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41. General Topology: Chapters 1-4 by Nicolas Bourbaki | |
Paperback: 452
Pages
(1998-09-18)
list price: US$74.95 -- used & new: US$55.14 (price subject to change: see help) Asin: 3540642412 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description This is the softcover reprint of the 1971 English translation of the first four chapters of Bourbaki’s Topologie Generale. It gives all basics of the subject, starting from definitions. Important classes of topological spaces are studied, and uniform structures are introduced and applied to topological groups. In addition, real numbers are constructed and their properties established. Customer Reviews (2)
a solid introduction
the book that the experts study 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 |
42. Algebraic Topology by C. R. F. Maunder | |
Paperback: 384
Pages
(1996-06-14)
list price: US$16.95 -- used & new: US$10.00 (price subject to change: see help) Asin: 0486691314 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (3)
Solid
Shouldn't be your first text in algebraic topology. 1. Needs more pictures, especially for the simplicialhomology Chapter. 2. CW complexes should be covered before duality and not after. 3. Needs more examples and exercises. Overall, the book is very good, if you have already someexperience in Algebraic Topology. I found that the Croom'sbook "Basic concepts of Algebraic Topology" is an excellent first textbook. Too bad it is out of print, since it is very popular, every time I get it from the library, someone else recalls it. The combination of these two books probablyis the right thing to have: Maunder's book picks up whereCroom has left you.
Not bad. |
43. Differential Topology: First Steps by Andrew H. Wallace | |
Paperback: 144
Pages
(2006-10-27)
list price: US$9.95 -- used & new: US$5.39 (price subject to change: see help) Asin: 0486453170 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (5)
Difficult to learn from.
pictorial approach is great for total beginners, but lacks rigor
Your First Time
a delight
A quickie on differential topology |
44. Algebraic Topology: An Introduction (Graduate Texts in Mathematics) (v. 56) by William S. Massey | |
Hardcover: 292
Pages
(1977-11-02)
list price: US$84.95 -- used & new: US$48.66 (price subject to change: see help) Asin: 0387902716 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (1)
one of the best books on algebraic topology |
45. Differential Topology: An Introduction (Dover Books on Mathematics) by David B. Gauld | |
Paperback: 256
Pages
(2006-03-24)
list price: US$15.95 -- used & new: US$7.99 (price subject to change: see help) Asin: 048645021X Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (2)
Should've been better, but a bit too unorthodox
Very good product |
46. Categories, Bundles and Spacetime Topology (Mathematics and Its Applications) by C.T. Dodson | |
Paperback: 268
Pages
(2010-11-02)
list price: US$214.00 -- used & new: US$214.00 (price subject to change: see help) Asin: 9048184525 Canada | United Kingdom | Germany | France | Japan | |
47. A General Topology Workbook by Iain T. Adamson | |
Paperback: 164
Pages
(1995-11-29)
list price: US$59.95 -- used & new: US$38.33 (price subject to change: see help) Asin: 081763844X Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (1)
A concentrated, intense way to learn general topology The Moore method has its defenders and detractors. It certainly encourages originality of thought and strict intellectual honesty. Students can find incredible reinforcment as they discover that they can indeed give original proofs of sometimes very difficult (and famous) results in general topology. The downside is that not as much material is covered as compared to a traditional course in general topology. Students who are hungry to get to the frontiers of research might become impatient because of this. This book does not follow the strict methodologies that we followed in our class, but instead reveals to the reader which results are true and then encourages their proof. Readers are also lead through the construction of examples and counterexamples, allowing them to gain more of the intuition needed for a thorough understanding of general topology. It is also a good book to use for independent study, as the answers to the results are given in the book (and this actually is the major portion of its bulk). ... Read more |
48. Topology Now! (Classroom Resource Material) by Robert Messer, Philip Straffin | |
Hardcover: 240
Pages
(2006-03-15)
list price: US$59.95 -- used & new: US$45.00 (price subject to change: see help) Asin: 0883857448 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Anyone using this book should have some exposure to the geometry of objects in higher-dimensional Euclidean spaces together with an appreciation of precise mathematical definitions and proofs.Multivariable calculus, linear algebra, and one further proof-oriented mathematics courses are suitable preparation. Customer Reviews (3)
Don't buy this book
Product exactly as ordered, arrived quickly in great condition
Understandable is an understatement of the quality of the presentations |
49. Algebraic Topology by William Fulton | |
Paperback: 430
Pages
(1995-07-27)
list price: US$49.95 -- used & new: US$29.92 (price subject to change: see help) Asin: 0387943277 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description The first part of the book emphasizes relations with calculus and uses these ideas to prove the Jordan curve theorem. The study of fundamental groups and covering spaces emphasizes group actions. A final section gives a taste of the generalization to higher dimensions. Customer Reviews (3)
A book of ideas As a warm-up in Part 1, the author gives an overview of calculus in the plane, with the intent of eventually defining the local degree of a mapping from an open set in the plane to another. This is done in the second part of the book, where winding numbers are defined, and the important concept of homotopy is introduced. These concepts are shown to give the fundamental theorem of algebra and invariance of dimension for open sets in the plane. The delightful Ham-Sandwich theorem is discussed along with a proof of the Lusternik-Schnirelman-Borsuk theorem. I would like to see a constructive proof of this theorem, but I do not know of one. Part 3 is the tour de force of algebraic topology, for it covers the concepts of cohomology and homology. The author pursues a non-traditional approach to these ideas, since he introduces cohomology first, via the De Rham cohomology groups, and these are used to proved the Jordan curve theorem. Homology is then effectively introduced via chains, which is a much better approach than to hit the reader with a HOM functor.Part 4 discusses vector fields and the discussion reads more like a textbook in differential topology with the emphasis on critical points, Hessians, and vector fields on spheres. This leads naturally to a proof of the Euler characteristic. The Mayer-Vietoris theory follows in Part 5, for homology first and then for cohomology. The fundamental group finally makes its appearance in Part 6 and 7, and related to the first homology group and covering spaces. The author motivates nicely the Van Kampen theorem. A most interesting discussion is in part 8, which introduces Cech cohomology. The author's treatment is the best I have seen in the literature at this level. This is followed by an elementary overview of orientation using Cech cocycles. All of the constructions done so far in the plane are generalized to surfaces in Part 9. Compact oriented surfaces are classified and the second de Rham cohomology is defined, which allows the proof of the full Mayer-Vietoris theorem. The most important part of the book is Part 10, which deals with Riemann surfaces. The author's treatment here is more advanced than the rest of the book, but it is still a very readable discussion. Algebraic curves are introduced as well as a short discussion of elliptic and hyperelliptic curves. The level of abstraction increases greatly in the last part of the book, where the results are extended to higher dimensions. Homological algebra and its ubiquitous diagram chasing are finally brought in, but the treatment is still at a very understandable level. For examples of the author's pedagogical ability, I recommend his book Toric Varieties, and his masterpiece Intersection Theory.
This is one of the great algebraic topology books!
Probably better as a 2nd (or 3rd) course rather than 1st |
50. Introduction to Topology: Pure and Applied by Colin Adams, Robert Franzosa | |
Hardcover: 512
Pages
(2007-06-28)
list price: US$141.33 -- used & new: US$63.95 (price subject to change: see help) Asin: 0131848690 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Learn the basics of point-set topology with the understanding of its real-world application to a variety of other subjects including science, economics, engineering, and other areas of mathematics. Introduces topology as an important and fascinating mathematics discipline to retain the readers interest in the subject. Is written in an accessible way for readers to understand the usefulness and importance of the application of topology to other fields. Introduces topology concepts combined with their real-world application to subjects such DNA, heart stimulation, population modeling, cosmology, and computer graphics. Covers topics including knot theory, degree theory, dynamical systems and chaos, graph theory, metric spaces, connectedness, and compactness. A useful reference for readers wanting an intuitive introduction to topology. Customer Reviews (5)
Very understandable
Not for Math Majors
Fabulous Introduction to Topology!
An excellent text with supporting website
A great introduction to pure and applied topology |
51. Topology: An Introduction to the Point-Set and Algebraic Areas by Donald W. Kahn | |
Paperback: 217
Pages
(1995-07-19)
list price: US$12.95 -- used & new: US$2.95 (price subject to change: see help) Asin: 0486686094 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (5)
Good book / Great supplement
Who cares who writes the reviews
Not Funny, Professor
Excellent Text--Dad you were right.
Dad approves! |
52. Basic Topology: A Developmental Course for Beginners by Dan Edwin Christie | |
Hardcover: 256
Pages
(1976-04)
list price: US$16.95 -- used & new: US$65.72 (price subject to change: see help) Asin: 0023224401 Canada | United Kingdom | Germany | France | Japan | |
53. Elementary Topology: Second Edition by Michael C. Gemignani | |
Paperback: 288
Pages
(1990-11-01)
list price: US$11.95 -- used & new: US$6.65 (price subject to change: see help) Asin: 0486665224 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (8)
Not really elementary but fine for self-study
classic introduction
Too Abbreviated
A model of textbook writing
A wonderful introduction |
54. Homology theory: A first course in algebraic topology (Holden-Day series in mathematics) by Sze-Tsen Hu | |
Hardcover: 247
Pages
(1966)
Asin: B0006BOF7M Canada | United Kingdom | Germany | France | Japan | |
55. Topology and Geometry for Physicists by Charles Nash, Siddhartha Sen | |
Paperback: 320
Pages
(2011-01-20)
list price: US$14.95 -- used & new: US$10.08 (price subject to change: see help) Asin: 0486478521 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (6)
Excellent overview and graphical explanation
Excellent overview and graphical explanation
Good attempt Some of the concepts that need more in-depth explanation include: the theory of characteristic classes, sheaf theory, the theory of schemes in algebraic geometry, and spectral sequences in algebraic topology. There are of course many others, and some of the ones that the authors do a fairly good job of explaining in this book include: 1. the reason that the continuity of a function is defined in terms of inverses of open sets; 2. The orientability of a manifold; 3. The fundamental group and its relation with the first homology group. 4. The discussion on Morse theory.
Covers a lot of ground . . . but not always well
flawed and incomplete |
56. Algorithmic Topology and Classification of 3-Manifolds (Algorithms and Computation in Mathematics) by Sergei Matveev | |
Paperback: 492
Pages
(2010-11-02)
list price: US$89.95 -- used & new: US$80.96 (price subject to change: see help) Asin: 3642079601 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description From the reviews of the 1st edition: "This book provides a comprehensive and detailed account of different topics in algorithmic 3-dimensional topology, culminating with the recognition procedure for Haken manifolds and including the up-to-date results in computer enumeration of 3-manifolds. Originating from lecture notes of various courses given by the author over a decade, the book is intended to combine the pedagogical approach of a graduate textbook (without exercises) with the completeness and reliability of a research monograph… All the material, with few exceptions, is presented from the peculiar point of view of special polyhedra and special spines of 3-manifolds. This choice contributes to keep the level of the exposition really elementary. In conclusion, the reviewer subscribes to the quotation from the back cover: "the book fills a gap in the existing literature and will become a standard reference for algorithmic 3-dimensional topology both for graduate students and researchers". Zentralblatt für Mathematik 2004 For this 2nd edition, new results, new proofs, and commentaries for a better orientation of the reader have been added. In particular, in Chapter 7 several new sections concerning applications of the computer program "3-Manifold Recognizer" have been included. |
57. Measure, Topology, and Fractal Geometry (Undergraduate Texts in Mathematics) by Gerald Edgar | |
Hardcover: 272
Pages
(2007-11-26)
list price: US$54.95 -- used & new: US$35.00 (price subject to change: see help) Asin: 0387747486 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description From reviews of the first edition: "In the world of mathematics, the 1980's might well be described as the "decade of the fractal". Starting with Benoit Mandelbrot's remarkable text The Fractal Geometry of Nature, there has been a deluge of books, articles and television programmes about the beautiful mathematical objects, drawn by computers using recursive or iterative algorithms, which Mandelbrot christened fractals. Gerald Edgar's book is a significant addition to this deluge. Based on a course given to talented high- school students at Ohio University in 1988, it is, in fact, an advanced undergraduate textbook about the mathematics of fractal geometry, treating such topics as metric spaces, measure theory, dimension theory, and even some algebraic topology...the book also contains many good illustrations of fractals (including 16 color plates)." Mathematics Teaching "The book can be recommended to students who seriously want to know about the mathematical foundation of fractals, and to lecturers who want to illustrate a standard course in metric topology by interesting examples." Christoph Bandt, Mathematical Reviews "...not only intended to fit mathematics students who wish to learn fractal geometry from its beginning but also students in computer science who are interested in the subject. Especially, for the last students the author gives the required topics from metric topology and measure theory on an elementary level. The book is written in a very clear style and contains a lot of exercises which should be worked out." H.Haase, Zentralblatt About the second edition: Changes throughout the text, taking into account developments in the subject matter since 1990; Major changes in chapter 6. Since 1990 it has become clear that there are two notions of dimension that play complementary roles, so the emphasis on Hausdorff dimension will be replaced by the two: Hausdorff dimension and packing dimension. 6.1 will remain, but a new section on packing dimension will follow it, then the old sections 6.2--6.4 will be re-written to show both types of dimension; Substantial change in chapter 7: new examples along with recent developments; Sections rewritten to be made clearer and more focused. Customer Reviews (4)
some new material->same approach
A nice book
Good starting point to study fractal geometry. Suitable for 3rd-year undergrads.Interesting examples and exercises. Extensive bibliography. Please checkmy other reviews in my member page (just click on my name above).
A difficult but worthy book! |
58. Topology for Analysis by Albert Wilansky | |
Paperback: 400
Pages
(2008-10-17)
list price: US$22.95 -- used & new: US$9.69 (price subject to change: see help) Asin: 0486469034 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (1)
Excellent complement for General Topology |
59. Algebraic Topology: An Intuitive Approach (Translations of Mathematical Monographs) by Hajime Sato | |
Paperback: 118
Pages
(1999-02)
list price: US$29.00 -- used & new: US$22.99 (price subject to change: see help) Asin: 0821810464 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description In response to suggestions from readers of the original edition of this book, Sato has added an appendix of useful definitions and results on sets, general topology, groups and such. He has also provided references. Topics covered include fundamental notions such as homeomorphisms, homotopy equivalence, fundamental groups and higher homotopy groups, homology and cohomology, fiber bundles, spectral sequences and characteristic classes. Objects and examples considered in the text include the torus, the Möbius strip, the Klein bottle, closed surfaces, cell complexes and vector bundles. Customer Reviews (5)
"Intuition" more a prerequisite than a result
Excelent Start
Excellent accompaniment to Hatcher
Good Supplementary Reading The book presents the most basic ideas pertaining to homotopy, homology, cohomology, fibre bundles, spectral sequences, and characteristic classes. The emphasis is on simple examples and simple calculations to demonstrate what is going on. Rigorous definitions, proofs, and even frequently even the statements of theorems, are avoided. One good aspect of the treatment is the axiomatic presentation of homology and cohomology a la Eilenberg and Steenrod. Some of the essential material is also presented, e.g. the cup product that gives a ring structure to the cohomology group, the Kunneth theorem, the Universal Coefficient theorem, and so on. The book would afford a bird's-eye view, a conspectus, to a bright undergraduate or beginning graduate student. It goes without saying, of course, that this is for motivation, and it doesn't replace the hard technical grind required to master the subject. The book suffers in comparison to the one by Fomenko, Fuchs and Gutenmacher (Homotopic Topology), but that, alas, can't be had for love or money.
algeblaic topology |
60. A First Course in Algebraic Topology by Czes Kosniowski | |
Paperback: 280
Pages
(1980-10-31)
list price: US$38.99 -- used & new: US$31.29 (price subject to change: see help) Asin: 0521298644 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (1)
Very well written introduction. |
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