Theory) or Burde-Zieshcang (Knots), and would be a good "stepping stone" to these classics.

A very thorough volume for the serious student
Livingston's book is very concise and dense. It contains a lot of information, but is not the kind of book you could sit down and read through from cover to cover. It is excellent as a reference, a sort-of knot theory encyclopedia. ... Read more

Reviews (24)

good resource for geometry teachers
This book is appropriate for highly motivated middle school students whe have studied algebra in the seventh grade. The text uses a guided exploration approach to discovering the facts of geometry. For students who take any pleasure in math, this book can be fun. It is attuned to the 13 year old mind. Proof is introduced in a systematic way in the last two chapters.

The teacher must compensate for the fact that the book is not self-contained and is not useful as a reference (no glossary for example). Students must develop a notebook to organize what they learn and for future reference. Students who are left on their own to "construct" their knowledge of geometry through group activities and reflection could find it very tedious. The teacher has to be both a "sage on the stage" as well as a "guide on the side".

The book would not be appropriate at the high school level unless aggressively supplemented with a systematic treatment of Euclidean synthetic geometry. Some high school students would find its comic book style childish and unappealing.

I would recommend the book to math teachers and those studying to teach math as a rich source of ideas, activities and problems.

I HATE THIS BOOK!!!!
OMG! This book was so complicated to understand. They expect you to know everything. Because of this mindless crap, I failed Geometry and had to take the regular one. And the worst part is that they don't include enough examples to explain how to work the problem. I wouldn't recommend this God forsaken piece of crap to anyone who wants to do good in Geometry.

A terrible textbook
Whoever wrote this book has a great idea in having students actually working things out to find solutions, but to expect students to discover in an hour what geniuses discovered after many years is unrealistic. There are little to no examples, no glossary, and the hints are useless in helping the student understand the concept. All in all, a very poor book.

This Book SUCKS!
I don't know who would waste their money on such a horrilbe text book. I'm currently using this book right now for Geometry and I never experince such a bad textbook. This book is hard to understand and it's also usless to use this book if you are a "learn it yourself type of person." I rate this book an "F" and I wouldn't recommended this textbook to a genius, that's how horrible it is!

Terrible text
I have taught HS and college level Math for many years. I have never encountered a less user-friendly text. It is only with complete arrogance that an instructor or district would adopt this text. No examples to speak of, no odd-numbered answers in the back, no glossary (!), hints that don't help. How would anyone say that this is a good way to teach? Instead it sets up students for failure. If you are looking for a supplemental resource instead of a text, keep looking. There is no value to this text as a supplement since there is nothing that is self-explanatory. ... Read more

Book Description

This well-accepted introduction to computational geometry is a textbook for high-level undergraduate and low-level graduate courses. The focus is on algorithms and hence the book is well suited for students in computer science and engineering. Motivation is provided from the application areas: all solutions and techniques from computational geometry are related to particular applications in robotics, graphics, CAD/CAM, and geographic information systems. For students this motivation will be especially welcome. Modern insights in computational geometry are used to provide solutions that are both efficient and easy to understand and implement. All the basic techniques and topics from computational geometry, as well as several more advanced topics, are covered. The book is largely self-contained and can be used for self-study by anyone with a basic background in algorithms. In the second edition, besides revisions to the first edition, a number of new exercises have been added. ... Read more

Reviews (11)

The best computational geometry book!
I also completely disagree with the one-star review below. The "Dutch book" is the clearest, most complete, most up-to-date, best designed, best illustrated computational geometry textbook out there. Some of the material may be a bit advanced for undergraduates (and for those people I would recommend Joe O'Rourke's excellent "Computational Geometry in C"), but for graduate students and other researchers who want to learn computational geometry, this book is absolutely essential.

This is an algorithms textbook, though, not a textbook full of code. You will not find compilable code in the author's favorite programming language du jour -- this may be what the first reviewer meant by "desperately needed details". What you will find is clear, correct, well-motivated explanations of the underlying algorithms, data structures, and mathematics.

The book does have a few faults. The motivating examples are often forced ("mixing things" for convex hulls??). The authors deliberately chose to show only one algorithm for each problem they consider, and occasionally the algorithm they chose is not the simplest or most efficient. But these are minor points.

If you're going to buy just one computational geometry book, this is the one to get.

Interesting read, excellent theory, no code
This book serves as a survey of computational geometry algorithms. The explanations are very readable. The authors have taken special care to prove algorithm correctness and time complexity bounds.

Although I have yet to actually implement one of the algorithms in the book directly, I was exposed to a number of general techniques which I have used, such as randomized techniques to eliminate pathological worst-case performance problems, and various space partitioning techniques.

The algorithms are all presented in pseudocode, unfortunately, which is the reason for only 4 out of 5 stars. Also, some important details are omitted which make a few of their algorithms practically useless (although they are interesting theoritically). For example, there is an algorithm for pathfinding and collision avoidance for a translating (but not ROTATING!) robot.

If you're lookin for a computational geometry bible, this isn't it. But there are certainly some gems in this book and it is a very interesting read.

Good Introduction but look elsewhere for detailed reference
Pro:
(1) Each chapter begins with a practical example. For example, the chapter computing intersections of lines starts with a discussion of a map-making application that goes into enough detail to see how the algorithms they present would be useful. This is a considerable step up from the common practice in algorithms literature of motivation by way of vaguely mentioning some related field (i.e. "These string matching algorithms are useful in computational biology"). This book does a much better job of motivating the material it presents, but if you're primarily interested in the abstract problem, these sections can be skipped.

(2) Each chapter is relatively self-contained. Feel free to skip ahead to subjects that interest you.

(3) Surprisingly readable. Unlike most technical material, one can read an entire chapter in a single sitting without missing much. Generally, each chapter will develop a single algorithm for a single kind of problem.

(4) It's very up to date. This second edition is less than two years old, it includes some new results in the field.

Con:
(1) Algorithms are only given in pseudocode. The emphasis is on describing algorithms and data structures clearly and completely. If you're looking for a "cookbook" with code to copy and paste into an application, perhaps O'Rourke's "Computational Geometry in C" would be a better choice.

(2) There are many important advanced results that are not discussed in the main text. An obvious example is the first chapter, which describes a well-known convex hull algorithm that takes O(n log n) time but algorithms that are faster for most inputs are mentioned only in the "Notes and Comments" at the end of the chapter. Someone interested in lots of gory details would be well-served to combine this book with Boissonnat and Yvinec's more detailed and mathematical "Algorithmic Geometry".

Extremely well written
Algorithm books are often quite hard to understand, but this is not the case with this book. The information is very compact so it is a slow read but due to the high quality of the text this is only an advantage. You are never left wondering what the authors might have meant with a certain statement.

The book focuses solely on theory, so it presents no real source code (only pseudo-code) which I think is good thing since that would otherwise have polluted the clarity of the explanations.

Many of the topics it covers has been a help to me as a programmer. Can be recommended for anyone interested in computation geometry - but it requires some computer science maturity so I don't recommend it unless you have a bachelor's degree in C.S. or something similar.

Jacob Marner, M.Sc.

Clear and concise
The book is well written and easy to understand. An ideal book for someone planning to apply computation geometry for real-life problems. This is not a definitive book for computational geometry, but does give you good examples and ideas. Could do with more references to figures. There is scope for expansion of this book to include more detailed case studies and more pseudo code examples ... Read more

Book Description

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

Reviews (5)

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

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

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

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

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

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

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

okay content, mediocre presentation
This book provides a reasonable introduction to the field of computational geometry, although the notation is sometimes sloppy and the author frequently makes inconsistent assumptions about the reader. For example, on the first page he refers to a circle as a "one-dimensonial set of points," which although valid from a toplogical perspective is a little confusing in an introductory text. As another example, the first exercise refers to "every point in dP," presumably meaning just the corner points (otherwise the problem would be unsolvable). The book also sets up a lot of irrelevant mathematical definitions that generally obfuscate the presentation rather than clarifying it. Although not prohibitive for the ambitious reader, these needless hindrances are at best a little annoying.

Secondly, I must criticize the text's scope, in light of the important role computational geometry has played in modern computer graphics. There is no discussion of clipping, culling, occlusion (e.g. BSP, octree, OBB), or even non-polygon primitives -- important topics arguably more useful to the target audience than e.g. convex hulls (to which over 1/4 of the book's pages are devoted).

Regardless, this book (combined with a professor and a course) probably would serve quite well as an undergraduate text. Readers interested in a cookbook of applied graphics algorithms, however, should look elsewhere.

A clear, concise text on fundamental Computational Geometry
O'Rourke's approach reflects the essence of both "Computational Geometry" and the "C language" --- concise yet profound. The book covers the core subjects of Computational Geometry: polygon partitioning, convex hulls, Voronoi diagrams / Delaunay triangulation, "arrangements" of lines, geometric searching, and motion planning.

The book assumes some familiarity with the C language, but is very readable even for non-C programmers. This is an excellent text for use as an introduction to Computational Geometry, a primer for Preparata & Shamos, while at the same time it's an excellent addendum to that more seminal text. By weaving working code into his presentation, O'Rourke gives traction to the powerful engine of Preparata & Shamos. ... Read more

Book 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

Reviews (12)

Amazing concepts of space and time !!!
An excellent introduction to concepts of space and time in modern physics, including non-Euclidean geometry - the geometry of the curved spaces. Minimal background in mathematics is requested and multiple diagrams help a better understanding of the most difficult passages. The book is so interesting that I finished it in 5 days !!!

Solid Intro to Special Relativity and Non-Euclidean Geometry
In his own introduction the author, Mr. R. Rucker, states, "My goal has been to present an intuitive picture of the curved space-time we call home. There are a number of excellent introductions to the separate topics treated here, but there has been no prior weaving of them into a sustained visual account. I looked for a book like this for many years- and finding none, I wrote it." His dedication has been rewarded, as the text is one of the finer introductory books on the curvature of space time and special relativity.

The 'book like this' as the author calls it, walks the reader through several visual explanations that allow a solid mathematical and graphical explanation of modern physics. This isn't always a simple explanation, but there is a certain reward to struggling with the concepts before understanding them. In particular, Chapter 4 on time as a higher dimension makes the entire book worth reading, with many fascinating examples and a host of thought-provoking examples, such as "Schrodinger's Cat."

This is a very interesting book which would be of use to anyone who wishes to push just a little bit further than the typical popular physics text. For those who wish to push even further to solidify their knowledge, there are even questions at the end of each chapter. I highly recommend this book.

an extra dimension
This book is mainly concerned with exactly what the title says and I have been searching for a book like this for a very long time. because for one, it provides a very detailed explanation of topics that are intersting in the realm of physics. Such as the fourth dimension. it is very visual and explains things in a way that I can understand. I also like this book because it doesn't spend half the book telling you about which scientist hated the other scientist, Or the entire biography of Dr. Planck before they tell me what the planck length is

Good but Missing a Few Things
I haven't completely read this book, but I've read several like it. I want to point out some things that other reviewers haven't touched on. There is no index to the Dover edition. Maybe the original one had an index. That automatically knocks off one star in any book rating I give. It has some pretty sturdy exercises at the end of each chapter. There are no answers in the book. That's OK though. One can get some additional sense of the subject by looking at the questions. There is a very good annotated bibliography at the end of the book. It is not tied into page numbers, but I get the feeling the order of the list and their reference in the book are in the same order. There's good and bad news about the list. He makes many of these books sound very appealing, but many are long out of print. Rucker's book was produced around 1975.

There are times when I wish the author would have pressed a little harder one some seemingly simple points. Maybe by giving an alternative view. For example, early on in the book he talks about a flatlander being inside a balloon as he expands the balloon from the inside. Suddenly the flatlander is on the outside. Maybe it's me, but how that happens is not clear. I've found other such passages. However, a studious reader will find the topics interesting. The price is certainly right.

Weird in all the right ways
I really enjoy Rudy Rucker's nonfiction, and some of his fiction too (_White Light_ is great). He's very good at presenting mind-blowingly cool ideas in accessible expository prose, and he knows _just_ when to throw in the bombs.

This particular book is published by Dover, and it's not one of their usual reprints; it was _originally_ published by Dover. (In 1977, but the geometry of spacetime hasn't changed much since then.) It's an exploration of just what the title says: the geometry of the four-dimensional spacetime that the theory of relativity says is Really Out There.

Well, this is a good book on the subject, but you can get others (although one of the best -- Cornelius Lanczos's delightful _Space Through the Ages_ -- has long been out of print). What's coolest about this one is that Rudy Rucker wrote it.

Which means you get those little bombs thrown in at all the right places. Of course Rucker gives you what any competent mathematician will give you -- a sound introductory presentation of the mathematics of 4D spacetime and relativity theory, which are weird enough if you haven't encountered them before (and maybe even if you have) -- but he doesn't stop there. You also get an argument that the apparent passage of time is an illusion, and a little speculation about how this might tie in with the Many-Worlds Interpretation of quantum mechanics. And even that isn't all: you get a suggestion that it's possible to _develop a spacetime consciousness_ via some sort of meditation techniques or mystical insight, together with an entry in the annotated bibliography referring you (cautiously) to Robert A. Monroe's _Journeys Out of the Body_, whose experiments Rucker himself has tried.

It's like Raymond Smullyan on acid, if you know what I mean. But honest, it really does make sense. And it really will knock your mind loose from your brain even without the use of chemical aids.

This is the sort of thing Rucker does best. He does it in _Infinity and the Mind_, too (with which this volume has a little bit of overlap, but you won't care). Check out that book as well, along with _White Light_. Mathematical hippie mysticism just doesn't get any better. ... Read more

Book Description

This is an introduction to the theory and applications of modern geometry. It differs from other books in its field in its emphasis on applications and its discussion of Special Relativity as a major example of a non-Euclidean geometry. Besides Special Relativity, it covers two other important ares of non-Euclidean goemetry: spherical geometry (used in navigation and astronomy) and projective geometry (used in art). In addition, it reviews many useful topics from Euclidean geometry, emphasizing transformations, and includes a chapter on conics and planetary orbits. Applications are stressed throughout the book. Every topic is motivated by an application and many additional applications are given in the exercises. The book would be an excellent introduction to higher geometry for those students, especially prospective mathematics and teachers, who need to know how geometry is used in addition to its formal theory. ... Read more

Reviews (1)

Excellent elementary introduction to modern geometry
I am a Ph.D student in the field of symplectic geometry and topology. This book introduces the foundations of modern geometry in a beautiful and a very clear way,and I am saying this having some experience with geometry and topology books. If you are a skilled high school student or an under graduate student for mathematics or related area,this is a good book to start with in understanding what is modern geometry. The level of the book is about undergraduate level using very elementary notions. The content of the book is: Euclidean geometry and its logical foundations(so one could understand the motivation of the other geometries), Sphirical geometry,conic sections,Projective geometry,and the ending chapter is about the geometrical foundations of special relativity. The approach is not theorem-proof style but rather a more intuitive approch!. This is a recommended book. ... Read more

Reviews (4)

A Definite 5 Star Book
This book is full of wonderful theorems and other facts about geometry. But don't miss an equally wonderful book of his - The Penguin Dictionary of Curious and Interesting Numbers. When I semi-retired several years ago, I gave away many of my math books, but I would not part with these two.

Excellently researched encyclopedia of Geometry
This is my favorite David Wells book. Scads of illustrations motivate hundreds of interesting branches of Geometry. Much of the information in the book was new to me, such as the 14th tiling pentagon. This well-researched book is top-notch.

Invaluable for enriching Geometry courses
I was asked to enrich a school geometry course. Not much came off the top of my head. After discovering this book, I had so many leads I can enrich for years! It gave an insight into every topic covered in the standard