Book Description

This book is a clear exposition, with exercises, of the basic ideas of algebraic topology: homology (singular, simplicial, and cellular), homotopy groups, and cohomology rings. It is suitable for a two-semester course at the beginning graduate level, requiring as a prerequisite a knowledge of point set topology and basic algebra. Although categories and functors are introduced early in the text, excessive generality is avoided, and the author explains the geometric or analytic origins of abstract concepts as they are introduced, making this book of great value to the student. ... Read more

Reviews (1)

Good textbook
Rotman's book presents all the material one would expect of an introductory text, in the language of Categories although still accessible to those who have never seen categories before. While Rotman's style and exposition is excellent, the book often gets bogged down in cumbersome notation. Also some other textbooks(e.g. Munkres Elements of Algebraic Topology) give more motivation to the material and explain what is actually going on geometrically(as opposed to algebraically). Also, the exercises are generally quite easy. Overall, I recommend Rotmans book to people who don't mind being patient, and waiting to see the whole picture. ... Read more

Book Description

This volume is an introduction to mathematical Knot Theory; the theory of knots and links of simple closed curves in three-dimensional space. It consists of a selection of topics which graduate students have found to be a successful introduction to the field. Three distinct techniques are employed; Geometric Topology Manoeuvres, Combinatorics, and Algebraic Topology. Each topic is developed until significant results are achieved and chapters end with exercises and brief accounts of state-of-the-art research. What may reasonably be referred to as Knot Theory has expanded enormously over the last decade and while the author describes important discoveries throughout the twentienth century, the latest discoveries such as quantum invariants of 3-manifolds as well as generalisations and applications of the Jones polynomial are also included, presented in an easily understandable style. Thus this constitutes a comprehensive introduction to the field, presenting modern developments in the context of classical material. Readers are assumed to have knowledge of the basic ideas of the fundamental group and simple homology theory although explanations throughout the text are plentiful and well-done. Written by an internationally known expert in the field, this volume will appeal to graduate students, mathematicians and physicists with a mathematical background who wish to gain new insights in this area. ... Read more

Book Description

This book is an introduction to surgery theory: the standard classification method for high-dimensional manifolds. It is aimed at graduate students, who have already had a basic topology course, and would now like to understand the topology of high-dimensional manifolds. This text contains entry-level accounts of the various prerequisites of both algebra and topology, including basic homotopy and homology, Poincare duality, bundles, co-bordism, embeddings, immersions, Whitehead torsion, Poincare complexes, spherical fibrations and quadratic forms and formations. While concentrating on the basic mechanics of surgery, this book includes many worked examples, useful drawings for illustration of the algebra and references for further reading. ... Read more

Reviews (1)

Part 2, Singular Homology Theory is recommended.
This text is suitable for students of mathematics without prior knowledge of algebraic topology. The best thing with this is Part 2 which treats singular homology theory. However, you may want to resort to Maunder for an effeective introductin to elelmentary homotopy theory, and to Dold for and intruduction to orientation and duality. ... Read more

Book Description

This book is an introduction to knot and link invariants as generalized amplitudes (vacuum-vacuum amplitudes) for a quasi-physical process. The demands of knot theory, coupled with a quantum statistical framework, create a context that naturally and powerfully includes an extraordinary range of interrelated topics in topology and mathematical physics. The author takes a primarily combinatorial stance toward knot theory and its relations with these subjects. This has the advantage of providing very direct access to the algebra and to the combinatorial topology, as well as the physical ideas. This book is divided into 2 parts: Part I of the book is a systematic course in knots and physics starting from the ground up. Part II is a set of lectures on various topics related to and sometimes based on Part I. Part II also explores some side-topics such as frictional properties of knots, relations with combinatorics and knots in dynamical systems. ... Read more

Reviews (1)

math grad.
Overview of knots/physics. The book is fairly self-contained. It also has lots of pictures and works through the mathematics.
Introduces bracket polynomial, temperly-lieb algebra, and modeling physics ideas out of this stuff. ... Read more

Book Description

De Rham cohomology is the cohomology of differential forms. This book offers a self-contained exposition to this subject and to the theory of characteristic classes from the curvature point of view. It requires no prior knowledge of the concepts of algebraic topology or cohomology. The first ten chapters study cohomology of open sets in Euclidean space, treat smooth manifolds and their cohomology and end with integration on manifolds. The last eleven chapters cover Morse theory, index of vector fields, Poincaré duality, vector bundles, connections and curvature, Chern and Euler classes, Thom isomorphism, and the general Gauss-Bonnet theorem. The text includes over 150 exercises, and gives the background necessary for the modern developments in gauge theory and geometry in four dimensions, but it also serves as an introductory course in algebraic topology. It will be invaluable to anyone who wishes to know about cohomology, curvature, and their applications. ... Read more

Reviews (4)

Too advanced for the targeted audience
De Rham cohomology and the theory of characteristic classes are not only two of the most important topics in mathematics, but also in theoretical physics. Indeed, an understanding of the geometry and topology of fiber bundles requires a mastery of these topics, and, if one is to make sense of topological phenomena in quantum field theory, one must understand how to perform the calculation of characteristic classes. This book gives a fairly good start in meeting these goals, and, the authors say, is written for upper-level undergraduates with no background in topology or differential geometry. However topological spaces are not defined in the book, but the authors use them as though the reader has had prior exposure.

De Rham cohomology is introduced very early in the book (p. 15), with a differential p-form defined as a smooth map from an open set in n-dimensional Euclidean space to the space of alternating forms. The authors do motivate the definition through the consideration of ordinary vector calculus, which serves to ease the transition to the more formal theory. Concepts from algebraic topology immediately follow, these being chain complexes and their corresponding homological algebra. The foremost strategy for the calculation of the De Rham cohomology, the Mayer-Vietoris sequence is given, the treatment emphasizing the role of the Poincare lemma. Considerations from homotopy are used to calculate the de Rham cohomology of punctured Euclidean space. The De Rham theory is then used to prove the Brouwer fixed point theorem. The famous theorem of J.F. Adams on the maximal number of linearly independent vector fields on the n-dimensional sphere is stated but not proved. No doubt the proof was omitted due to the advanced techniques that must be used to prove it.

Differential forms on smooth manifolds are discussed also, along with the accompanying topics of curvature and integration on smooth manifolds. Stokes' theorem is proved in detail. A very detailed study of the concept of degree, linking numbers, and indexes of vector fields is given, as preparation for later discussions on Morse theory and the Poincare-Hopf theorem. The physicist reader will definitely want to pay attention to this discussion because of its importance in applications.This discussion also marks the beginning of the more advanced topics in the book, which continues to its end. Readers will definitely have to pay attention to more of the details here, and the authors replace geometric intuition by more formal, algebraic considerations.

The theory of fiber bundles and vector bundles are given fair treatment in the book too, but the authors should have motivated the subject with some examples of elementary bundles, such as the Mobius strip. They do however prove that a vector bundle over a compact base space has an inner product and they do this with the help of partitions of unity. Partitions of unity are one of most useful concepts to illustrate how the different fibers of a bundle can be joined together. Also, they show how vector bundles over a compact base can be trivialized by taking the direct sum with a suitable bundle, called its complement. This motivates the definition of an Abelian semigroup of isomorphism classes of vector bundles over compact bases. This semigroup can, and the authors show this, be completed to an Abelian group via the Grothendieck construction. These considerations are the origin of the famous K-theory of vector bundles. Along these same lines the authors show that there is a homotopy classification of vector bundles by using the notion of a "pull-back" of vector bundles (the pull-back of a vector bundle "dilutes" the bundle, i.e. makes it less "twisted").

The way the authors present the theory of characteristic classes is much too formal, and does not give the reader an appreciation of their origins and why they work as well as they do. Readers at this level need to be given a lot more motivation to the underlying intuition behind characteristic classes. Physicists in particular, who are faced with these objects in many applications, need a more in-depth discussion. Indeed, the authors really take off in their proof of the Thom isomorphism theorem. They do not discuss why this result is so important nor give concrete examples of its utilization.

A fairly long list of exercises is given in the back of the book, and the reader should work most of these in order to be able to understand the results in the book. It will also help to go back to some of the original papers on vector and fiber bundles, even ones published in the 1930s, to gain more of an appreciation of the concepts in the book.

Rigor is of upmost importance in mathematics, but so is understanding.

A considerable leap, for those who like challenges
This book is true to his objectives: teaching cohomology and characteristic classes starting from calculus in several variables, in the sense that the background needed is more or less just about this start (along with some linear algebra). However, the mathematical maturity needed to fully understand the topics is a great deal bigger than that. The book can get quite esoteric very quickly, and I feel somehow that it could have been more natural to insert the example of cohomology from calculus given in the first chapter after differential forms, for example.

Nevertheless, I like this book. The authoritative books that treat more or less the same topics (Milnor & Stasheff's "Characteristic Classes", Bott & Tu's "Differential Forms in Algebraic Topology"), although more inspired and clearer (for the initiated), ask for more background and even more maturity than this one. Madsen & Tornehave introduces you to some very powerful machinery of algebraic topology, being at the same time challenging and rewarding. It succeds in the sense that it really teaches the way of thinking "algebro-topologically", a thing that can be invaluable on the study of recent topics in theoretical physics. You also can try to read the classics after reading this book: then you can at the same time understand better the point of view of these authors, and get a better grasp of the topics you've seen before.

Ambitious, dense, altogether not motivated
It is a bit ambitious to use deRham cohomology as an introduction to differential forms and analysis on manifolds (compare with the easier and clearer 'Analysis on Manifolds' by Munkres). A bit too much for newcomers, too little for graduate students (compare with Bott and Tu). It is good for advanced undergraduates who are able to handle the pace and abstraction. Few examples and computations.

An elegant introduction to characeteristic classes.
This book studies caharacteristic classes via de Rham cohomology. Compared with Bott and Tu's similar book "Differential Forms in Algebraic Topology", this one is more refined and more sophisticated. Warning: this book contains few applications of characteristic classes. For that matter, Milnor's "Characteritic Classes" is still the best source of information. ... Read more

Book Description

This is the first of two volumes providing an introduction to modern developments in the representation theory of finite groups and associative algebras, which have transformed the subject into a study of categories of modules.Thus, Dr. Benson's unique perspective in this book incorporates homological algebra and the theory of representations of finite-dimensional algebras. This volume is primarily concerned with the exposition of the necessary background material, and the heart of the discussion is a lengthy introduction to the (Auslander-Reiten) representation theory of finite dimensional algebras, in which the techniques of quivers with relations and almost-split sequences are discussed in some detail. ... Read more

Reviews (4)

Not bad..
It's worth noting that there are quite a few in number of books out there on introductory (i.e. a first course in) alg. top.
In particular, I should mention that the book by Rotman and sizeable portions of Bredon, "Geometry and Topology" can serve as good supplementary reading. I still don't think \pi_1 should have been left out; although one *could* refer to the prequel, there's still more to be desired by way of completeness, if anything, as this book is intended for beginners. For instance, the relation between the fundamental group and the first homology group would have certainly shed some light on these seemingly (at first glance, anyway) disparate invariants (as it is heavy-going on the (co)homological apparatus altogether).

Munkres is by no means encyclopaedic, which is good, in opposition to, say, Spanier or Whitehead, and certainly warrants attention to worked-out examples in detail and some (not-so) routine exercises which makes this book accessible to wider mathematical audiences wishing to learn a little about this fascinating subject (fascinating, in my opinion, as it is my passion :)

A little incomplete
This well written text is one of the standard references in algebraic topology courses because of its conciseness, and I find it very useful as a reference text.

However I think it is a little incomplete because of several reasons.

(1)It pays no attention to one basic concept of algebraic topology: the fundamental group.

(2) It doesn't cover ^Cech homology, important in other areas, like dimension theory for example.

(3) It doesn't stress the most important feature of algebraic topology: its connection to other areas of mathematics (analysis, differential geometry, etc.).

(4) Its list of references is too short, and lacks almost completely HISTORICAL references which are always important to become an expert in any field.

Conclusion: a good reference on homology and cohomology essentials, but not "the" reference on algebraic topology as a whole.

The book binding is horrible
The material in the book (homology and cohomology theory, universal coefficient theorems, Kunneth theorem, duality in manifolds, applications to classical theorems of point-set topology) is for the most part solid. However...

- Munkres really belabors the simplicial theory, and it gets to be quite painful (especially the *CHAPTER* on the topological invariance of simplicial homology groups).

- Some very important topics (homotopy theory, fiber bundles) are not at all discussed.

- The book binding is horrible -- my copy is in two pieces, with several loose pages, and I don't think the hardcover edition is still in print.

Excellent text on homology and cohomology
Algebraic topology is a tough subject to teach, and this book does a very good job. Some prerequisites, however, are essential:

* point set topology (e.g. in Munkres' Topology)

* Abstract algebra

* Mathematical maturity to be willing to follow a definition and argument even when it seems like a weird side-track

In addition, this would not be the first book I would recommend to those interested in algebraic topology. First might be Massey's "Algebraic Topology: and Introduction" that introduces the fundamental group (conceptually easier than homology and cohomology).

At some point, however, a prospective student in topology will have to learn homological algebra and this provides the most concrete approach I know to the subject.

Algebraic topology is a lot of fun, but many of the previous textbooks had not given that impression. This one does. ... Read more

Reviews (4)

For reference ONLY
This book is a highly advanced and very formal treatment of algebraic topology and meant for researchers who already have considerable background in the subject. A category-theoretic functorial point of view is stressed throughout the book, and the author himself states that the title of the book could have been "Functorial Topology". It serves best as a reference book, although there are problem sets at the end of each chapter.

After a brief introduction to set theory, general topology, and algebra, homotopy and the fundamental group are covered in Chapter 1. Categories and functors are defined, and some examples are given, but the reader will have to consult the literature for an in-depth discussion. Homotopy is introduced as an equivalence class of maps between topological pairs. Fixing a base point allows the author to define H-spaces, but he does not motivate the real need for using pointed spaces, namely as a way of obtaining the composition law for the loops in the fundamental group. By suitable use of the reduced join, reduced product, and reduced suspension, the author shows how to obtain H-groups and H co-groups. The fundamental group is defined in the last section of the chapter, and the author does clarify the non-uniqueness of the fundamental group based at different points of a path-connected space.

Covering spaces and fibrations are discussed in the next chapter. The author does a fairly good job of discussing these, and does a very good job of motivating the definition of a fiber bundle as a generalized covering space where the "fiber" is not discrete. The fundamental group is used to classify covering spaces.

In chapter 3 the author gets down to the task of computing the fundamental group of a space using polyhedra. Although this subject is intensely geometrical. only six diagrams are included in the discussion.

Homology is introduced via a categorical approach in the next chapter. Singular homology on the category of topological pairs and simplicial homology on the category of simplicial pairs. The author begins the chapter with a nice intuitive discussion, but then quickly runs off to an extremely abstract definition-theorem-proof treatment of homology theory. The discussion reads like one straight out of a book on homological algebra.

This approach is even more apparent in the next chapter, where homology theory is extended to general coefficient groups. The Steenrod squaring operations, which have a beautiful geometric interpretation, are instead treated in this chapter as cohomology operations. The logic used is impeccable but the real understanding gained is severely lacking.

General cohomology theory is treated in the next chapter with the duality between homology and cohomology investigated via the slant product. Characteristic classes, so important in applications, are discussed using algebraic constructions via the cup product and Steenrod squares. Characteristic classes do have a nice geometric interpretation, but this is totally masked in the discussion here.

The higher homotopy groups and CW complexes are discussed in Chapter 7, but again, the functorial approach used here totally obscures the underlying geometrical constructions.

Obstruction theory is the subject of Chapter8, with Eilenberg-Maclane spaces leading off the discussion. The author does give some motivation in the first few paragraphs on how obstructions arise as an impediment to a lifting of a map, but an explicit, concrete example is what is needed here.

The last chapter covers spectral sequences as applied to homotopy groups of spheres. More homological algebra again, and the same material could be obtained (and in more detail) in a book on that subject.

Definitely not for beginners
I gave Spanier only three stars not because I think it is a bad book: as the previous two reviewers have pointed out, Spanier is a comprehensive (and still good) account of the subject, but is by no means for beginners. Now that more user-frinedly ones like Bredon, Fomenko-Novikov, and Hatcher (forthcoming) are available, it would hardly justify giving it four or five stars. And for reference purposes, there is a small (and sometimes too terse) but attractive account by May that covers topics not touched by Spanier.

Excellent reference, poor textbook
This book is terrific as a reference for those who already know the subject, but if you teach algebraic topology it would be dangerous to use it as a graduate text (unless you're willing to supplement it extensively). The basic problem is that Spanier does not teach students how to compute effectively because his abstract, high-powered algebraic approach obscures the underlying geometry, which is not developed at all. Here I'd recommend the books by Munkres, or Greenberg; even the old-fashioned treatment of Lefschetz, with its explicit and rather cumbersome treatment of cohomology, could serve as an antidote to Spanier. Somewhere, the student has to acquire a good intuitive feeling for the geometry underlying the subject (the same can be said of algebraic geometry -- here earlier work (e.g., of the Italian school, Weil's old book on intersection theory, ...) should not be neglected entirely in favor of Grothendieck et al., for something essential is lost)

That said, if you already know the subject Spanier's book is an excellent reference. Even here, though, you'll need to provide some details toward the ends of the later chapters. Each chapter starts out relatively easily and works up to a crescendo, the treatment becoming terser and more advanced.

I give it four stars (5 for mathematical quality, 3 for usefulness as a text). The first three chapters deal with covering spaces and fibrations; the middle three with (co)homology and duality; the last three with general homotopy theory, obstruction theory, and spectral sequences. Some of Serre's classical results on finiteness theorems for homotopy groups are presented.

Thorough treatment of algebraic topology
Spanier's book is a wonderful treatment of many important ideas in algebraic topology, from covering spaces to Cech Cohomology. However, the going is difficult for those not initiated into the basic ideas. The proofs are correct, but often too terse for graduate students. It would also be nice if there were more explicit examples in the text, as in Greenberg and Harper's book, for example. There are plentiful exercises that go deep into the theoretical aspects of the subject. I use this book as a reference for my research and for that purpose it is excellent! ... Read more

Book Description

This expertly written volume presents a useful, coherent account of the theory of the cohomology ring of a finite group. The book employs a modern approach from the point of view of homological algebra, and covers themes such as finite generation theorems, the cohomology of wreath products, the norm map, and variety theory. Prerequisites comprise a familiarity with modern algebra comparable to that offered in introductory graduate courses, although otherwise the book is self-contained. As a result, it will be useful for those already engaged or commencing research in this area of mathematics by providing an up-to-date survey of important techniques and their applications to finite group theory. ... Read more

Book Description

Topology is a relatively young and very important branch of mathematics. It studies properties of objects that are preserved by deformations, twistings, and stretchings, but not tearing. This book deals with the topology of curves and surfaces as well as with the fundamental concepts of homotopy and homology, and does this in a lively and well-motivated way. There is hardly an area of mathematics that does not make use of topological results and concepts. The importance of topological methods for different areas of physics is also beyond doubt. They are used in field theory and general relativity, in the physics of low temperatures, and in modern quantum theory. The book is well suited not only as preparation for students who plan to take a course in algebraic topology but also for advanced undergraduates or beginning graduates interested in finding out what topology is all about. The book has more than 200 problems, many examples, and over 200 illustrations. ... Read more

Book Description

This book presents a computational approach to the analysis of nonlinear and uncertain systems. The main focus is systems with piecewise linear dynamics. The class of piecewise linear systems examined has nonlinear, possibly discontinuous dynamics, and allows switching rules that incorporate memory and logic. These systems may exhibit astonishingly complex behaviors. Some aspects of the successful theory of linear systems and quadratic criteria are extended here to piecewise linear systems and piecewise quadratic criteria. The book also describes numerical procedures for assessing stability, computing induced gains, and solving optimal control problems for piecewise linear systems. These developments enable researchers to analyze a large and practically important class of control systems that are not easily dealt with when using other techniques. ... Read more

Book Description

Knot theory is a concept in algebraic topology that has found applications in a variety of mathematical problems as well as in computer science, biological and medical research, and mathematical physics. This book is directed to a broad audience of research workers and beginning graduate students in these fields. It contains most of the fundamental classical facts about the theory, such as knot diagrams, braid representations, Seifert surfaces, tangles, and Alexander polynomials, as well as more recent developments and special topics such as chord diagrams and covering spaces. It is an introduction to the fascinating study of knots and provides insight into recent applications to such studies as ... Read more

Book Description

This introduction to topology emphasizes a geometric approach with a focus on surfaces. A primary feature is a large collection of exercises and projects, which fosters a teaching style making the student an active class participant. A wide range of material at different levels supports flexible use of the book for a variety of students. Part I is appropriate for a one semester or two quarter course, and Part II, which id problem based allows the book to be used for a year long course which supports a variety of syllabuses. ... Read more

Reviews (1)

A Terrific Book for a Concrete Understanding
Dr. Lawson's book is great for the reader who wants a concrete understanding of topology to complement an abstract appreciation for its beauty.Many motivating and explanatory examples in the text help to flesh out the general results of the field.The book is divided as to be accessible not only to undergraduates and newcomers to topology, but also to graduates and those looking for higher level results.There are exercises guiding the reader though difficult results, so it is excellent for independent study or a source for projects. ... Read more

Book Description

This book provides a comprehensive account of a key, perhaps the most important, theory that forms the basis of Taylor-Wiles proof of Fermat's last theorem. Hida begins with an overview of the theory of automorphic forms on linear algebraic groups and then covers the basic theory and recent results on elliptic modular forms, including a substantial simplification of the Taylor-Wiles proof by Fujiwara and Diamond. He offers a detailed exposition of the representation theory of profinite groups (including deformation theory), as well as the Euler characteristic formulas of Galois cohomology groups. The final chapter presents a proof of a non-abelian class number formula. ... Read more

Book Description

This is the first of two volumes on the qualitative theory offoliations. This volume is divided into three parts. It isextensively illustrated throughout and provides a large numberof examples.

Part 1 is intended as a "primer" in foliation theory. A workingknowledge of manifold theory and topology is a prerequisite.Fundamental definitions and theorems are explained to preparethe reader for further exploration of the topic. This sectionplaces considerable emphasis on the construction of examples,which are accompanied by many illustrations.

Part 2 considers foliations of codimension one. Using veryhands-on geometric methods, the path leads to a completestructure theory (the theory of levels), which was establishedby Conlon along with Cantwell, Hector, Duminy, Nishimori,Tsuchiya, et al. Presented here is the first and only fulltreatment of the theory of levels in a textbook.

Part 3 is devoted to foliations of higher codimension, includingabstract laminations (foliated spaces). The treatment emphasizesthe methods of ergodic theory: holonomy-invariant measures andentropy. Featured are Sullivan's theory of foliation cycles,Plante's theory of growth of leaves, and the Ghys, Langevin,Walczak theory of geometric entropy.

This comprehensive volume has something to offer a broad spectrumof readers: from beginners to advanced students to professionalresearchers. Packed with a wealth of illustrations and copiousexamples at varying degrees of difficulty, thishighly-accessible text offers the first full treatment in theliterature of the theory of levels for foliated manifolds ofcodimension one. It would make an elegant supplementary text fora topics course at the advanced graduate level. ... Read more

Book Description

This book is an introduction to topological dynamics and ergodic theory. It is divided into a number of relatively short chapters with the intention that each may be used as a component of a lecture course tailored to the particular audience. The authors provide a number of applications, principally to number theory and arithmetic progressions (through Van der Waerden's theorem and Szemerdi's theorem). This text is suitable for advanced undergraduate and beginning graduate students. ... Read more

Book Description

This textbook presents the foundations of tensor calculus and the elements of tensor analysis. In addition, the authors consider numerous applications of tensors to geometry, mechanics and physics.

While developing tensor calculus, the authors emphasize its relationship with linear algebra. Necessary notions and theorems of linear algebra are introduced and proved in connection with the construction of the apparatus of tensor calculus; prior knowledge is not assumed. For simplicity and to enable the reader to visualize concepts more clearly, all exposition is conducted in three-dimensional space. The principal feature of the book is that the authors use mainly orthogonal tensors, since such tensors are important in applications to physics and engineering.

With regard to applications, the authors construct the general theory of second-degree surfaces, study the inertia tensor as well as the stress and strain tensors, and consider some problems of crystallophysics. The last chapter introduces the elements of tensor analysis.

All notions introduced in the book, and also the obtained results, are illustrated with numerous examples discussed in the text. Each section of the book presents problems (a total over 300 problems are given). Examples and problems are intended to illustrate, reinforce and deepen the presented material. There are answers to most of the problems, as well as hints and solutions to selected problems at the end of the book. ... Read more

Book Description

Helaman Ferguson is a sculptor who works in stone and bronze. He also holds a Ph.D. in mathematics. Although Helamans sculptures are mathematically-based, they are organic, textural, and mysterious. This dramatically photographed book has won several awards including an OZZIE and a National Gold Ink Award. ... Read more

Reviews (2)

A bridge between two worlds
This luscious book amply attests to the affinity between art and mathematics, and does so in an unusual and striking way.Bertrand Russel once wrote: "Mathematics, rightly viewed, possesses not only truth,but supreme beauty---a beauty cold and austere, like that ofsculpture." Russell's beauty is that of intangibles, as whenmathematicians speak of an elegant proof, a beautiful theory.Fergusonimbues mathematics with another kind of beauty, accessible toeveryone.

Ferguson's sculptures are attractive both in their shape and intheir materials.This lavishly illustrated book exhibits them toadvantage. The artist's comments on each piece, at the end of the book, arequite valuable; in spite of the mathematical nature of some of them, theyconvey a sense of personal intimacy.

The beauty of mathematics revealed thru sculpture
A reality check for those of us who were brought up to think that mathematics is dry and esoteric. ... Read more