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21. Elements of Point-Set Topology (Dover Books on Advanced Mathematics) by John D. Baum | |
Paperback: 176
Pages
(2010-07-21)
list price: US$8.95 -- used & new: US$8.95 (price subject to change: see help) Asin: 0486668266 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (2)
What you need to know
An unusual, and unusually good, book on topology |
22. Topology, Geometry and Gauge fields: Foundations (Texts in Applied Mathematics) by Gregory L. Naber | |
Hardcover: 440
Pages
(2010-09-21)
list price: US$74.95 -- used & new: US$64.25 (price subject to change: see help) Asin: 1441972536 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (6)
An Introduction with Mathematical Integrity
correction to dost
Easy reading, complete proofs, plenty of exercises
Don't waste your money
MATH AND TOPOLOGY |
23. A Taste of Topology (Universitext) by Volker Runde | |
Paperback: 182
Pages
(2005-07-06)
list price: US$49.95 -- used & new: US$34.87 (price subject to change: see help) Asin: 038725790X Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description If mathematics is a language, then taking a topology course at the undergraduate level is cramming vocabulary and memorizing irregular verbs: a necessary, but not always exciting exercise one has to go through before one can read great works of literature in the original language. The present book grew out of notes for an introductory topology course at the University of Alberta. It provides a concise introduction to set theoretic topology (and to a tiny little bit of algebraic topology). It is accessible to undergraduates from the second year on, but even beginning graduate students can benefit from some parts. Great care has been devoted to the selection of examples that are not self-serving, but already accessible for students who have a background in calculus and elementary algebra, but not necessarily in real or complex analysis. In some points, the book treats its material differently than other texts on the subject: * Baire's theorem is derived from Bourbaki's Mittag-Leffler theorem; * nets are used extensively, in particular for an intuitive proof of Tychonoff's theorem; * a short and elegant, but little known proof for the Stone-Weierstrass theorem is given. Customer Reviews (1)
Flawless exposition, great examples, short enough to read cover to cover |
24. Algebraic Topology (Volume 0) by Edwin H. Spanier | |
Paperback: 548
Pages
(1994-12-06)
list price: US$79.95 -- used & new: US$40.00 (price subject to change: see help) Asin: 0387944265 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (6)
Pioneering text
For reference ONLY 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 complexesare 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
Excellent reference, poor textbook That said, if you already know the subject Spanier'sbook is an excellent reference. Even here, though, you'll need to providesome details toward the ends of the later chapters. Each chapter starts outrelatively easily and works up to a crescendo, the treatment becomingterser and more advanced. I give it four stars (5 for mathematicalquality, 3 for usefulness as a text). The first three chapters deal withcovering spaces and fibrations; the middle three with (co)homology andduality; the last three with general homotopy theory, obstruction theory,and spectral sequences. Some of Serre's classical results on finitenesstheorems for homotopy groups are presented.
Excellent reference, poor textbook That said, if you already know the subject Spanier'sbook is an excellent reference.Even here, though, you'll need to providesome details toward the ends of the later chapters.Each chapter startsout relatively easily and works up to a crescendo, the treatment becomingterser and more advanced. I give it four stars (5 for mathematicalquality, 3 for usefulness as a text).The first three chapters deal withcovering spaces and fibrations; the middle three with (co)homology andduality; the last three with general homotopy theory, obstruction theory,and spectral sequences.Some of Serre's classical results on finitenesstheorems for homotopy groups are presented. ... Read more |
25. Intuitive Topology (Mathematical World, Vol 4) by V.V. Prasolov | |
Paperback: 93
Pages
(1995-01-01)
list price: US$22.00 -- used & new: US$19.35 (price subject to change: see help) Asin: 0821803565 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description |
26. Experiments in Topology by Stephen Barr | |
Paperback: 210
Pages
(1989-03-01)
list price: US$12.95 -- used & new: US$3.95 (price subject to change: see help) Asin: 0486259331 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (2)
Great book for high school teachers and the popular audience In chapter 1, the author attempts to give an intuitive definition of topology. The author uses various pictures and handwaving arguments to explain various notions in topology, such as homeomorphism ("coffee cup = donut"), simply connected (object with no holes), homology (two circles can intersect at one point only), Jordan curves, and Euler's theorem. In chapter 2, the author uses paper models to illustrate the topology of surfaces, both orientable and nonorientable. The author gives instructions on how to make a paper model of a Klein bottle, but cautions the reader that such a model is not an exact representation of the mathematical object rigorously defined in topology, since the surface passes through itself in the paper construction. Chapter 3 is a set of instructions on how to make a "shortest" Moebius strip. The procedures for doing this are interesting and fun, for the author constructs a Moebius strip whose length is less than its width, by a factor of 1 over the square root of 3. He devotes an appendix for an improvement due to Martin Gardner of Scientific American fame. In chapter 4 the author constructs what he calls a "conical Moebius strip". The author asks the reader to consider an annulus with a radial slit, with which of course one can construct a Moebius strip by twisting the ends and joining them. But he asks how large the hole must be in relation to the outside diameter. The answer to this is that one does not need any hole at all in order to carry out the construction. In fact, an angular segment can be cut out instead of the radial cut, and this leads him to construct the conical Moebius strip. The author returns to the Klein bottle in chapter 5, and shows first what happens if the usual construction of the Klein bottle is cut down the center symmetrically: two Moebius strips are obtained. But to construct this model is difficult, so he gives alternate constructions for making the Klein bottle. He then shows what happens to the various models when the pieces are cut. But how do you make a projective plane using scissors and paper? Intuitively one can imagine this would be very difficult, but the author shows ways to do it in chapter 6. His strategy for making these models is to teach the concept of symmetry in topology, and he pulls this off very well. The famous 4-color problem for maps, i.e. that one needs only 4 colors for a map, is considered in chapter 7. At the time of publication, the 4-color problem was still open, so the author attempts to try and explain it using various diagrams and subdivisions thereof. The 4-color problem was proved using computer algorithms by the mathematicians K. Appel and W. Haken in 1976. Network topology is considered in chapter 8, with the famous Koenigsberg bridge problem leading off the discussion. The author also introduces the very important Betti numbers, these having far-reaching ramifications in topology. And interestingly, the author is able, via a consideration of loop-cuts and cross-cuts in paper models of the Klein bottle and projective plane, to introduce the very important concept of "duality". The theory of knots makes its appearance here, although the discussion is very short. The author is well-aware of the difficulties in finding a classification theory of knots, but more could possibly be done here in the lines of the rest of the book to illustrate some of the peculiarities of knots. Chapter 9 is really fun, for it concerns the torus with a puncture, and how to turn it inside out. The diagrams are helpful and the intuition gained valuable. The mathematician Steven Smale found a way of turning the sphere inside out in the early 1060s, but the author does not tackle Smale's method! This is unfortunate, since it is very difficult to follow the steps in Smale's method, at least for me. The author does not want to leave the reader with the impression that topology is all scissors, paper, and tape, so he devotes the last two chapters of the book to point-set topology. Concepts such as continuity, limit points, and neighborhoods are discussed. It is quite difficult to explain to beginning readers and students of topology what a neighborhood actually does without having the notion of a metric or distance, but the author does a fairly good job here.
useful but not broad enough |
27. Differential Forms in Algebraic Topology (Graduate Texts in Mathematics) by Raoul Bott, Loring W. Tu | |
Paperback: 350
Pages
(2010-11-02)
list price: US$74.95 -- used & new: US$60.14 (price subject to change: see help) Asin: 1441928154 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (7)
a masterpiece of exposition
So far so good
good book
wonderfully clear, useful book
A unique mathematics book That makes this one of my all time favourite mathematics texts. ... Read more |
28. Geometry, Topology and Physics, Second Edition (Graduate Student Series in Physics) by Mikio Nakahara | |
Paperback: 596
Pages
(2003-06-04)
list price: US$73.95 -- used & new: US$72.46 (price subject to change: see help) Asin: 0750306068 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (13)
Excellent review of math for (particle) physicists
Too many errors to be useful for study
Geometry Topology and Physics: A condesed view
An excellent book
A great reference book. |
29. Elements Of Algebraic Topology by James R. Munkres | |
Paperback: 464
Pages
(1996-01-01)
list price: US$76.00 -- used & new: US$68.40 (price subject to change: see help) Asin: 0201627280 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Customer Reviews (4)
Not bad..
A little incomplete However I think it is a little incomplete because of several reasons. (1)It pays no attention to one basic concept ofalgebraic topology: the fundamental group. (2) It doesn't cover ^Cechhomology, important in other areas, like dimension theory forexample. (3) It doesn't stress the most important feature of algebraictopology: 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 alwaysimportant to become an expert in any field. Conclusion: a good referenceon homology and cohomology essentials, but not "the" reference onalgebraic topology as a whole.
The book binding is horrible - Munkres really belabors the simplicial theory, and it getsto be quite painful (especially the*CHAPTER* on the topologicalinvariance of simplicial homology groups). - Some very important topics(homotopy theory, fiber bundles) are not at all discussed. - The bookbinding 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 * point set topology (e.g. in Munkres' Topology) * Abstract algebra * Mathematicalmaturity to be willing to follow a definition and argument even when itseems like a weird side-track In addition, this would not be the firstbook I would recommend to those interested in algebraic topology.Firstmight be Massey's "Algebraic Topology: and Introduction" thatintroduces the fundamental group (conceptually easier than homology andcohomology). At some point, however, a prospective student in topologywill have to learn homological algebra and this provides the most concreteapproach I know to the subject. Algebraic topology is a lot of fun, butmany of the previous textbooks had not given that impression.This onedoes. ... Read more |
30. Topology of Surfaces (Undergraduate Texts in Mathematics) by L.Christine Kinsey | |
Hardcover: 296
Pages
(1993-10-08)
list price: US$74.95 -- used & new: US$49.00 (price subject to change: see help) Asin: 0387941029 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Exercises are an integral part of the text. Students taking the course should have some knowledge of linear algebra. An appendix provides a brief survey of the necessary background of group theory. Customer Reviews (4)
Not great but good
The best undergrad topology text
great Topology text
A very readable introduction to homology. |
31. Elementary Concepts of Topology by Paul Alexandroff | |
Paperback: 57
Pages
(1961-06-01)
list price: US$5.95 -- used & new: US$2.85 (price subject to change: see help) Asin: 048660747X Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (5)
Homology theory
A very bad topology book
a mental roadmap For sophisticated mathematical readers only. Perfect adjunct to any first course. (And a "lemniscate" is a figure 8).
A Gem Anyone can follow this who has had multivariable calculus, plus seen the definition of a group (as in, say, arithmetic modulo 2).In 55 profusely illustrated yet rigorous pages Alexandroff shows how to define topological manifolds, cut them into "simplices", and keep track of simplices algebraically. He proves the two founding theorems of topology: the dimension of manifolds, and their homology groups, are both preserved by topological isomorphisms. Alexandroff was a favorite student of Emmy Noether, and L.E.J. Brouwer, and followed Hilbert's lectures. The greatest algebraist, the greatest topologist, and the greatest mathematician of the early 20th century all had direct input into this book. All believed the most important, deepest mathematics can be made the clearest. They were right.
Excellent first exposure to algebraic topology. |
32. An Introduction to Algebraic Topology (Dover Books on Mathematics) by Andrew H. Wallace | |
Paperback: 208
Pages
(2007-02-27)
list price: US$12.95 -- used & new: US$8.26 (price subject to change: see help) Asin: 0486457869 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description |
33. Basic Concepts of Algebraic Topology (Undergraduate Texts in Mathematics) by F.H. Croom | |
Paperback: 196
Pages
(1978-03-18)
list price: US$69.95 -- used & new: US$14.77 (price subject to change: see help) Asin: 0387902880 Canada | United Kingdom | Germany | France | Japan | |
34. Topology and Geometry (Graduate Texts in Mathematics) by Glen E. Bredon | |
Paperback: 557
Pages
(2010-11-02)
list price: US$79.95 -- used & new: US$64.09 (price subject to change: see help) Asin: 1441931031 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description This book offers an introductory course in algebraic topology. Starting with general topology, it discusses differentiable manifolds, cohomology, products and duality, the fundamental group, homology theory, and homotopy theory. From the reviews: "An interesting and original graduate text in topology and geometry...a good lecturer can use this text to create a fine course....A beginning graduate student can use this text to learn a great deal of mathematics."—-MATHEMATICAL REVIEWS Customer Reviews (7)
never really liked it
a different perspective
excellent for first year graduate study
Among the best textbooks in algebraic topology.
The Graduate Sudent's Topology Bible |
35. Topology (Second Edition) by James R Munkres | |
Paperback: 537
Pages
(2000)
Isbn: 0876922906 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Customer Reviews (8)
Quite possibly the best text book written on any subject eve Many books, especially thosein the more theoretic regions of upper level mathematics are difficult toread, let alone use as a self-study text.The truth is that there is noreal need for an instructor when using this book.The only book that Ithink may be its equal or better is Griffith's book onElectro-Magnetics. I have studied a great deal of mathematics, and I wishall the books I have laerned from (or tried!) were written HALF as well asthis one. The content includes most, if not all, regions of fundamentalpoint-set topology.There is next to know differential or algebraictopology, but there are other texts for that.The illustrations areextremely helpful (and I am not even a visual learner!).It would bedifficult to give too much praise to this book, which is as comprehensiveas it is lucid.
Greatest math textbook I've read Butthis detail does not obfuscate matters.Munkres remains understandable. On the harder proofs he usually breaks things up into several steps, whichkeeps things readable.His examples are interesting, and his exercisesrange from easy to extremely difficult; actually most of them are of mediumdifficulty/somewhat hard variety. I really feel that I'm getting a goodunderstanding of topology in my topology class, mainly because of thisbook.The challenging exercises give me confidence that my feeling isbased on some actual fact.All in all, a good experience.Hmmm...I guessI better finish reading the proof of the Jordan Curve Theorem.And getcracking on those homework problems.
great for independent studies
Would be better iff....
Excellent introduction: makes point set topology fun Although not a hot research topic (compared to the rest of topology), it is foundationaland as such many have assumed that point set topology could only bepresented as a dull prerequisite for more interesting mathematics. Munkres' book, though, treats it as a goal of itself, as a fun world toplay in, and as such, has attracted many students to topology. It isrecommended that a student first learn about metric spaces in a first-yearundergraduate analysis class before learning about point set topology. Although the material is self-contained, the motivations for thedefinitions are hard to understand without knowing the more mundaneexamples. ... Read more |
36. A basic course in algebraic topology (v. 127) by W.S. Massey | |
Hardcover: 452
Pages
(1980-04-29)
list price: US$74.95 -- used & new: US$45.31 (price subject to change: see help) Asin: 038797430X Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (2)
Good for newbies
Excellent text on algebraic topology |
37. Essentials of Topology with Applications (Textbooks in Mathematics) by Steven G. Krantz | |
Hardcover: 420
Pages
(2009-07-28)
list price: US$89.95 -- used & new: US$58.00 (price subject to change: see help) Asin: 1420089749 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Brings Readers Up to Speed in This Important and Rapidly Growing Area Supported by many examples in mathematics, physics, economics, engineering, and other disciplines, Essentials of Topology with Applications provides a clear, insightful, and thorough introduction to the basics of modern topology. It presents the traditional concepts of topological space, open and closed sets, separation axioms, and more, along with applications of the ideas in Morse, manifold, homotopy, and homology theories. After discussing the key ideas of topology, the author examines the more advanced topics of algebraic topology and manifold theory. He also explores meaningful applications in a number of areas, including the traveling salesman problem, digital imaging, mathematical economics, and dynamical systems. The appendices offer background material on logic, set theory, the properties of real numbers, the axiom of choice, and basic algebraic structures. Taking a fresh and accessible approach to a venerable subject, this text provides excellent representations of topological ideas. It forms the foundation for further mathematical study in real analysis, abstract algebra, and beyond. Customer Reviews (1)
Poorly conceived and executed |
38. General Topology by John Leroy Kelley | |
Paperback: 314
Pages
(2008-09-10)
list price: US$25.95 -- used & new: US$20.00 (price subject to change: see help) Asin: 0923891552 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (6)
a splendid technical book
Generally great; a few annoyances
Topology with the analyst in mind!
May have been good in its day
The great classic of point set topology |
39. Three-Dimensional Geometry and Topology by William P. Thurston | |
Hardcover: 320
Pages
(1997-01-17)
list price: US$78.50 -- used & new: US$41.95 (price subject to change: see help) Asin: 0691083045 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (4)
a decent book, but
This book is the real deal by comparison
A refreshing style of writing
fun and geometric-intuition-minded Most of it isreadable to undergraduates.Its target audience, though, is beginninggraduate students in mathematics.If not already familiar with hyperbolicgeometry, you might want to get an introduction to the subject first.Oncewith this background, though, you will discover there is another level ofunderstanding of hyperbolic space you never realized was possible.Oneimagines Thurston able to skateboard around hyperbolic space with the kindof geometric understanding he conveys here. What made Thurston so famousand successful as a pioneer in 3-d topology and geometry was hisother-worldly geometric intuition.This book takes the reader along thefirst step of the 10000 miles of getting to that intuition. ... Read more |
40. Combinatorial Algebraic Topology (Algorithms and Computation in Mathematics) by Dimitry Kozlov | |
Paperback: 390
Pages
(2008-01-30)
list price: US$59.95 -- used & new: US$39.37 (price subject to change: see help) Asin: 3540730516 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Combinatorial algebraic topology is a fascinating and dynamic field at the crossroads of algebraic topology and discrete mathematics. This volume is the first comprehensive treatment of the subject in book form. The first part of the book constitutes a swift walk through the main tools of algebraic topology, including Stiefel-Whitney characteristic classes, which are needed for the later parts. Readers - graduate students and working mathematicians alike - will probably find particularly useful the second part, which contains an in-depth discussion of the major research techniques of combinatorial algebraic topology. Our presentation of standard topics is quite different from that of existing texts. In addition, several new themes, such as spectral sequences, are included. Although applications are sprinkled throughout the second part, they are principal focus of the third part, which is entirely devoted to developing the topological structure theory for graph homomorphisms. The main benefit for the reader will be the prospect of fairly quickly getting to the forefront of modern research in this active field. Customer Reviews (1)
Help, where are the editors? |
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