Product Description
Meyer's Geometry and Its Applications, Second Edition, combines traditional geometry with current ideas to present a modern approach that is grounded in real-world applications. It balances the deductive approach with discovery learning, and introduces axiomatic, Euclidean geometry, non-Euclidean geometry, and transformational geometry. The text integrates applications and examples throughout and includes historical notes in many chapters.

The Second Edition of Geometry and Its Applications is a significant text for any college or university that focuses on geometry's usefulness in other disciplines. It is especially appropriate for engineering and science majors, as well as future mathematics teachers.

* Realistic applications integrated throughout the text, including (but not limited to):
- Symmetries of artistic patterns
- Physics
- Robotics
- Computer vision
- Computer graphics
- Stability of architectural structures
- Molecular biology
- Medicine
- Pattern recognition
* Historical notes included in many chapters
* Instructor's Manual with solutions available for all adopters of the text ... Read more

Customer Reviews (2)

Good practical book
This book is a good college level textbook, with a lot of practical applications for geometry.Good for a college text to prepare geometry teachers to deal with questions from students like, "What will I ever need to use geometry for?"I really liked that the book has solutions to the odd numbered problems and the sections in each chapter on how geometry applies to everyday problems faced in physics and engineering.The CD was a nice supplement to use with geometers sketchpad.

THE BOOK OF IDEAS
I got this book as a second hand and shortly its very very nice book.
The applications are very smart and clear ,
Its contexts and illustrations are adequate ,precise and really easy to read and understand.
I realy loved this book ,and i guess this is how the geometry Should be taught as rich ideas with apps not in abstract form.
You will find a nice proof for fermat's least time principle,
and lots lots more intersting ideas good for physics and computer
graphics programming.
This book really worth any price. ... Read more

Product Description

For courses in Geometry or Geometry for Future Teachers.

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

Customer Reviews (3)

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

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

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

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

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

Product Description
Since its original publication in 1990, Kenneth Falconer's Fractal Geometry: Mathematical Foundations and Applications has become a seminal text on the mathematics of fractals. It introduces the general mathematical theory and applications of fractals in a way that is accessible to students from a wide range of disciplines. This new edition has been extensively revised and updated. It features much new material, many additional exercises, notes and references, and an extended bibliography that reflects the development of the subject since the first edition.
* Provides a comprehensive and accessible introduction to the mathematical theory and applications of fractals.
* Each topic is carefully explained and illustrated by examples and figures.
* Includes all necessary mathematical background material.
* Includes notes and references to enable the reader to pursue individual topics.
* Features a wide selection of exercises, enabling the reader to develop their understanding of the theory.
* Supported by a Web site featuring solutions to exercises, and additional material for students and lecturers.
Fractal Geometry: Mathematical Foundations and Applications is aimed at undergraduate and graduate students studying courses in fractal geometry. The book also provides an excellent source of reference for researchers who encounter fractals in mathematics, physics, engineering, and the applied sciences. ... Read more

Customer Reviews (6)

The Basic Text For Understanding Fractals
Fractal Geometry:Mathematical Foundations and Applications by Kenneth Falconer(second edition)is one of the most important mathematical books of this beginning of the 21-st century.It is a book of high mathematical level which can be very useful to non-mathematicians possessing a reasonable mathematical instruction and a logical mind.Mathematicians will find in this book deep and sophisticated notions and proofsand non-mathematicians will find all the concrete applications of the theory of fractals(see e.g.the new paragraph dedicated to fractals in finance).Prof.dr.Ion Chitescu
Faculty of Mathematics and Computer Science
University of Bucharest

A rare find
I agree with all that was said by the other reviews here but add one important point. The physical layout, (typeface, drawings, whitespace etc.) of this book is brilliantly done. This is often overlooked by the producers of technical works who do it "on the cheap", but it is vital if one is to use the book day after day, as I have had to.

While the subject matter is not easy, this is an excellent book to motivate one to get stuck into the underlying mathematics. The reward is a little insight into the often beatiful theorems and practical results found in this stimulating field of study.

What every student should know about fractals.
Fractals make headlines from time to time[--are they everywhere?], and and they make lovely color pictures; but they are also part of a substantial mathematical theory, one with an
exciting mathematical history. This very important book presents
the subject in a way that it can be taught to students, and it starts with the basics, systematically, step by step, building up the material. Or it can be used for selfstudy! It has great exercises too! In view of the many applications to geometric analysis, to PDE, and to statistics, it is likely that fractal geometry will soon be a standard math course taught in many (more) math departments. By now it is widely recognized that the selfsimilarity aspects of the wavelet algorithms are key to their sucess. The book came out in 1990, and the author has an equally attractive book on the subject from 1985[The geometry of fractal sets] with a slightly more potential theoretic bent.

Theoretical as well as practical insight
The first part of the book is essentially of a theoretical nature, with a thorough treatment of fractal geometry at a mathematical point of view. The second part on the other hand provides a flavour of the problems of fractal geometry in practice...so mathematicians as well as people interested in applications only should both find this book interesting. The maths are not easy but quite "understandable" for science undergrads...some notions of calculus or topology would help... but the introduction is excellent and allows anyone to follow the course of the book (but for understanding the proofs a good math background is required).

Excellent for understanding the geometrical properties of fractals.

Exposes fractal geometry as a real mathematical discipline.
I appreciate Falconer's books on fractal geometry because they show the topic as it really is: a whole mathematical discipline on its own right and not just a nice temporary fashion.

It begins introducing basictopological concepts and then proceeds to develop the theory for severalpossible definitions of fractal dimension, showing the relations betweenthem. Then it explores deeply the local geometry of different kinds offractal objects, and studies some other geometrical situations, like thepojection of fractals (ever thought of a DIGITAL sundial? Here it isdescribed!).

The book also includes a lot of applications to other areasof mathematics and physics, a great amount of graphics, and muchmore.

The text is suitable from third year undergraduate school and on.It is a larger but lighter version of "The Geometry of FractalSets". ... Read more

Product Description
This book is an exposition of semi-Riemannian geometry (also called pseudo-Riemannian geometry)--the study of a smooth manifold furnished with a metric tensor of arbitrary signature. The principal special cases are Riemannian geometry, where the metric is positive definite, and Lorentz geometry. For many years these two geometries have developed almost independently: Riemannian geometry reformulated in coordinate-free fashion and directed toward global problems, Lorentz geometry in classical tensor notation devoted to general relativity. More recently, this divergence has been reversed as physicists, turning increasingly toward invariant methods, have produced results of compelling mathematical interest. ... Read more

Customer Reviews (6)

The Best Introduction to General Relativity
If you want to engage in a serious study of general relativity, then you must master the mathematical language of semi-Riemannian manifolds in which it is cast. Sadly, the development of classical Riemannian geometry as studied by pure mathematicians only parallels the development of semi-Riemannian geometry in the early stages;eventually, the two subjects diverge rather drastically.For example, the famous Hopf-Rinow Theorem, one of the cornerstones of modern Riemannian geometry, simply has no Lorentzian analogue at all;every single equivalence in the theorem fails in Lorentzian geometry.Thus, one could master all five volumes of Spivak's definitive treatment of Riemannian geometry and still be unprepared to deal with light cones, timelike, null and spacelike geodesics, and the multitude of other uniquely semi-Riemannian constructs that appear in general relativity.

O'Neill's wonderful book, which first appeared in 1983, provides the well-prepared reader with a mathematically rigorous, thorough introduction to both Riemannian and semi-Riemannian geometry, showing how they are similar and pointing out clearly where they differ.After developing the mathematical machinery in the early chapters, the last part of the book turns to general relativity by offering lucid introductions to the Robertson-Walker cosmological models (Big Bang singularities), the Schwarzschild model for a single non-rotating star (including black holes), and a brief introduction to Penrose-Hawking causality theory.

If you would like to study a pure Riemannian text in parallel with this one, I would recommend the text by Boothby, written at a comparable level of difficulty, which remains one of the clearest and most accessible Riemannian geometry texts on the market.For the serious reader who wishes to continue on with a study of the Kerr solution to Einstein's equations, modeling the exterior spacetime of a rotating star, O'Neill wrote an entire book on the subject in 1995, now difficult to find but well worth tracking down.This 1995 text contains one of the clearest, most accessible introductions available to the difficult subjects of the algebraic classification of the Weyl curvature tensor and the corresponding Petrov classification of spacetimes.

I studied from O'Neill's 1983 text when it first came out and I have continued to use it as the primary text for an advanced undergraduate course I have taught over the past 20 years.It is not an "easy" text to read, but then, I have never found the "easy" introduction to differential geometry and general relativity.The reviewer who says this is not a suitable first text is simply in error;there is no better first text on the subject.If you have studied linear algebra, advanced calculus, and a little topology, then with dedication and hard work, you can learn more from O'Neill's text than from many of the far more popular recent texts, written by physicists, which attempt to circumvent the mathematics insofar as is possible while introducing general relativity.This is a perilous course for which the serious student will pay dearly later on, when she/he wants to study any of the many areas of modern physics in which differential geometry (differential forms, bundle theory, connections on a principle fiber bundle, gauge theory, etc.) plays an essential role.

Great book, terrible print quality
This is a wonderful book, with a clear, concise and precise exposition of the fundamental idea in riemannian and semi-riemannian geometry.Although I would not recommend it as a first text, it will be the text that you continue to reference later, and turn to when you want the best mathematical treatment.

However, I do not recommend that you buy a new copy.The print quality is terrible; the binding is poor, but even worse, the text quality is absurd.I have been using a library copy with cloth binding and sharp, clear text.It is obvious that the new printing in the green cover is based on a photocopy of the original rather than a new typesetting.While this means that no errors have been introduced, I found it painful to read.I would suggest looking for a used copy.

So 5 stars for the book, but only 3 stars for this printing.

Very good contents but..
The only drawback, and it is a serious one, is the binding. For a such expensive book, one could expect a DECENT binding, but the outcome is a SHAME.

So 5 star for the contents an 0 for the binding

Addendum
This book is now available at Amazon.co.uk!

Its contents are: Manifold Theory. Tensors. Semi-Riemannian Manifolds. Semi-Riemannian Submanifolds. Riemannian and Lorentz Geometry. Special Relativity. Constructions.Symmetry and Constant Curvature. Isometries. Calculus of Variations.Homogeneous and Symmetric Spaces. General Relativity; Cosmology.Schwarzschild Geometry. Causality in Lorentz Manifolds.

Let's go buy it!

Excellent for beginner and experienced mathematicians
This is one of the best books on Differential Geometry I've ever read. It includes a clear exposition of all the basic results and then goes on to the most deep aspects of the subject, making it useful for undergraduateand graduate students, as well as experienced working mathematicians. It'sa pitty that it's no longer available. ... Read more

Product Description

Stochastic geometry deals with models for random geometric structures. Its early beginnings are found in playful geometric probability questions, and it has vigorously developed during recent decades, when an increasing number of real-world applications in various sciences required solid mathematical foundations. Integral geometry studies geometric mean values with respect to invariant measures and is, therefore, the appropriate tool for the investigation of random geometric structures that exhibit invariance under translations or motions. Stochastic and Integral Geometry provides the mathematically oriented reader with a rigorous and detailed introduction to the basic stationary models used in stochastic geometry – random sets, point processes, random mosaics – and to the integral geometry that is needed for their investigation. The interplay between both disciplines is demonstrated by various fundamental results. A chapter on selected problems about geometric probabilities and an outlook to non-stationary models are included, and much additional information is given in the section notes.

Product Description
This is a comprehensive treatment of Minkowski geometry. The author begins by describing the fundamental metric properties and the topological properties of existence of Minkowski space. This is followed by a treatment of two-dimensional spaces and characterizations of Euclidean space among normed spaces. The central three chapters present the theory of area and volume in normed spaces--a fascinating geometrical interplay among the various roles of the ball in Euclidean space.Later chapters deal with trigonometry and differential geometry in Minkowski spaces.The book ends with a brief look at J. J. Schaffer's ideas on the intrinsic geometry of the unit sphere. ... Read more

Product Description
The Wiley Paperback Series makes valuable content more accessible to a new generation of statisticians, mathematicians and scientists.

Stochastic geometry and spatial statistics play a fundamental role in many modern branches of physics, materials sciences, biology and environmental sciences. They offer successful models for the description of random two- and three-dimensional micro and macro structures and statistical methods for their analysis. The book deals with the following topics:

• point processes
• random sets
• random measures
• random shapes
• fibre and surface processes
• tessellations
• stereological methods.

This book has served as the key reference in its field for over 20 years and is regarded as the best treatment of the subject of stochastic geometry, both as an subject with vital applications to spatial statistics and as a very interesting field of mathematics in its own right. ... Read more

Customer Reviews (2)

The best book on the subject
Stochastic geometry deals with the development and analysis of stochastic models for complicated geometrical patterns. The mathematical background comes from probability theory (e.g. point and Poisson processes, random fields and sets), as well as from convex and integral geometry (e.g. surface area measures and intrinsic volumes, kinematic and Crofton formulae).

Knowledge of convex geometry, probability, and measure theory are prerequisites to understanding this book, which is, quite frankly, the only game in town. As academic as this book can get, all of its competitors are compilations of disjoint symposium papers or pure exercises in theoretical mathematics.

In particular, this book has a very nice section on fibre and surface processes and also one on stereology, which is the set of methods that allow a 3-D interpretation of structures based on observations made on 2-D sections. Stereology is therefore often referred to as the science of estimating higher dimensional information from lower dimensional samples. This book even starts out with a brief review of some basic mathematical foundations, although it is fast paced.

All in all, I give it four stars because it is the best book on the subject out there, and it has quite a bit of material relevant to stochastic geometry's most interesting application - that of telecommunication network modeling. Also, the book makes heavy use of some very good illustrations. Just remember the notation can get dense and there are no exercises to speak of. There are some interesting examples, but they can get long and involved to the point where you can't see the forest for the trees unless you exercise considerable concentration.

Great! Bridges the gap between the abstract & the practical
This book covers the theory of spatial point processes at a level that is perfect for the practical scientist who needs to solve real-world problems or analyze data -- without details of measure theory and other abstractions. ... Read more

Product Description
Subriemannian geometries, also known as Carnot-Caratheodory geometries, can be viewed as limits of Riemannian geometries. They also arise in physical phenomenon involving "geometric phases" or holonomy. Very roughly speaking, a subriemannian geometry consists of a manifold endowed with a distribution (meaning a $k$-plane field, or subbundle of the tangent bundle), called horizontal together with an inner product on that distribution. If $k=n$, the dimension of the manifold, we get the usual Riemannian geometry. Given a subriemannian geometry, we can define the distance between two points just as in the Riemannin case, except we are only allowed to travel along the horizontal lines between two points.

The book is devoted to the study of subriemannian geometries, their geodesics, and their applications. It starts with the simplest nontrivial example of a subriemannian geometry: the two-dimensional isoperimetric problem reformulated as a problem of finding subriemannian geodesics. Among topics discussed in other chapters of the first part of the book we mention an elementary exposition of Gromov's surprising idea to use subriemannian geometry for proving a theorem in discrete group theory and Cartan's method of equivalence applied to the problem of understanding invariants (diffeomorphism types) of distributions. There is also a chapter devoted to open problems.

The second part of the book is devoted to applications of subriemannian geometry. In particular, the author describes in detail the following four physical problems: Berry's phase in quantum mechanics, the problem of a falling cat righting herself, that of a microorganism swimming, and a phase problem arising in the $N$-body problem. He shows that all these problems can be studied using the same underlying type of subriemannian geometry: that of a principal bundle endowed with $G$-invariant metrics.

Reading the book requires introductory knowledge of differential geometry, and it can serve as a good introduction to this new exciting area of mathematics. ... Read more

Product Description
This is an introduction to noncommutative geometry, with special emphasis on those cases where the structure algebra, which defines the geometry, is an algebra of matrices over the complex numbers. Applications to elementary particle physics are also discussed. This second edition is thoroughly revised and includes new material on reality conditions and linear connections plus examples from Jordanian deformations and quantum Euclidean spaces. Only some familiarity with ordinary differential geometry and the theory of fiber bundles is assumed, making this book accessible to graduate students and newcomers to this field. ... Read more

Customer Reviews (2)

Very nice, lots of good stuff
This book is (partially) the answer to my prays: an introductory book on noncommutative geometry, something I've been waiting since I discovered thetopic in Connes' seminal text, which I've also reviewed here. Instead ofexposing the historical origins, then firing a goddamn chaingun of advancedtopics(something quite fascinating, because of the potential of thetheory,but not pedagogical), Madore uses a more friendly way of exposingthings,by mantaining a compromise between the most natural motivations tothetechniques of the subject and the places where the background neededis not so overwhelming. He do teach much of the background (in the sensethatyou don't need to master functional analysis, operator algebras andadvanced differential geometry), but he goes quite fast on it, requiring arather maturemathematical mind. As noncommutative geometry is not for thefaint of theheart, I guess he's not asking too much after all.

Thepedagogy of the book is also benefitted from the post-"Connes'book" evolution of noncommutative geometry, because in 1999 the theoryand its (real and potential) applications were a great deal more mature andsolid than in 1994. Being this theory a work in progress, the better themathknowledge the reader has, the more he or she will learn from Madore'sbook, which stands maybe as the only pedagogical exposition ofnoncommutative geometry (now I'm waiting for the huge book fromGarcia-Bondia and his colaborators, to be published by Birkhauser in 2001,hope that it contains more background; it would be very useful for thoseinterested in beginning research on the area).

An Introduction to Noncommutative Differential Geometry and
FOR PHYSICIST, I strongly reccomend this book! There are so many physical examples in this book. Always we physicists hate mathamatical proofs likea torture. But this book concentrates applications to physics. If you wantto study Noncommutative Geometry as a physicist, this book should be chosenas the first introduction! ... Read more

Product Description
This is the first volume of a three-volume introduction to modern geometry, with emphasis on applications to other areas of mathematics and theoretical physics. Topics covered include tensors and their differential calculus, the calculus of variations in one and several dimensions, and geometric field theory. This material is explained in as simple and concrete a language as possible, in a terminology acceptable to physicists. The text for the second edition has been substantially revised. ... Read more

Customer Reviews (2)

Written for the physicist in mind
This book, written by some of the master expositors of modern mathematics, is an introduction to modern differential geometry with emphasis on concrete examples and concepts, and it is also targeted to a physics audience. Each topic is motivated with examples that help the reader appreciate the essentials of the subject, but rigor is not sacrificed in the book.

In the first chapter the reader gets a taste of differentiable manifolds and Lie groups, the later gving rise to a discussion of Lie algebras by considering, as usual, the tangent space at the identity of the Lie group. Projective space is shown to be a manifold and the transition functions explicitly written down. The authors give a neat example of a Lie group that is not a matrix group. A rather quick introduction to complex manifolds and Riemann surfaces is given, perhaps too quick for the reader requiring more details. Homogeneous and symmetric spaces are also discussed, and the authors plunge right into the theory of vector bundles on manifolds. Thus there is a lot packed into this chapter, and the authors should have considered spreading out the discussion more, as it leaves the reader wanting for more detail.

The authors consider more fundamental questions in smooth manifolds in chapter 3, with partitions of unity used to prove the existence of Riemannian metrics and connections on manifolds. They also prove Stokes formula, and prove the existence of a smooth embedding of any compact manifold into Euclidean space of dimension 2n + 1. Properties of smooth maps, such as the ability to approximate a continuous mapping by a smooth mapping, are also discussed. A proof of Sard's theorem is given, thus enabling the study of singularities of a mapping. The reader does get a taste of Morse theory here also, along with transversality, and thus a look at some elementary notions of differential topology. An interesting discussion is given on how to obtain Morse functions on smooth manifolds by using focal points.

Notions of homotopy are introduced in chapter 3, along with more concepts from differential topology, such as the degree of a map. A very interesting discussion is given on the relation between the Whitney number of a plane closed curve and the degree of the Gauss map. This leads to a proof of the important Gauss-Bonnet theorem. Degree theory is also applied to vector fields and then to an application for differential equations, namely the Poincare-Bendixson theorem. The index theory of vector fields is also shown to lead to the Hopf result on the Euler characteristic of a closed orientable surface and to the Brouwer fixed-point theorem.

Chapter 4 considers the orientability of manifolds, with the authors showing how orientation can be transported along a path, thus giving a non-traditional characterization as to when a connected manifold is orientable, namely if this transport around any closed path preserves the orientation class. More homotopy theory, via the fundamental group, is also discussed, with a few examples being computed and the connection of the fundamental group with orientability. It is shown that the fundamental group of a non-orientable manifold is homomorphic onto the cyclic group of order 2. Fiber bundles with discrete fiber, also known as covering spaces, are also discussed, along with their connections to the theory of Riemann surfaces via branched coverings. The authors show the utility of covering maps in the calculation of the fundamental group, and use this connection to introduce homology groups. A very detailed discussion of the action of the discrete group on the Lobachevskian plane is given.

Absolute and relative homotopy groups are introduced in chapter 5,and many examples are given of their calculation. The idea of a covering homotopy leads to a discussion of fiber spaces. The most interesting discussion in this chapter is the one on Whitehead multiplication, as this is usually not covered in introductory books such as this one, and since it has become important in physics applications. The authors do take a stab at the problem of computing homotopy groups of spheres, and the discussion is a bit unorthodox since it depends on using framed normal bundles.

The theory of smooth fiber bundles is considered in the next chapter. The physicist reader should pay close attention to this chapter is it gives many insights into the homotopy theory of fiber bundles that cannot be found in the usual books on the subject. The discussion of the classification theory of fiber bundles is very dense but worth the time reading. Interestingly, the authors include a discussion of the Picard-Lefschetz formula, as an example of a class of "fiber bundles with singularities". Those interested in the geometry of gauge field theories will appreciate the discussion on the differential geometry of fiber bundles.

Dynamical systems are introduced in chapter 7, first as defined over manifolds, and then in the context of symplectic manifolds via Hamaltonian mechanics. Liouville's theorem is proven, and a few examples are given from relativistic point mechanics. The theory of foliations is also discussed, although the discussion is too brief to be of much use. The authors also consider variational problems, and given its importance in physics, they continue the treatment in the last chapter of the book, giving several examples in general relativity, and in gauge theory via a consideration of the vacuum solutions of the Yang-Mills equation. The physicist reader will appreciate this discussion of the classical theory of gauge fields, as it is good preparation for further reading on instantons and the eventual quantization of gauge fields.

A masterful sequel!
Novikov et al's first volume was the defining book on differential geometry (S-V 93). The second volume picks up on the detailed theory of manifolds and topology and other advanced theories of differentialgeometry, including homotopy groups, Lie algebras and digressing intophysical theories as well (eg.Yang-Mills) giving one of the juciest bookson the subject - an utter delight! ... Read more

Product Description
This volume discusses results about quadratic forms that give rise to interconnections among number theory, algebra, algebraic geometry, and topology. The author deals with various topics including Hilbert's 17th problem, the Tsen-Lang theory of quasi-algebraically closed fields, the level of topological spaces, and systems of quadratic forms over arbitrary fields. Whenever possible, proofs are short and elegant, and the author has made this book as self-contained as possible. This book brings together thirty years' worth of results certain to interest anyone whose research touches on quadratic forms. ... Read more

Product Description

"From nothing I have created a new different world," wrote János Bolyai to his father, Wolgang Bolyai, on November 3, 1823, to let him know his discovery of non-Euclidean geometry, as we call it today. The results of Bolyai and the co-discoverer, the Russian Lobachevskii, changed the course of mathematics, opened the way for modern physical theories of the twentieth century, and had an impact on the history of human culture.

The papers in this volume, which commemorates the 200th anniversary of the birth of János Bolyai, were written by leading scientists of non-Euclidean geometry, its history, and its applications. Some of the papers present new discoveries about the life and works of János Bolyai and the history of non-Euclidean geometry, others deal with geometrical axiomatics; polyhedra; fractals; hyperbolic, Riemannian and discrete geometry; tilings; visualization; and applications in physics.

Product Description
Differential geometry has a long, wonderful history. It has found relevance in areas ranging from machinery design to the classification of four-manifolds to the creation of theories of nature's fundamental forces to the study of DNA. This book studies the differential geometry of surfaces with the goal of helping students make the transition from the compartmentalized courses in a standard university curriculum to a type of mathematics that is a unified whole. It mixes together geometry, calculus, linear algebra, differential equations, complex variables, the calculus of variations, and notions from the sciences. Differential geometry is not just for mathematics majors. It is also for students in engineering and the sciences. The mix of ideas offer students the opportunity to visualize concepts through the use of computer algebra systems such as Maple. The book emphasizes that this visualization goes hand-in-hand with the understanding of the mathematics behind the computer construction. Students will not only see geodesics on surfaces, but they will also observe the effect that an abstract result such as the Clairaut relation can have on geodesics. Furthermore, the book shows how the equations of motion of particles constrained to surfaces are actually types of geodesics. The book is rich in results and exercises that form a continuous spectrum, from those that depend on calculation to proofs that are quite abstract. ... Read more

Customer Reviews (3)

clearest undergrad differential geometry text around
This is a very well-written text on modern differential geometry for undergraduates. The content of the book is similar to O'Neill's "Elementary Differential Geometry" (e.g. covariant derivatives, shape operators), but it's easier to read. There are many undergrad texts around -- O'Neill, do Carmo, Pressley -- but this one is the most lucidly written one hands-down.

Afer going through Oprea, one might like to tackle O'Neill's "Elementary Differential Geometry" and Vols 2-4 of Spivak's "Comprehensive Introduction to D.G."

Like O'Neill, Oprea develops surface theory using the shape operator. But Oprea takes shortcuts and doesn't develop the theory in quite the same generality as O'Neill does. For example, Oprea doesn't introduce differential forms and the exterior calculus. As a consequence, Oprea restricts himself to the Serret-Frenet equations whereas O'Neill introduces Cartan's structural equations -- of which Serret-Frenet is simply a special case -- as the method of moving frames in full generality. The structural equations are then used (by O'Neill) in both curve and surface theory.

Nice introduction and applications of differential geometry
I found this book to be a fine introduction to this subject. I was particularly pleased with the practical examples outlined in the book. Even though I am not extremely proficient with Maple, I found the exercises using this software provided important illustrations of applications.

Not a text for a rigorous mathematics course
This book is not to be used as a rigorous introduction to differential geometry.There are some definitions and theorems that are casuallydescribed, and the motive behind particular definitions are vague. Thosenot interested in MAPLE might find constant instructions for MAPLEannoying. Not to be completely negative, there are some good excercizes inthe text that I especially enjoyed. ... Read more

Product Description
With the ever-rising volume worldwide of visual content on computers and communication networks, it becomes increasingly important to understand visual processing, to model and evaluate image formation, and to attempt to interpret image content. "Numerical Geometry of Images" presents an authoritative examination of new computational methods and algorithms in image processing and analysis.In addition to providing the requisite vocabulary for formulating problems, the book describes and utilizes tools from mathematical morphology, differential geometry, numerical analysis, and calculus of variations. Many applications, such as shape reconstruction, color-image enhancement and segmentation, edge integration, path planning, and calculation invariant signatures are explored.

Topics and features:

*Introduces new concepts in geometric image modeling and image interpretation (computer vision)

*Provides the requisite theoretical basis and progresses to using key tools

*Offers a solution to the face-recognition problem by generalizing principles from texture-mapping methods in computer graphics

*Contains numerous helpful exercises and solutions to facilitate learning

*Presents a new perspective on solving classic problems, as well as classic approaches to solving new problems

*Uses industry-proven variational geometric methods and numerical schemes. ... Read more

Customer Reviews (4)

CS Grad
I was searching for an introduction to this field, and hesitated after reading the two stars review. I found the book at a university bookstore and browsed through it. It is exactly what I was looking for.
A simple yet comprehensive introduction to the field, clear examples, sample code, and some solutions to exercises that helped me go through the chapters.

I like to learn by reading, and searched for an introduction to computer vision and image processing with PDE as tools (I took a classical course that did not cover these aspects). This book was great for the task. It does not pretend to push you into pure theoretical domains as most of the related books seem to enjoy doing, yet it keeps you on the edge when it deals with geometry of moving curves and the interesting model of color image as a surface. If you like geometry like me, you would like the book.

I already experimented with and used some of the tools I picked up from this book. I think it's a great asset to anyone who would like a direct access to a set of geometric tools for manipulating images.
I hesitated weather to give it only 4 stars as the last chapter breaks the flow. However, I saw the author made a whole new book out of it so I kept it 5. Worth the buck.

Numerical Geometry of Images
If there's one topic this books is not about, it's the numerical geometry of images
despite its title.

This book should have been titled "Introduction to Geometry of Curves on Surfaces."

The closest the author gets to anything resembling the study of the numerical
geometry of images is the Taylor series expansion of derivatives taught in most
undergraduate calculus courses - and two simple MATLAB program of questionable
value at the end the book.

There are a handful of simple algorithms in the chapter 7 but they only address
fast marching methods applied to two silly boundary value problems. The author
completely ignores the corresponding initial value problem.

I'm giving it 2 stars since the title of the book was completely misleading.
And after reading it, I was left wondering how would someone apply the information
presented in this book to a simple 2 dimensional image since there are absolutely
no examples of any practical value.

Numerical Geometry of Images
A very well-written, interesting and useful book covering a wide range of topics in image processing and computer vision and beyond. A good balance between theory and implementation issues that make the things work. A 100% recommendation to students and specialists in the field.

Some additional info.
The book is an extended version of my lecture notes. Including
introduction to variational methods, differential geometry,
level sets and fast marching numerical methods, and geometric active
contours for segmentation with Matlab pseudo code, 3D face recognition,
texture mapping and more applications.

Thanks to the many who bought the book. ... Read more

Product Description
Excellent teaching of mathematics at the elementary school level requires teachers to be experts in school mathematics. This textbook helps prospective teachers achieve this expertise by presenting topics from the K-6 mathematics curriculum at a greater depth than is found in most classrooms. The knowledge that comes from this approach gives prospective teachers essential insight into how topics interrelate and where the difficulties may lie.

Information is presented at a pace that makes it interesting, rewarding, and enjoyable. With the deeper mathematical preparation inherent in this book, prospective teachers will come away knowing how to explain concepts, demonstrate computational procedures, and lead students through problem-solving techniques. Both students and teachers will find this book key to learning the necessary material and knowing how to express it at the right level.

The primary focus is on the foundations of arithmetic, along with a selection of topics from geometry, and a wide range of applications. The number line is used throughout to visualize concepts and to tie them to solutions. The book emphasizes explanations: of concepts, of how to solve problems, and of how the concepts relate to the solutions of the problems. ... Read more

Product Description
Among the modern methods used to study prime numbers, the 'sieve' has been one of the most efficient. Originally conceived by Linnik in 1941, the 'large sieve' has developed extensively since the 1960s, with a recent realization that the underlying principles were capable of applications going well beyond prime number theory. This book develops a general form of sieve inequality, and describes its varied applications, including the study of families of zeta functions of algebraic curves over finite fields; arithmetic properties of characteristic polynomials of random unimodular matrices; homological properties of random 3-manifolds; and the average number of primes dividing the denominators of rational points on elliptic curves. Also covered in detail are the tools of harmonic analysis used to implement the forms of the large sieve inequality, including the Riemann Hypothesis over finite fields, and Property (T) or Property (tau) for discrete groups. ... Read more

Product Description
Orthonormal Systems and Banach Space Geometry describes the interplay between orthonormal expansions and Banach space geometry. Using harmonic analysis as a starting platform, classical inequalities and special functions are used to study orthonormal systems leading to an understanding of the advantages of systems consisting of characters on compact Abelian groups. Probabilistic concepts such as random variables and martingales are employed and Ramsey's theorem is used to study the theory of super-reflexivity. The text yields a detailed insight into concepts including type and co-type of Banach spaces, B-convexity, super-reflexivity, the vector-valued Fourier transform, the vector-valued Hilbert transform and the unconditionality property for martingale differences (UMD). A long list of unsolved problems is included as a starting point for research. This book should be accessible to graduate students and researchers with some basic knowledge of Banach space theory, real analysis, probability and algebra. ... Read more

Product Description
This volume contains 11 papers presented at the First IMA Conference on Fractal Geometry: Mathematical Methods, Algorithms and Applications, held at De Montfort University in September 2000. Researchers include many from Europe, Russia, and the United States, giving a multinational emphasis to the fractal geometry problems described. Emphasized are the mathematical exposure given to a problem and the practicalities required to create and implement an algorithm. ... Read more

Product Description
This volume is based on the lectures given at the FirstInter-University Graduate School on Gravitation and Cosmologyorganized by IUCAA, Pune, India. The material offers a firmmathematical foundation for a number of subjects including geometricalmethods for physics, quantum field theory methods and relativisticcosmology. It brings together the most basic and widely usedtechniques of theoretical physics today. A number of speciallyselected problems with hints and solutions have been added to assistthe reader in achieving mastery of the topics.
Audience: The style of the book is pedagogical and should appealto graduate students and research workers who are beginners in thestudy of gravitation and cosmology or related subjects such asdifferential geometry, quantum field theory and the mathematics ofphysics. This volume is also recommended as a textbook for courses orfor self-study. ... Read more