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1. Renormalization and Galois Theories (Irma Lectures in Mathematics and Theoretical Physics) by Frederic Fauvet, and Jean-Pierre Ramis Alain Connes | |
Paperback: 279
Pages
(2009-09-15)
list price: US$58.00 -- used & new: US$52.17 (price subject to change: see help) Asin: 3037190736 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description |
2. Noncommutative Geometry by Alain Connes | |
Hardcover: 661
Pages
(1994-12-06)
list price: US$134.00 -- used & new: US$93.80 (price subject to change: see help) Asin: 012185860X Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (4)
The place to find it!
A beautiful subject The main idea of this book is to generalize measure and operator theory to non-commutative situations. In the usual operator theory, von Neumann algebras serve as a generalization of "classical" measure theory. Commutative von Neumann algebras, or W*-algebras as they are sometimes called, are essentially bounded meausurable functions, and have measure spaces as their dual. These facts and a fine movtivation for the subject appear in the introduction to the book. The author shows with great clarity what is involved in extending measure theory to the non-commutative case. What is most interesting about the extensions is that they involve ideas from quantum physics. In addition, readers familiar with K-theory will see some brilliant uses of it in the book, particularly in the extension of BDF-theory to noncommutative situations, namely the KK-theory of Kasparov. The author also gives a taste of physics applications in the very last section of the book. He shows, interestingly, that when space-time is replaced by a product with a certain finite space, the Lagrangian of quantum electrodynamics becomes that of the Standard Model. Although such "add-ons" to space-time are not uncommon in physics (Kaluza-Klein theories being one example), the author's strategy is unique in its use of bimodules, and gives the three lepton generations. There are also many other interesting topics as well in the book, such as how to deal with non-Hausdorff quotient spaces using noncommutative C*-algebras, deformation theory and the Kasparov group, the notion of Morita equivalence, leaf spaces of foliations, the E-theory of morphisms of separable C*-algebras, the extension of de Rham cohomology to a noncommutative framework (cyclic cohomology) and its relation to K-theory, the noncommutative torus and the quantum Hall effect. The book is an excellent source of information on noncommutative geoemtry and with the many references given one can find more detailed proofs. It is a subject that will no doubt continue to make its presence known in mathematics (and physics) in years to come.
Does not stand on its own
One of the most beautiful mathematical ideas of all time |
3. Conversations on Mind, Matter, and Mathematics by Jean-Pierre Changeux, Alain Connes | |
Paperback: 272
Pages
(1998-12-07)
list price: US$30.95 -- used & new: US$14.50 (price subject to change: see help) Asin: 0691004056 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description The problematic status of mathematical objects leads Changeux and Connes to the organization and function of the brain, the ways in which its embryonic and post-natal development influences the unfolding of mathematical reasoning and other kinds of thinking, and whether human intelligence can be simulated, modeled,--or actually reproduced-- by mechanical means. The two men go on to pose ethical questions, inquiring into the natural foundations of morality and the possibility that it may have a neural basis underlying its social manifestations. This vivid record of profound disagreement and, at the same time, sincere search for mutual understanding, follows in the tradition of Poincaré, Hadamard, and von Neumann in probing the limits of human experience and intellectual possibility. Why order should exist in the world at all, and why it should be comprehensible to human beings, is the question that lies at the heart of these remarkable dialogues. Customer Reviews (3)
. . . another man's poison
Pondering the philosophy of understanding mathematics
a pleasant surprise |
4. Noncommutative Geometry: Lectures given at the C.I.M.E. Summer School held in Martina Franca, Italy, September 3-9, 2000 (Lecture Notes in Mathematics / Fondazione C.I.M.E., Firenze) by Alain Connes, Joachim Cuntz, Erik G. Guentner, Nigel Higson, Jerome Kaminker, John E. Roberts | |
Paperback: 349
Pages
(2004-02-12)
list price: US$74.95 -- used & new: US$50.00 (price subject to change: see help) Asin: 3540203575 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Noncommutative Geometry is one of the most deep and vital research subjects of present-day Mathematics. Its development, mainly due to Alain Connes, is providing an increasing number of applications and deeper insights for instance in Foliations, K-Theory, Index Theory, Number Theory but also in Quantum Physics of elementary particles. The purpose of the Summer School in Martina Franca was to offer a fresh invitation to the subject and closely related topics; the contributions in this volume include the four main lectures, cover advanced developments and are delivered by prominent specialists. |
5. Triangle of Thought by Alain Connes, Andre Lichnerowicz, Marcel Paul Schutzenberger | |
Hardcover: 179
Pages
(2001-01-01)
list price: US$34.00 -- used & new: US$23.20 (price subject to change: see help) Asin: 082182614X Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Is there a "primordial truth" that exists beyond the realm of what is provable? More generally, is there a distinction between what is true in mathematics and what is provable? How is mathematics different from other sciences? How is it the same? Does mathematics have an "object" or an "object of study", the way physics, chemistry and biology do? Mathematics is a lens, through which we view the world. Connes, Lichnerowicz, and Schützenberger examine that lens, to understand how it affects what we do see, but also to understand how it limits what we can see. How does a well-informed mathematician view fundamental topics of physics, such as: quantum mechanics, general relativity, quantum gravity, grand unification, and string theory? What are the relations between computational complexity and the laws of physics? Can pure thought alone lead physicists to the right theories, or must experimental data be the driving force? How should we compare Heisenberg's arrival at matrix mechanics from spectral data to Einstein's arrival at general relativity through his thought experiments? The conversations are sprinkled with stories and quotes from outstanding scientists, which enliven the discourse. The book will make you think again about things that you once thought were quite familiar. Customer Reviews (1)
A too abstract triangle |
6. Cyclic cohomology within the differential envelope: An introduction to Alain Connes' non-commutative differential geometry (Travaux en cours) by Daniel Kastler | |
Paperback: 183
Pages
(1988)
Isbn: 2705660445 Canada | United Kingdom | Germany | France | Japan | |
7. Introduction to the Baum-Connes Conjecture by Alain Valette | |
Paperback: 116
Pages
(2002-06-10)
list price: US$34.95 -- used & new: US$32.57 (price subject to change: see help) Asin: 3764367067 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Like the Atiyah-Singer theorem, the Baum-Connes conjecture states that a purely topological object coincides with a purely analytical one. For a given group G, the topological object is the equivariant K-homology of the classifying space for proper actions of G, while the analytical object is the K-theory of the C*-algebra associated with G in its regular representation. The Baum-Connes conjecture implies several other classical conjectures, ranging from differential topology to pure algebra. This book is intended for graduate students and researchers in geometry (commutative or not), group theory, algebraic topology, harmonic analysis, and operator algebras. It presents, for the first time in book form, an introduction to the Baum-Connes conjecture. It starts by defining carefully the objects in both sides of the conjecture, then the assembly map that connects them. Thereafter, it illustrates the main tool to attack the conjecture (Kasparov's theory), and it concludes with a rough sketch of V. Lafforgue's proof of the conjecture for co-compact lattices in Sp(n,1), SL(3,3) and SL(3,"). |
8. Proper Group Actions and the Baum-Connes Conjecture (Advanced Courses in Mathematics - CRM Barcelona) by Guido Mislin, Alain Valette | |
Paperback: 131
Pages
(2003-09-17)
list price: US$49.95 -- used & new: US$43.27 (price subject to change: see help) Asin: 3764304081 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description The Baum-Connes conjecture predicts that the K-homology of the reduced C^*-algebra of a group can be computed as the equivariant K-homology of the classifying space for proper actions. The approach is expository, but it contains proofs of many basic results on topological K-homology and the K-theory of C^*-algebras. It features a detailed introduction to Bredon homology for infinite groups, with applications to K-homology. It also contains a detailed discussion of naturality questions concerning the assembly map, a topic not well documented in the literature. The book is aimed at advanced graduate students and researchers in the area, leading to current research problems. |
9. Géométrie non commutative by Alain Connes | |
Paperback: 240
Pages
(1990-01-01)
Isbn: 2729602844 Canada | United Kingdom | Germany | France | Japan | |
10. Matière à pensée by Jean-Pierre Changeux, Alain Connes | |
Paperback: 267
Pages
(2000-03-30)
Isbn: 2738108156 Canada | United Kingdom | Germany | France | Japan | |
11. Triangle des pensees (Sciences) (French Edition) by Alain Connes | |
Paperback: 214
Pages
(2000)
Isbn: 2738107621 Canada | United Kingdom | Germany | France | Japan | |
12. On Space and Time | |
Hardcover: 320
Pages
(2008-10-31)
list price: US$25.00 -- used & new: US$14.00 (price subject to change: see help) Asin: 052188926X Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (6)
The mathematical universe
On Space and Time
Great book for right audience
Very difficult to follow
Mixed quality |
13. Fields Medalists: Alexander Grothendieck, Paul Cohen, Atle Selberg, René Thom, Edward Witten, Enrico Bombieri, Alain Connes, John Milnor | |
Paperback: 230
Pages
(2010-09-15)
list price: US$31.26 -- used & new: US$31.26 (price subject to change: see help) Asin: 1155862678 Canada | United Kingdom | Germany | France | Japan | |
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14. Differential Geometers: Carl Friedrich Gauss, Bernhard Riemann, Felix Klein, Alain Connes, Gaspard Monge, Elmer Rees | |
Paperback: 250
Pages
(2010-09-14)
list price: US$33.03 -- used & new: US$25.10 (price subject to change: see help) Asin: 1155176898 Canada | United Kingdom | Germany | France | Japan | |
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15. Vanderbilt University Faculty: Alain Connes, Bill Frist, Max Delbrück, Stanley Cohen, Mitchell A. Seligson, John Seigenthaler, Dana D. Nelson | |
Paperback: 258
Pages
(2010-09-15)
list price: US$33.86 -- used & new: US$25.73 (price subject to change: see help) Asin: 1155604318 Canada | United Kingdom | Germany | France | Japan | |
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16. Norwegian Academy of Science and Letters: Thor Heyerdahl, Atle Selberg, Kristen Nygaard, Alain Connes, Gro Harlem Brundtland, Harald Sverdrup | |
Paperback: 528
Pages
(2010-09-15)
list price: US$58.84 -- used & new: US$58.84 (price subject to change: see help) Asin: 115571413X Canada | United Kingdom | Germany | France | Japan | |
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17. Visions in Mathematics: GAFA 2000 Special Volume, Part Ipp. 1-453 (Modern Birkhäuser Classics) | |
Paperback: 453
Pages
(2010-03-22)
list price: US$59.95 -- used & new: US$39.87 (price subject to change: see help) Asin: 3034604211 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description "Visions in Mathematics - Towards 2000" was one of the most remarkable mathematical meetings in recent years. It was held in Tel Aviv from August 25th to September 3rd, 1999, and united some of the leading mathematicians worldwide. The goals of the conference were to discuss the importance, the methods, the past and the future of mathematics as we enter the 21st century and to consider the connection between mathematics and related areas. The aims of the conference are reflected in the present set of survey articles, documenting the state of art and future prospects in many branches of mathematics of current interest. This is the first part of a two-volume set that will serve any research mathematician or advanced student as an overview and guideline through the multifaceted body of mathematical research in the present and near future. |
18. Gedankenmaterie (German Edition) by Jean-Pierre Changeux, Alain Connes | |
Hardcover: 175
Pages
(1992-07-06)
list price: US$35.95 -- used & new: US$35.95 (price subject to change: see help) Asin: 354054559X Canada | United Kingdom | Germany | France | Japan | |
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19. Visions in Mathematics: GAFA 2000 Special Volume, Part IIpp. 455-983 (Modern Birkhäuser Classics) | |
Paperback: 528
Pages
(2010-03-08)
list price: US$59.95 -- used & new: US$49.12 (price subject to change: see help) Asin: 3034604246 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description "Visions in Mathematics - Towards 2000" was one of the most remarkable mathematical meetings in recent years. It was held in Tel Aviv from August 25th to September 3rd, 1999, and united some of the leading mathematicians worldwide. The goals of the conference were to discuss the importance, the methods, the past and the future of mathematics as we enter the 21st century and to consider the connection between mathematics and related areas. The aims of the conference are reflected in the present set of survey articles, documenting the state of art and future prospects in many branches of mathematics of current interest. This is the second part of a two-volume set that will serve any research mathematician or advanced student as an overview and guideline through the multifaceted body of mathematical research in the present and near future. |
20. Matiere a Pensee by Jean-Pierre and Alain Connes Changeux | |
Paperback:
Pages
(1989)
Asin: B000NGT2LY Canada | United Kingdom | Germany | France | Japan | |
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