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Reviews (1)

A wonderful work
Geometry and meaning is an amazing book. It discusses NLP (natural language processing) and how common geometric ideas and theories can be applied in NLP with often excellent or quite satisfactory results.

The strongest point of the book is its clarity. Widdows has a gift in writing. For a book that attempts to convey so many ideas it is surprisingly refreshing to see that it accomplishes its task with the minimal amount of jargon (if any at all indeed). Besides the main text, the insets with historic or scientific references are very enjoyable as well.

I would have personally preferred some more detail on the methods developed for similarity and distance in hierarchies in chapter 4 (there is only the formulae from Leacock's and Resnik's algorithms) as well as a more in-depth coverage of the word-document vector model in chapter 5. Still these details can be found by consulting the very detailed and carefully compiled bibliography at the end of the book.

With the exceptions of NLP experts who may find such a book rather simplistic and a reference to things they already know, I suspect that the rest of us who want a clear and consise introduction to the field will greatly benefit from it. And at such a reasonable price I dont see why any one interested in the subject wouldnt want this gem in their library.

A related book which makes a case for the application of geometry in the way humans reason and judge similarities between objects and concepts is Gardenfors' Conceptual Spaces--another wonderful book--albeit slightly more difficult to understand. ... Read more

Book Description

This is the softcover reprint of the English translation of 1971 (available from Springer since 1989) of the first 4 chapters of Bourbaki's Topologie générale. It gives all the basics of the subject, starting from definitions. Important classes of topological spaces are studied, uniform structures are introduced and applied to topological groups. Real numbers are constructed and their properties established. Part II, comprising the later chapters, Ch. 5-10, is also available in English in softcover. ... Read more

Reviews (2)

N. Bourbaki is the greatest mathematician ever!! Well,...
After reading the story of N. Bourbaki, I HAD to order every book by Bourbaki that I could find.All I'll say is I love the book, but perhaps even more I love the concept of Bourbaki (if you've never heard of Bourbaki, google it for an interesting read).

the book that the experts study
i recently ordered "A GENERAL TOPOLOGY WORKBOOK" by Iain Adamson, as i very much wish to understand the mathematics of topology.as i would do with any other book, i started by reading the introduction and suggested readings.Mr. Adamson highly recommends the BOURBAKI series on topology as a reference material.he ascribes to this series as his text of choice and further states that this is the text that he has studied the most closely.it is for this reason that i am ordering this series.

i extend my thanks to mr. adamson for the recommendation.with the plethora of choices in study materials and a limited budget, i needed to narrow my scope and decide which text would best serve me.

thanks again:-) ... Read more

Book Description

This book covers topology and geometry beginning with an accessible account of the extraordinary and rather mysterious impact of mathematical physics, especially gauge theory, on the study of the geometry and topology of manifolds.Much of the mathematics developed in the book to study the classical field theories of physics (de Rham cohomology, Chern classes, Semi-Riemannian manifolds, Cech cohomology, spinors etc. ) is standard, but the treatment always keeps one eye on the physics and unhesitatingly sacrifices generality to clarity.The author brings the reader up to the level needed to conclude with a brief discussion of the Seiberg-Witten invariants. Although this volume can be read independently Naber carries on the program initiated in his earlier volume, Topology, Geometry and Gauge Fields: Foundations, Springer, 1997, and writes in much the same spirit with precisely the same philosophical motivation. A large number of exercises are included to encourage active participation on the part of the reader.This work will be of great interest to researchers and graduate students in the field of mathematical physics. REVIEWS OF TOPOLOGY, GEOMETRY, AND GAUGE FIELDS: FOUNDATIONS"It is unusual to find a book so carefully tailored to the needs of this interdisciplinary area of mathematical physics. . . Naber combines a knowledge of his subject with an excellent informal writing style. "NZMS NEWSLETTER". . . this book should be very interesting for mathematicians and physicists (as well as other scientists) who ae concerned with gauge theories. "ZENTRALBLATT FUER MATHEMATIK ... Read more

Reviews (2)

MATH AND TOPOLOGY
Topology is very important scince in the fields of mathematics. And it using in many of another sinceis.

required reading for a topologist interested in physics
As a mathematician turned physics grad student, it is often difficult to read "Math for Physicists" books simply because of the focus on making "numbers churn out;" which, at least for me personally, more difficult to get a handle on the subject and then, in turn, use it fruitfully.

This book on the other hand, is exemplary of why I got into physics in the first place. The first chapter (Physical motivations) and the last chapter (Gauge Fields and Instantons) can be read by any one with undergraduate topology under their belt and come away with a more powerful understanding of gauge theory than, in my opinion, can be found in other introductory gauge theory texts I've been directed to.

Of course I'll read all those said texts as well, but I'm thankful that I found this one. ... Read more

Book Description

Over the past fifteen years, the geometrical and topological methods of the theory of manifolds have as- sumed a central role in the most advanced areas of pure and applied mathematics as well as theoretical physics. The three volumes of Modern Geometry - Methods and Applications contain a concrete exposition of these methods together with their main applications in mathematics and physics. This third volume, presented in highly accessible languages, concentrates in homology theory. It contains introductions to the contemporary methods for the calculation of homology groups and the classification of manifesto. Both scientists and students of mathematics as well as theoretical physics will find this book to be a valuable reference and text. ... Read more

Reviews (1)

You should read this if you can afford the price.
I feel puzzled nobody so far has reviewd this excellent text by Novikov (and Fomenko).The view-point is somewhat different from Bredon or May or Spanier, but together with Part 2, they forma good introduction to"geometric" topology. ... Read more

Book Description

This book is primarily a textbook introduction to various areas of discrete geometry. In each area, it explains several key results and methods, in an accessible and concrete manner. It also contains more advanced material in separate sections and thus it can serve as a collection of surveys in several narrower subfields. The main topics include: basics on convex sets, convex polytopes, and hyperplane arrangements; combinatorial complexity of geometric configurations; intersection patterns and transversals of convex sets; geometric Ramsey-type results; polyhedral combinatorics and high-dimensional convexity; and lastly, embeddings of finite metric spaces into normed spaces. ... Read more

Book Description

Karl Menger, one of the founders of dimension theory, belongs to the most original mathematicians and thinkers of the twentieth century. He was a member of the Vienna Circle and the founder of its mathematical equivalent, the Viennese Mathematical Colloquium. Both during his early years in Vienna, and after his emigration to the United States, Karl Menger made significant contributions to a wide variety of mathematical fields, and greatly influenced some of his colleagues. The “Selecta Mathematica” contain Menger's major mathematical papers, based on a personal selection by himself out of his extensive writings. They deal with topics as diverse as topology, geometry, analysis and algebra, as well as writings on economics, sociology, logic, philosophy and mathematical results. The two volumes are a monument to the diversity and originality of Menger's ideas. ... Read more

Book Description

Spectral sequences are among the most elegant and powerful methods of computation in mathematics.This book describes some of the most important examples of spectral sequences and some of their most spectacular applications.The first part treats the algebraic foundations for this sort of homological algebra, starting from informal calculations. The heart of the text is an exposition of the classical examples from homotopy theory, with chapters on the Leray-Serre spectral sequence, the Eilenberg-Moore spectral sequence, the Adams spectral sequence, and, in this new edition, the Bockstein spectral sequence.The last part of the book treats applications throughout mathematics, including the theory of knots and links, algebraic geometry, differential geometry and algebra. This is an excellent reference for students and researchers in geometry, topology, and algebra. ... Read more

Reviews (5)

A good start
Very clearly written, full of examples and counterexamples, making use of pictures but never sacrificing rigor, the authors of this book have given students of topology a superb introduction to the field. Many students have been educated in topology by using this book, and it is sure to remain a classic in the field. It builds a solid understanding of the basic rudiments and intuition behind point-set, geometric, and algebraic topology. There is a lot of material covered in the book, and some very specialized subjects, such as Cech and Vietoris homology and some dimension theory, but with some preserverance and concentration, the entire book can be grasped within reasonable time constraints. Probably the only minus to the book is the lack of exercises. This is a quite serious omission, for the only way to master a subject is to work problems that require careful thought for their solution.

The beginning student of topology should probably read this book with the following mindset: try to think of ways and techniques that you would devise to study the structure of a topological space. Homotopy and homology (in various forms) are the standard techniques for doing this. These strategies have varying degrees of success, but their use in topology now seems to be reaching a saturation limit, even though the explicit calculation of homotopy groups is still a very active area. New techniques and concepts, representing sort of a "large deviation" from the standard ones discussed in this book, will be needed to make further progress in the study of complicated topological spaces. Something more is needed now, that is completely different than homology and homotopy theory, that will make more transparent the properties of these spaces. These new techniques will be somewhat radical from the standpoint of current ones, but they will be more effective from a conceptual (and computational) point of view.

A Professional Topologist loves this book.
When I was a graduate student 40 years ago there were very few texts in topology. The only two that I recall being in use were Hocking and Young and the book by Kelley. Over the years my copy of Hocking and Young has become quite worn. It is a wonderful book that gives the true flavor of topology. It is also contains a large number of topics that one can refer to later on. It becomes quite apparent very earlier that no one will be able to fully appreciate the book in the time span of one course. It is a book that must be read and reread over and over again. It is a real classic. I do not believe that it is the type of book that would be of much or any general interest but to a point set topologist it is a classic and must for his bookself. I am quite surprised over its low price. I can not help but compare it with the newer book by Munkres. I recall seeing Munkres book many years ago and disliking it. But the current edition seems much closer in flavor to HY and Munkres book is quite good. Munkres style is much clearer than HY, but both books target a very specialized group of people. Neither book is for the faint of heart and will take many years to absorb. Considering that Munkres book is 9 times as expensive as HY, HY seems to be the better buy.

Theoretical Dictionary
An excellent book, not for those persons unfamiliar with the topic of topolgy; yet, combined with simpler texts this book is a goldmine of topological theorems and their proofs.

Quite good for self-study
Hocking's book on point-set and algebraic topology is better suited for self-study than any other books covering these subjects that I have read. Any student who has taken one or two analysis/algebra courses might give it a try.

One of the best topology texts with a less formal feel.
I find many areas of this text as lucid and captivating as some of the most famous topology works. While I prefer Munkres' text in a classroom setting, Hocking and Young give an enjoyably different approach with more discussion in some interesting topics. It serves as possibly the best book for self teaching or quick reference. ... Read more

Reviews (1)

It's the Beauty of Mathematics
Well, I have studied these numbers and other fascinating phenomena in mathematics, and I never found it enough. So, every book I read about this stuff I found a new set of new things, or at least a new view/review of the old things I knew. After my short study (7 years now) in the field of Number theory and Related topics, I dare say, that this book was another addition to my knowledge that -thanks GOD- I didn't waste. ... Read more

Book Description

Superb introduction to rapidly expanding area of mathematical thought. Fundamentals of metric spaces, topologies, convergence, compactness, connectedness, homotopy theory and other essentials. Numerous exercises, plus section on paracompactness and complete regularity. References throughout. 107 illustrations.
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Reviews (4)

A wonderful introduction
I used this book for my first course in topology. It's easy to read and well organized. While it is an introduction, the author covers more than other books in it's price range (Baum or Mendelson, for example). The author starts with some set theory basics and then moves to metric spaces, which he uses as motivation for his definition of a topology (Baum and some others use neighborhood systems instead). He then discusses homeomorphism, seperation axioms (T0 through T4), compactness and other topics. The exercises provide a nice level of challenge; they require thought but aren't impossible. I'd recommend this book as a reference, or to anyone interested in higher mathematics. And since it's a Dover book, the prices is right!

A good book as intro in topo
the book follows the straightforward style of proposition-theorem-proof-corollary and full of examples and helpful diagrams. but the notation is not fully compliant with modern topology.

Very interesting Book
This book is very interesting, it is easy to read, it presents many examples and proofs.

It's usefull if you want to make a BS or a MS in topology

Very interesting book
This book is a very good introduction to the topology theory. It is easily understandable, full of examples and proofs. ... Read more

Book Description

This book gives senior undergraduate and beginning graduate students and researchers in computer vision, applied mathematics, computer graphics, and robotics a self-contained introduction to the geometry of 3D vision; that is the reconstruction of 3D models of objects from a collection of 2D images. Following a brief introduction, Part I provides background materials for the rest of the book. The two fundamental transformations, namely rigid body motion and perspective projection are introduced and image formation and feature extraction discussed. Part II covers the classic theory of two view geometry based on the so-called epipolar constraint. Part III shows that a more proper tool for studying the geometry of multiple views is the so- called rank considtion on the multiple view matrix. Part IV develops practical reconstruction algorithms step by step as well as discusses possible extensions of the theory. Exercises are provided at the end of each chapter. Software for examples and algorithms are available on the author's website. ... Read more

Reviews (1)

a must-have book for computer vision students & researchers
The authors do an outstanding job of balancing theory and practice in this book. In particular, Ch. 11 (Step-by-Step Building of a 3-D Model from Images) is a gem. The new student of computer vision that finds Structure from Motion (SFM) daunting should read this chapter first to build motivation by means of seeing concrete examples.
What's most notable about this book is its thoroughness. The authors humbly get their hands dirty with crucial low-level matters like interest point detection and feature tracking. In Ch. 5 and 6 (calibrated and uncalibrated reconstruction) you'll get an excellent treatment of the necessary background in these areas, along with numerous new insights and `nuggets.' This is particularly true in their treatment of homographies. Ch. 2 has all the material on rigid body motion and the exponential map that students used to need to get from Murray, Li and Sastry, once again with substantial added value.
The exercises in all the chapters are very well thought out, and they -- together with the clearly written Algorithm Boxes -- greatly simplify the job of the instructor. (I am currently using this as the text for my graduate level class this quarter.) The appendices (especially the one on Linear Algebra) also help to make this a self-contained resource for SFM.
I haven't gotten into the material on multi-body motion and n>2 views, so I can't comment on those parts(...)In summary, this is a great book, well worth the money. ... Read more

Book Description

Massey's well-known and popular text is designed to introduce advanced undergraduate or beginning graduate students to algebraic topology as painlessly as possible. The principal topics treated are 2-dimensional manifolds, the fundamental group, and covering spaces, plus the group theory needed in these topics. The only prerequisites are some group theory, such as that normally contained in an undergraduate algebra course on the junior/senior level, and a one-semester undergraduate course in general topology. From the reviews: "This book is highly recommended: as a textbook for a first course in algebraic topology and as a book for selfstudy. The spirit of algebraic topology and of good mathematics is present at every page of this almost perfect book." Bulletin de la Société Mathématique de Belgique#1 ... Read more

Reviews (1)

one of the best books on algebraic topology
This is a charming book on algebraic topology.It doesnt teach homology or cohomology theory,still you can find in it:about the fundamental group, the action of the fundamental group on the universal cover (and the concept of the universal cover),the classification of surfaces and a beautifull chapter on free groups and the way it is related to Van-kampen theorem .After reading this book you will have a strong intuitive picture on "what is algebraic topology all about"(well at list on part of algebraic topology)read it an enjoy it!!!. ... Read more

Book Description

This is a softcover reprint of the English translation of 1987 of the second edition of Bourbaki's Espaces Vectoriels Topologiques (1981). This second edition is a brand new book and completely supersedes the original version of nearly 30 years ago. But a lot of the material has been rearranged, rewritten, or replaced by a more up-to-date exposition, and a good deal of new material has been incorporated in this book, all reflecting the progress made in the field during the last three decades. ... Read more

Book Description

Traces effects of geometry on artistic achievement and clearly discusses its importance to artists, scientists, architects, philosophers and others. Special chapters on Vitruvius, Albrecht Dürer and da Vinci, plus a survey of projective geometry, mathematical curves, theories of perspective, architectural form and concepts of space.
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Reviews (1)

Masterpiece!
Most books about arts and mathematics are written by non-mathematicians and often contain dubious or unclear statements. The late professor Pedoe was not just an outstanding mathematician, but also a great expositor. This book shows the breadth of his scholarship.

It is not as flashy as some of the modern books. If you are looking for pretty pictures, then this is not the book for you. However, if you are looking for mathematically and historically correct info, and you have the persistence to actually read it, you will be rewarded.

Highly recommended for teachers of mathematics! ... Read more

Book Description

Some remarkable connections between commutative algebra and combinatorics have been discovered in recent years. This book provides an overview of two of the main topics in this area. The first concerns the solutions of linear equations in nonnegative integers. Applications are given to the enumeration of integer stochastic matrices (or magic squares), the volume of polytopes, combinatorial reciprocity theorems, and related results. The second topic deals with the face ring of a simplicial complex, and includes a proof of the Upper Bound Conjecture for Spheres. An introductory chapter giving background information in algebra, combinatorics and topology broadens access to this material for non-specialists.

New to this edition is a chapter surveying more recent work related to face rings, focusing on applications to f-vectors.

Reviews (3)

This is a research monograph!
For those looking for a thorough introduction to the theory in this book, I would suggest a look at Miller and Sturmfels recent book on combinatorial commutative algebra or the book on Cohen-Macaulay rings by Bruns and Herzog. This is a great book, but I don't think it was intended as a beginners first book . Instead its style concentrates on presenting results found in research-articles ( prior to this book, there doesn't seem to have been any texts giving an overview of the theory ). It is great for looking up results, reading the needed prerequisites without going into details and finding important references.

Green book
Stanley's "green book" is an overview of a new aspect in commutative algebra:its links with combinatorics.Stanley,as one of the pionners on the subject,is the right one to give us this compendius.But,unfortunally,its hard to beguiners.

I dont read this book yet!
I dont read this book yet! ... Read more

Book Description

This book provides an in-depth, state-of-the-art discussion of the theory of finite packings and coverings by convex bodies. It contains various new results and arguments, collects other key data scattered about the literature, and provides a comprehensive treatment of problems whose interplay was not clearly understood prior to this text. Arrangements of congruent convex bodies in Euclidean space are covered, and the density of finite packing and covering by balls in Euclidean, spherical and hyperbolic spaces is considered. ... Read more