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1. 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$72.28 (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. |
2. 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 |
3. 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 |
4. From Geometry to Topology by H. Graham Flegg | |
Paperback: 208
Pages
(2001-09-04)
list price: US$14.95 -- used & new: US$9.27 (price subject to change: see help) Asin: 0486419614 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (3)
Perfect book for the right reader
Easy, but okay...
Very nice and intuitive introducation to topology |
5. 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 |
6. A First Course in Geometric Topology and Differential Geometry by Ethan D. Bloch | |
Hardcover: 440
Pages
(1996-12-01)
list price: US$89.95 -- used & new: US$67.41 (price subject to change: see help) Asin: 0817638407 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (5)
Great Book
a remark on omissions
Good introduction After a brief overview of the elementary topology of subsets of Euclidean space in chapter 1, topological surfaces are discussed in chapter 2. Surfaces are built up from arcs, disks, and one-spheres. Unfortunately, the proofs of the theorem of invariance of domain and the Schonflies Theorem are not included, but references are given. Gluing techniques though are effectively discussed, and the author does not hesitate to use diagrams to explain the relevant concepts. The more popular constructions in surface topology, namely the Mobius strip and the Klein bottle are given as examples of the cutting and pasting techniques. The amusing fact that the Klein bottle can be obtained from gluing two Mobius strips along their boundaries is proven. The theory of simplicial surfaces is discussed in the next chapter. Simplicial surfaces are much easier to deal with for beginning students of topology. Simplicial complexes are introduced first, and the author then studies which simplicial complexes have underlying spaces that are topological surfaces. He proves that this is the case when each one-dimensional simplex of the complex is the face of precisely two two-dimensional simplices, and the underlying space of each link of each zero-dimensional simplex of the complex is a one-dimensional sphere. Unfortunately, the author does not prove that any compact topological surface in n-dimensional Euclidean space can be triangulated. The Euler characteristic is defined first for 2-complexes and it is shown that it is the same for two simplicial surfaces that triangulate a compact topological surface. The author does prove in detail the classification of compact connected surfaces. Interestingly, the author also proves a simplicial analogue of the Gauss-Bonnet theorem, and gives a proof of the Brouwer fixed point theorem. The author turns to smooth surfaces in the next few chapters, wherein curves are defined along with the relevant differential-geometric notions such as curvature and torsion. The fundamental theorem of curves is proven. The reader is first introduced to the concept of what in more advanced treatments is called a differentiable manifold, and several concrete examples are given of smooth surfaces. The differential geometry of smooth surfaces is outlined, with the first fundamental form and directional derivatives discussed in great detail. The reader should be familiar with the inverse function theorem to appreciate the discussion of regular values. Even more interesting differential geometry is discussed in chapter 6, which covers the curvature of smooth surfaces. The important Gauss map is defined, along with the Weingarten map and the second fundamental form. This allows an intrinsic notion of curvature, but the author does perform explicit computations of curvature using various choices of coordinates. The proof that Gaussian curvature is intrinsic (Theorema Egregium) is proven, along with the fundamental theorem of surfaces. Geodesics, so important in physical applications, are discussed in the next chapter. The reader gets a first look at the "Christoffel symbols", even though they are not designated as such in the book. The book ends with a thorough treatment of the Gauss-Bonnet theorem for smooth surfaces. The smooth case is much more difficult to prove than the simplicial case, as the reader will find out when studying this chapter. The author also gives a very brief introduction to non-Euclidean geometry.
Presentation of The Spirit...
Just a mediocre book of lesser extent |
7. Three-Dimensional Geometry and Topology by William P. Thurston | |
Hardcover: 320
Pages
(1997-01-17)
list price: US$78.50 -- used & new: US$41.87 (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 |
8. Geometry and Topology in Hamiltonian Dynamics and Statistical Mechanics (Interdisciplinary Applied Mathematics) by Marco Pettini | |
Paperback: 456
Pages
(2010-11-02)
list price: US$79.95 -- used & new: US$56.59 (price subject to change: see help) Asin: 1441921648 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description This book covers a new explanation of the origin of Hamiltonian chaos and its quantitative characterization. The author focuses on two main areas: Riemannian formulation of Hamiltonian dynamics, providing an original viewpoint about the relationship between geodesic instability and curvature properties of the mechanical manifolds; and a topological theory of thermodynamic phase transitions, relating topology changes of microscopic configuration space with the generation of singularities of thermodynamic observables. The book contains numerous illustrations throughout and it will interest both mathematicians and physicists. |
9. 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! |
10. Visual Geometry and Topology by Anatolij T. Fomenko | |
Hardcover: 324
Pages
(1994-02-18)
list price: US$94.00 -- used & new: US$71.70 (price subject to change: see help) Asin: 3540533613 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description |
11. Essential Topology (Springer Undergraduate Mathematics Series) by Martin D. Crossley | |
Paperback: 224
Pages
(2005-07-01)
list price: US$39.95 -- used & new: US$30.74 (price subject to change: see help) Asin: 1852337826 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description This book brings the most important aspects of modern topology within reach of a second-year undergraduate student. It successfully unites the most exciting aspects of modern topology with those that are most useful for research, leaving readers prepared and motivated for further study. Written from a thoroughly modern perspective, every topic is introduced with an explanation of why it is being studied, and a huge number of examples provide further motivation. The book is ideal for self-study and assumes only a familiarity with the notion of continuity and basic algebra. Customer Reviews (4)
Best Intro to Topology
Surely not optimal
Best undergraduate topology book
A pleasure to read |
12. Topology (Undergraduate Texts in Mathematics) by K. Jänich | |
Hardcover: 208
Pages
(1984-01-30)
list price: US$64.95 -- used & new: US$43.79 (price subject to change: see help) Asin: 0387908927 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (5)
great as motivation but not a textbook
A simple introduction to advanced mathematical concepts
Full of motivations Since it does not have any problem sections, I can see why Munkres' book is more popular in college. It still gives some inspiring questions from time to time. Besides the basic pot-set topology, it also covers some algebraic topology and differentialtopology. The author does not hesitate to use examples from those advanced areas without formal definitions, and this was a bit annoying when I read it the first time. In this sense, the book is not really selfcontained. However, when finally a notion is formally defined, I can see it from various aspects in those examples. This really helps me understand topology better, and makes me want to explore them. After reading the existence thm of covering spaces in chapter 9, I realized that mathematics is really an art. The index in the back of the book is in the format of short definitions, which can be used as a quick reference.
Students: BUY THIS BOOK!!! At the end of chapter three, which deals with the quotient topology, the author writes the following paragraph: "If is often said against intuitive, spatial argumentation that it is not really argumentation but just so much gesticulation - just 'handwaving'. Shall we then abandon all intuitive arguments? Certainly not. As long as it is backed by the gold standard of rigorous proofs, the paper money of gestures is an invaluable aid for quick communication and fast circulation of ideas. Long live handwaving!". This has to rank as one of the best paragraphs that has every appeared in a mathematics book, for it nicely summarizes the need for developing a feel for the concepts behind mathematics before moving on to the rigorous proofs. Physicists in particular, who must assimilate mathematics very quickly in order to apply it to real problems must have a pictorial, "playful" understanding of the mathematical constructions. Thus the language that the author employs is informal, and a listing of the best discussions in the book would really entail a listing of every one in the book. There is not one part of the book that is not helpful or interesting, and the author delves into many different areas that involve the use of topology. If you are a beginning student in mathematics, BUY AND STUDY THIS BOOK...BUY AND STUDY THIS BOOK. You will take away so much for the price paid.
Excellent |
13. Differential Geometry and Topology: With a View to Dynamical Systems (Studies in Advanced Mathematics) by Keith Burns, Marian Gidea | |
Hardcover: 400
Pages
(2005-05-27)
list price: US$99.95 -- used & new: US$69.97 (price subject to change: see help) Asin: 1584882530 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Smooth manifolds, Riemannian metrics, affine connections, the curvature tensor, differential forms, and integration on manifolds provide the foundation for many applications in dynamical systems and mechanics. The authors also discuss the Gauss-Bonnet theorem and its implications in non-Euclidean geometry models. The differential topology aspect of the book centers on classical, transversality theory, Sard's theorem, intersection theory, and fixed-point theorems. The construction of the de Rham cohomology builds further arguments for the strong connection between the differential structure and the topological structure. It also furnishes some of the tools necessary for a complete understanding of the Morse theory. These discussions are followed by an introduction to the theory of hyperbolic systems, with emphasis on the quintessential role of the geodesic flow. The integration of geometric theory, topological theory, and concrete applications to dynamical systems set this book apart. With clean, clear prose and effective examples, the authors' intuitive approach creates a treatment that is comprehensible to relative beginners, yet rigorous enough for those with more background and experience in the field. Customer Reviews (2)
Excellent book
A very good book |
14. Invitations to Geometry and Topology (Oxford Graduate Texts in Mathematics, 7) | |
Hardcover: 338
Pages
(2003-01-02)
list price: US$115.00 -- used & new: US$81.68 (price subject to change: see help) Asin: 0198507720 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description |
15. Geometry and Topology for Mesh Generation (Cambridge Monographs on Applied and Computational Mathematics) by Herbert Edelsbrunner | |
Paperback: 190
Pages
(2006-01-09)
list price: US$39.99 -- used & new: US$34.06 (price subject to change: see help) Asin: 052168207X Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (2)
A very nice, clear book
Excellent read for mathematically inclined reader |
16. Topology and Geometry in Physics (Lecture Notes in Physics) | |
Paperback: 360
Pages
(2009-12-15)
list price: US$99.00 -- used & new: US$89.10 (price subject to change: see help) Asin: 3642062091 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Application of the concepts and methods of topology and geometry have led to a deeper understanding of many crucial aspects in condensed matter physics, cosmology, gravity and particle physics. This book can be considered an advanced textbook on modern applications and recent developments in these fields of physical research. Written as a set of largely self-contained extensive lectures, the book gives an introduction to topological concepts in gauge theories, BRST quantization, chiral anomalies, sypersymmetric solitons and noncommutative geometry. It will be of benefit to postgraduate students, educating newcomers to the field and lecturers looking for advanced material. |
17. Geometry and Topology by Miles Reid, Balazs Szendroi | |
Paperback: 196
Pages
(2005-12-19)
list price: US$51.00 -- used & new: US$32.39 (price subject to change: see help) Asin: 0521613256 Canada | United Kingdom | Germany | France | Japan | |
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18. Quadratic Forms with Applications to Algebraic Geometry and Topology (London Mathematical Society Lecture Note Series) (Volume 0) by Albrecht Pfister | |
Paperback: 188
Pages
(1995-10-27)
list price: US$50.00 -- used & new: US$40.89 (price subject to change: see help) Asin: 0521467551 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description |
19. Differential Geometry and Topology (Monographs in Contemporary Mathematics) by A.T. Fomenko | |
Hardcover: 344
Pages
(1987-05-31)
list price: US$245.00 -- used & new: US$217.54 (price subject to change: see help) Asin: 0306109956 Canada | United Kingdom | Germany | France | Japan | |
20. Lectures on Differential Geometry (Conference Proceedings and Lecture Notes in Geometry and Topology) by Richard Schoen, Shing-Tung Yau | |
Hardcover: 414
Pages
(1994-06-01)
list price: US$55.00 -- used & new: US$54.00 (price subject to change: see help) Asin: 1571460128 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description |
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