Product Description
This volume is the outcome of a CIRM Workshop on Renormalization and Galois Theories held in Luminy, France, in March 2006. The subject of this workshop was the interaction and relationship between four currently very active areas: renormalization in quantum field theory (QFT), differential Galois theory, noncommutative geometry, motives and Galois theory. The last decade has seen a burst of new techniques to cope with the various mathematical questions involved in QFT, with notably the development of a Hopf-algebraic approach and insights into the classes of numbers and special functions that systematically appear in the calculations of perturbative QFT (pQFT). The analysis of the ambiguities of resummation of the divergent series of pQFT, an old problem, has been renewed, using recent results on Gevrey asymptotics, generalized Borel summation, Stokes phenomenon and resurgent functions. The purpose of the present book is to highlight, in the context of renormalization, the convergence of these various themes, orchestrated by diverse Galois theories. It contains three lecture courses together with five research articles and will be useful to both researchers and graduate students in mathematics and physics. ... Read more

Product Description
This English version of the path-breaking French book on this subject gives the definitive treatment of the revolutionary approach to measure theory, geometry, and mathematical physics developed by Alain Connes. Profusely illustrated and invitingly written, this book is ideal for anyone who wants to know what noncommutative geometry is, what it can do, or how it can be used in various areas of mathematics, quantization, and elementary particles and fields.

Key Features
* First full treatment of the subject and its applications
* Written by the pioneer of this field
* Broad applications in mathematics
* Of interest across most fields
* Ideal as an introduction and survey
* Examples treated include:
@subbul* the space of Penrose tilings
* the space of leaves of a foliation
* the space of irreducible unitary representations of a discrete group
* the phase space in quantum mechanics
* the Brillouin zone in the quantum Hall effect
* A model of space time ... Read more

Customer Reviews (4)

The place to find it!
This is *the book* on noncommutative geometry. Alain Connes created the main parts of the theory, and paved the way for
its many exciting applications. As most would expect, the book
covers operator algebras, quantum theory, and other areas of mathematical physics; --but, in addition, there is a lovely treatment of tiling theory[Penrose tilings, cartwheel tilingsand the like], of the Dixmier trace, of groupoids, and of foliations.-- All new subjects: intriguing and penetrating!

A beautiful subject
Even though detailed proofs are omitted for most of the major results, the book is an excellent overview of a beautiful subject that the author has made substantial contributions to. The subject of noncommutative geometry has recently made its way into theoretical physics, and so a perusal of this book would be of interest to individuals working in string theory or quantum field theory.

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
I must depart a bit from the previous breathless outpourings about this book. The fact is, it is a whirlwind TOUR (or travellog) of noncommutative geometry, not anything like a handbook of it, or even an atlas of detailed maps of it. I say this because theorems are asserted but almost never proved, no 'problems' are worked, and it is my experience and universally that of all mathematicians/physicists I know, no matter how gifted, that one cannot really understand the subject matter without doing problems! The previous reviewer does hint: "even if you do not know the subject matter" - aye, there's the rub! I appreciate the author's gifts, and I can compass his vision of how useful his approach might be, but between rather trivial points in quantum mechanics to very abstruse theorems in abstract harmonic analysis there is no bridge provided, and the original literature, either by Connes or his predecessor Dixmier, is practically all in French. If you already know this stuff, it might be useful to have all the relevant topics gathered together in one place, but if you don't already know it, you are going to be disappointed. Customers should be aware of this fact before they shell out the bucks. A much better book covering similar ground, but at a more directly physical and more elementary level, is Souriau's: "Structure of Dynamical Systems. A Symplectic View of Physics" Although that work again doesn't have worked exercises. I wonder, is it just the STYLE in French literature nowadays to DISCOURSE about mathematics, instead of DEMONSTRATING it? Rather like a self-fulfillment of the Derrida-Lacan-Latour-deconstructionist position about scientific communities and their provenance, I'd say.

One of the most beautiful mathematical ideas of all time
This book is a source of inspiration. Alain Connes' breathtaking idea of taking Heisenberg's matrix mechanics to the last consequences - substituting algebras of vector spaces by algebras of operators in allbranches of mathematics in which this concept arises - gave rise to a newworld of concepts that permits to treat deep and esoteric topics in manybranches of mathematics and physics. It provides so a deep and shockinginsight into geometric topics as did quantum mechanics with the microscopicphysics. However, his book has its problems: beyond the lack of apedagogical introduction to noncommutative geometry, which is a inexistentthing in the realm of mathematical texts, it asks too many prerequisites:operator algebras, differential geometry, abstract algebra, measure theory,topology... It collects much more results than basic principles (as seen bythe enormous quantity of papers in the bibliography). Nevertheless, theseprovisos don't obscure the captivating power of this work, and although Icouldn't manage to understand many of the topics treated, it moved me somuch that I became really interested in doing research on this field. Evenif you don't have all the needed knowledge, but have interests in math andphysics (particularly in "quantizing" things), give a try to thisbook (no wonder Connes is a Fields Medalist). ... Read more

Product Description
Do numbers and the other objects of mathematics enjoy a timeless existence independent of human minds, or are they the products of cerebral invention? Do we discover them, as Plato supposed and many others have believed since, or do we construct them? Does mathematics constitute a universal language that in principle would permit human beings to communicate with extraterrestrial civilizations elsewhere in the universe, or is it merely an earthly language that owes its accidental existence to the peculiar evolution of neuronal networks in our brains? Does the physical world actually obey mathematical laws, or does it seem to conform to them simply because physicists have increasingly been able to make mathematical sense of it? Jean-Pierre Changeux, an internationally renowned neurobiologist, and Alain Connes, one of the most eminent living mathematicians, find themselves deeply divided by these questions.

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. ... Read more

Customer Reviews (3)

. . . another man's poison
It's taken me about a decade to finish reading this relatively short book.I'm a mathematician with a modest interest in philosophy, so I thought I'd find something worthwhile in this dialogue between a prominent mathematician and a prominent neuroscientist, but it just didn't click for me.

I have learned some things through this prolonged reading experience, though:

(1)Being a fly on the wall during an unrehearsed conversation between two intellectual heavyweights is overrated.Connes' and Changeux's thoughts are often disorganized, and when they disagree they usually seem to end up speaking past each other.

(2)People with profound knowledge in one field don't necessarily have a lot of deep insights to share when speaking outside of that field.

(3)If the final chapter is representative of the views of elite scientists, then scientism has a stronger foothold than I'd thought.In particular, I found Changeux's vision of science's role in the future of human society to be rather disturbing.If nothing else, this book was a good wake-up call, I suppose.

Pondering the philosophy of understanding mathematics
When reading this account of a series of conversations between Jean-Pierre Changeux and Alain Connes, two main themes emerge. The first is how little progress there has been made in the philosophy of mathematics and knowledgesince the time of Plato and the second is how much fun it is to discuss it.Changeux is Director of the Molecular Neurobiology Laboratory at theInstitut Pasteur and Connes is a previous winner of the Fields Medal formathematical excellence. His prime areas of work are in analysisandgeometry. These two superb minds jointly explore the realm ofconsciousness, knowledge, and the inherent ambiguities in the search fortruth and understanding.
As the conversations progress, many of themain themes of philosophy are covered, with an emphasis on mathematics andthe abstract nature of the human mind. My favorite chapter was "TheNeuronal Mathematician", where the neural basis of understanding theoremsis discussed. If it were possible for Plato to eavesdrop on theconversation, he would be baffled by the references to computers, but thediscussion on the "forms" of mathematics would seem like old news. One veryprofound question raised in this book bears repeating, "Is it necessary fora computer to experience pain and suffering to be consideredconscious?"
A book that should be thought of as a primer only, this isone work that can keep you thinking and pondering for years.

Published in Journal of Recreational Mathematics, reprinted withpermission.

a pleasant surprise
There are many "dialogue" books of this sort, but personally I haven't read anything matching the brilliance of this one.The two men featured in this book, both true masters in their fields, represent twovery different philsophical views, which become quite obvious immediately,yet they manage to engage in an intellectual dialogue free of the venomcharacterizing so much academic polemics nowadays, true to the spirit ofthose "pre-modern" French intellectuals, even reminiscent ofSocrates & company. This is a minor masterpiece. ... Read more

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.

Product Description
Our view of the world today is fundamentally influenced by twentieth century results in physics and mathematics. Here, three members of the French Academy of Sciences: Alain Connes, André Lichnerowicz, and Marcel Paul Schützenberger, discuss the relations among mathematics, physics and philosophy, and other sciences. Written in the form of conversations among three brilliant scientists and deep thinkers, the book touches on, among others, the following questions:

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. ... Read more

Customer Reviews (1)

A too abstract triangle
The goal of this book is "to enable a broad but enlightened audience to bridge the growing gap between the subtleties of these advances (meaning quantum mechanics, relativity and Gödel's theorem), usually accessible only to specialists, and the often unbelievably deformed images of them presented by popularized accounts".

I must disagree. Although the reader will attend an interesting dialogue between some of the top minds of the XXth century and Alain Connes is one of the greatest living mathematicians, it is difficult to follow a great part of this conversation if you are not familiar with advanced mathematics and physics. The publisher could have made the reading easier by including a lot of sidebars as Scientific American does.On the other hand I have read quite a number of books by very good scientists on the topics mentioned (therefore they could not be deformed images) and these books are much more accessible than "Triangle of Thoughts".If you have read the other Connes co-authored book, "Conversations on Mind, Matter and Mathematics", the level of accessibility of this one is similar.

That said, the book is worth reading and there are sections which are quite readable like that on Cosmology, ongame theory or even on Gödel's theorem. Alain Connes introduces a distinction between primordial mathematics and axiomatic mathematics which he considers an (limited) instrument of comprehension at our disposal. Gödel affirms that any sufficiently rich axiomatic system contains truths that are not provable and it has the curious consequence that you can add a countertruth to an axiomatic system which will be free of contradiction if the former system was non contradictory.

That the book needs some editing is clear. On one hand the authors describe what a well ordering is, something that is explained in Europe in the first year of college mathematics, on the other the paragraphs such as: "The phase space is sympletic and the Hamiltonian is a function on this space that we call the `energy', and it generates the evolution of observable quantities with its Poisson bracket" give an idea of what the authors understand as "enlightened audience".
In conclusion, the book deserves 5 stars if you are part of such audience, but only three if you are a mere mortal with a good science education.
... Read more

Product Description
The Baum-Connes conjecture is part of A. Connes' non-commutative geometry program. It can be viewed as a conjectural generalization of the Atiyah-Singer index theorem, to the equivariant setting (the ambient manifold is not compact, but some compactness is restored by means of a proper, co-compact action of a group G).

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,"). ... Read more

Product Description
This book contains a concise introduction to the techniques used to prove the Baum-Connes conjecture.

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. ... Read more

Product Description
What is the true nature of space and time? These concepts are at the heart of science, but they remain deeply wrapped in mystery. Both house their structure at the smallest pre-subatomic and the largest cosmological levels continues to defy modern physics and may require revolutionary new ideas for which science is still grasping. This unique volume brings together world leaders in cosmology, particle physics, quantum gravity, mathematics, philosophy and theology, to provide fresh insights into the deep structure of space and time. Andrew Taylor, Shahn Majid, Roger Penrose, Alain Connes, Michael Heller, and John Polkinghorne all experts in their respective fields, explain their theories in this outstanding compiled text.

A note from Simon Capelin, one of scholarly science publishing's leading editors:What is space? What is time? Is space infinite? Does time have a beginning? These questions have fascinated scientists, philosophers and theologians alike for hundreds of years, and the answers continue to elude us today. Current theories fall short of answers to the deeper questions, and the structure of space and time continues to defy modern physics. But the quest to understand the nature of space and time does not just lie with scientists. The search raises theological questions about the nature of physical reality itself, and what it means to exist. So, after more than two thousand years of thought and several hundred years of science, what do we know about the nature of space and time? This question was posed to a panel of six world leaders in physics, mathematics, and theology in a public discussion held at Emmanuel College, Cambridge: Sir Roger Penrose, who has made many remarkable contributions to science; John Polkinghorne KBE, a renowned theologian and particle physicist; Alain Connes, Fields medalist, and one of the world's foremost mathematicians; Michael Heller, a key contributor to the fields of science, theology, and philosophy; Shahn Majid, one of the pioneers in the theory of quantum symmetry; and Andrew Taylor, who has made major contributions in the study of dark matter and dark energy. In this book, each of these very distinguished authors expands on the theories presented at the discussion. They offer their personal perspectives, providing unique insights on this matter, from the structure of spacetime, dark matter, quantum spacetime, and what happened before the Big Bang, to the nature of time, metaphysics, and the philosophical and theological implications of spacetime. ... Read more

Customer Reviews (6)

The mathematical universe
I found "On Space and Time" a refreshing change from the usual, related popular book fare. The latter too often proselytize about string theory-related approaches, without making the reader adequately aware about how speculative are the theories. After a very readable and usefully up-to-date introductory overview of cosmology by astrophysicist Andrew Taylor, we have the core three chapters by leading mathematicians Shahn Majid, Roger Penrose, and Alain Connes, who each present quite different ideas about the possible fundamental structure of space-time. I particularly enjoyed the contributions by Majid and Penrose. Majid introduces in a leisurely and not overly technical way the subject of 'non-commutative geometry' and describes how it might furnish a mathematical framework for quantum space-time. Particularly intriguing is Majid's thesis that a fundamental theory of space-time (and hence physics) will involve so-called 'self-dual structures'. I liked very much his original use of Plato's cave allegory to help explain his thesis.

Penrose's chapter begins with a nice overview about how classical space-time is described using the tools of geometry. Later on, he reviews his longstanding ideas about the nature of the birth and ultimate fate of our expanding universe. His main thesis is that the laws of physics around the time of the big bang and in the remote future are 'conformally invariant'. This has the remarkable consequence that no meaning can be attached to the question of when the universe began and when it ends: there is simply no notion of time passing.

This book is not quite a 'popular' account of the subject, with equations and technical language frequently making an appearance. Yet, it is breathtaking ideas such as those exampled above that make the book well worth the effort. A reader without a mathematics background will still get a lot out of this book, not least a rare impression about the invaluable insights mathematicians have about the unsolved problems of the quantum nature of space-time.

On Space and Time
It started out good but got way to technical for the non- physics person.
I have a BS in Math and Physics and got lost in his equations and use of functions and swaping functions.

Had I known I would not have bought it. I was much more interested in understanding how time is dilated by speed and time and how that affects cosmology.

Great book for right audience
The books falls very nicely between casual mass-market popularization literature and professional PhD texts. The average reader can easily follow the popular books, yet one can read only so many times about ray of light in moving train and curved spacetime. To follow the real developments in modern physics is next to impossible without well-developed math skills.

Majid does a terrific job of leading to the very edge of layman understanding, proving minimal math concepts to explain structure of his ideas... and then just at the moment where loosing his train of thoughts seems inescapable provide simple and yet brilliant summation of surprising insights on his ideas about reality.

The book is not trivial to follow, and knowledge of basic math concepts would be very helpful. However, it doesn't require the actual PhD level math or deriving anything. You just need to be ready to apply much more math thinking when reading the text then it would be typical for say Brian Greene book. Working your mental gears through very simple yet fun facts like (x*y)^-1 = (y^-1*y)(x*y)^-1=(y^-1*x^-1*x*y)*(x*y)^-1==(y^-1*x^-1)*(x*y)*(x*y)^-1= y^-1*x^-1 is very satisfying.

Of many recently purchased books (including terrific works by Lee Smolin, Lisa Randal, etc) this one lets you come as close as one can to watch actual workings of modern theoretical physicist research, and almost grasp the building blocks and connections without the nitty-gritty details of rigid proof. Majid conjectures are very thought provoking, and put new light on many familiar physical concepts. Strongly recommend and just wish there were more high-end popularization books like that one.

Very difficult to follow
I really love the idea behind this book, which is that a unified theory of forces requires a rethink of the nature of space and time.However the passages written by Alain Connes and Majid are very difficult to follow, because the mathematics is way beyond me.I can understand the concept of noncommutative geometry both of these are working with but the actual application to physics and practical understanding is hard to follow.Some of Connes' remarks regarding solving physical problems through his theory surprise me in their optimism.Roger Penrose's article is very much indebted to 'the road to reality' in its ideas and expositions.

For some reason there are philosophical chapters and religious ones included, which appear to me completely gratuitous, hence the 3-star rating.The first chapter is a very quick and brief review of cosmology and quantum theory, ending with the puzzle of unifying standard model and gravity (i.e. general relativity).I would love to understand more about Connes and Majid but unfortunately these mathematicians are not intending to make their theories too understandable for the educated layperson in this particular book.

Mixed quality
I bought this book in the hope to learn in particular about noncommutative spacetime theories. This new book by Fields medalist and undisputed world leader in the field of noncommutative geometry, Alain Connes, would be the first popular science book presenting these ideas for a non-specialist audience. So my expectations were high.

Too high it appears.

First, let it be stated very clear here: this book is not by Connes. Amazon should update their database and display "Shahn Majid (Ed.)" as author. Connes is just one of the contributers, yet his name is conveniently displayed as first author. The blurb claims: "this unique volume brings together world leaders in cosmology, particle physics, quantum gravity, mathematics, philosophy and theology". As far as I can judge, there are only two big names amongst the contributers (Connes and Penrose). The others might be established names, but they seem far removed from being "world leaders".

The contribution by Connes itself (covering about 40 pages of the book) I found disappointing. Lots of generalities and very little about noncommutative geometry. Where it goes deeper into mathematics, the notation and definitions are unclear, and it seems he never gets to the heart of the matter.

The contribution of the other 'big name', Roger Penrose is better, but contains a lot of material presented already in his superb book 'The Road to Reality'. The new material Penrose has added is about conformal cyclic cosmology.

In my opinion, the best contribution (and certainly the largest at close to 90 pages) comes from the editor Shahn Majid. He actually does go into noncommutative geometry, explains its relevance to quantum gravity, and presents some simple examples of noncommutative algebras one can play with mathematically. The last two sections of his text (on 'self-dual structures and 'relative reality') were however rather vague.

Amongst the other contributors you will find Michael Heller and John Polkinghorne. The former is linked to the Vatican, and the latter an Anglican theologian. Their contributions are of metaphysical nature and try to make a link between modern physics and theology. In my opinion the book would have been better without these two contributions.

The editor, Majid, has also written the preface. I suspect it proved impossible to attract a renowned scientist to write a preface to this collection of popular science texts of rather mixed quality.

On the positive side, this hardcover edition is of good binding quality, with an attractive cover, and certainly priced favourably (even surprisingly so for a book in this category). Yet, someone interested to read a book containing a collection of contemporary theories on quantum gravity and the nature of spacetime, I would advise similar, perhaps more expensive but content wise better,collections such as Callender and Huggett's "Physics Meets Philosophy at the Planck Scale: Contemporary Theories in Quantum Gravity".

Barely three stars, with the very affordable price and Majid's contribution preventing this book from dropping below that level.
... Read more

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Chapters: Alexander Grothendieck, Paul Cohen, Atle Selberg, René Thom, Edward Witten, Enrico Bombieri, Alain Connes, John Milnor, William Thurston, Michael Atiyah, Lars Ahlfors, Stephen Smale, Heisuke Hironaka, Vladimir Voevodsky, Laurent Lafforgue, Maxim Kontsevich, Richard Borcherds, Grigori Perelman, Shing-Tung Yau, David Mumford, Terence Tao, Lars Hörmander, Jean-Pierre Serre, Grigory Margulis, Timothy Gowers, Simon Donaldson, Alan Baker, Laurent Schwartz, John G. Thompson, Vladimir Drinfel'd, Sergei Novikov, Pierre Deligne, Kunihiko Kodaira, Charles Fefferman, Michael Freedman, Daniel Quillen, Vaughan Jones, Wendelin Werner, Andrei Okounkov, Pierre-Louis Lions, Jesse Douglas, Jean Bourgain, Curtis T. Mcmullen, Efim Zelmanov, Gerd Faltings, Shigefumi Mori, Jean-Christophe Yoccoz, Klaus Roth. Source: Wikipedia. Pages: 229. Not illustrated. Free updates online. Purchase includes a free trial membership in the publisher's book club where you can select from more than a million books without charge. Excerpt: Sir Michael Francis Atiyah, OM, FRS, FRSE (born 22 April 1929) is a British mathematician, and one of the most influential mathematicians of the twentieth century. He grew up in Sudan and Egypt, and spent most of his academic life at Oxford, Cambridge, and the Institute for Advanced Study in Princeton. He has been President of the Royal Society (19901995), Master of Trinity College, Cambridge (19901997), Chancellor of the University of Leicester (19952005), and President of the Royal Society of Edinburgh (20052008). He is currently retired and an honorary professor at the University of Edinburgh. He has had many mathematical collaborations, in particular with Raoul Bott, Friedrich Hirzebruch and Isadore Singer, and his students include Graeme Segal, Nigel Hitchin and Simon Donaldson. With Hirzebruch he founded topological K-theory, a major tool in algebraic topology, that describes the ways in which high dimensional space...More: http://booksllc.net/?id=20698 ... Read more

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Purchase includes a free trial membership in the publisher's book club where you can select from more than a million books without charge. Chapters: Carl Friedrich Gauss, Bernhard Riemann, Felix Klein, Alain Connes, Gaspard Monge, Elmer Rees, Joseph Louis François Bertrand, Grigori Perelman, Heinz Hopf, Shing-Tung Yau, Brian Bowditch, Hermann Weyl, Aleksandr Danilovich Aleksandrov, Carl Gustav Jacob Jacobi, Eugenio Beltrami, Shiing-Shen Chern, Tullio Levi-Civita, Jan Arnoldus Schouten, Élie Cartan, Edward Kasner, Patrick Du Val, Werner Fenchel, Herbert Busemann, Johann Christian Martin Bartels, Luigi Bianchi, Gheorghe Ţiţeica, André Lichnerowicz, Nigel Hitchin, Abraham Haskel Taub, Octav Onicescu, Luis Santaló, Shlomo Sternberg, Yum-Tong Siu, Dmitri Egorov, Yuri Dmitrievich Burago, Ferdinand Minding, Abram Ilyich Fet, Heinrich Guggenheimer, David J. Simms, Victor Zalgaller, Arthur Milgram, Veniamin Kagan, Aleksei Pogorelov, Luther P. Eisenhart, Eugenio Calabi, Mikhail Katz, Victor Guillemin, Boleslav Mlodzeevskii, Gheorghe Vrânceanu, Lazar Lyusternik, Elwin Bruno Christoffel, Ernesto Cesàro, Michael Spivak, Detlef Gromoll, Stephan Cohn-Vossen, Charles Dupin, Nikolai Efimov, Robert Connelly, Gregorio Ricci-Curbastro, Thomas Banchoff, Georges Henri Halphen, Viktor Wagner, Hidehiko Yamabe, Thierry Aubin, Corrado Segre, Alfred Enneper, Michael Anderson, Delfino Codazzi. Source: Wikipedia. Free updates online. Not illustrated. Excerpt: Johann Carl Friedrich Gauss (pronounced ; German: · ), Latin: ) (30 April 1777 23 February 1855) was a German mathematician and scientist who contributed significantly to many fields, including number theory, statistics, analysis, differential geometry, geodesy, geophysics, electrostatics, astronomy and optics. Sometimes referred to as the Princeps mathematicorum (Latin, "the Prince of Mathematicians" or "the foremost of mathematicians") and "greatest mathematician since antiquity," Gauss had a remark...More: http://booksllc.net/?id=6125 ... Read more

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Chapters: Alain Connes, Bill Frist, Max Delbrück, Stanley Cohen, Mitchell A. Seligson, John Seigenthaler, Dana D. Nelson, Alp Ikizler, Chester E. Finn, Jr., Rubel Shelly, Pierre Colas, Albert Gore, Sr., Earl Wilbur Sutherland, Jr., John Crowe Ransom, Langdon Brown Gilkey, Houston A. Baker, Jr., Taylor Wang, Virginia Abernethy, Donald Ault, Melvyn P. Leffler, Mark Jarman, Richard C. Mccarty, Karl Dean, Elijah Embree Hoss, Jeff Balser, Ronald Spores, Jim Rossi, George W. Stocking, Sr., Charlotte Froese Fischer, Arthur Demarest, Larry Dalton, Rick Hilles, James Barr, Tinsley Randolph Harrison, David Keene, Colin Dayan, Lyman Ray Patterson, Carol M. Swain, Roy Clyde Clark, Michael Kearney, Kate Daniels, Steven C. Hebert, Sandy Solomon, John Donald Wade, Robert Donaldson, Steven Gabbe, Kenneth C. Catania, Tony Earley, Kent D. Syverud, Jim Foglesong, Raymond Winbush, Larry Soderquist, Tomlinson Fort, Jr., Beth Bachmann, James Cullen Martin, William Malone Baskervill, David Charles, Andrew C. Porter, Walter Nance, John Cowper Granbery, Suzanna Sherry, Jon Kaas, Richard Arenstorf, Charles Kiesler, Bjarni Jónsson, Elijah Millgram, Martha Craig Daughtrey, Brian T. Fitzpatrick, Gary Allan Polis, Dennis Kezar, Gary Gerstle, Tom Dillehay, Idit Dobbs-Weinstein, Lisa Schultz Bressman. Source: Wikipedia. Pages: 257. Not illustrated. Free updates online. Purchase includes a free trial membership in the publisher's book club where you can select from more than a million books without charge. Excerpt: Harvard Medical School William Harrison "Bill" Frist, Sr. (born February 22, 1952) is an American physician, businessman, and politician. He began his career as an heir and major stockholder to the for-profit hospital chain of Hospital Corporation of America. Frist later served two terms as a United States Senator representing Tennessee. He was the Republican Majority Leader from 2003 until his retirement in 2007. Frist was born in Nashville, Ten...More: http://booksllc.net/?id=160128 ... Read more

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Chapters: Thor Heyerdahl, Atle Selberg, Kristen Nygaard, Alain Connes, Gro Harlem Brundtland, Harald Sverdrup, Norman Borlaug, Johan Galtung, Per Kværne, Fred Kavli, Christopher Hansteen, Anton Wilhelm Brøgger, Jon Elster, Helge Ingstad, Edvard Moser, May-Britt Moser, Ragnar Skancke, Jon Bing, Thomas Edvard Krogh, Asbjørn Kjønstad, Johannes Andenæs, Torsten Hägerstrand, Finn E. Kydland, Christian Schweigaard Stang, Leif Ryvarden, Ludvig Kristensen Daa, Gunnar Skirbekk, Tore Gjelsvik, Berge Furre, Fredrik Barth, Francis Bull, Gerhard Gran, Hans Jacob Ustvedt, Knut Helle, Birger Bergersen, Gunnar Jahn, Harald K. Schjelderup, Unni Wikan, Ingrid Semmingsen, Endre Berner, Konrad Nielsen, Hartvig Caspar Christie, Nils Lid Hjort, Geir Lundestad, Jan Birger Jansen, Tor Hagfors, Sverre Dick Henriksen, Torstein Eckhoff, Knut S. Heier, Haaken Hasberg Gran, Anathon Aall, Anatol Heintz, Kåre Berg, Victor D. Norman, Bjørn Føyn, Harald Beyer, Sigve Tjøtta, Thekla Resvoll, Jens Fredrik Schroeter, Carl Jacob Arnholm, Lars Walløe, Hans Martin Seip, Alf Brodal, Marius Nygaard, Francis Sejersted, Kristian Birch-Reichenwald Aars, Grethe Rytter Hasle, Johan Bøgh, Jørgen Holmboe, Edvard Beyer, Odd Magnus Faltinsen, Sigvald Hasund, Ole Mørk Sandvik, Nils Christian Stenseth, Anne-Lise Seip, Preben Munthe, Trygve Braarud, Arne Odd Johnsen, Peter A. Munch, Ralph Tambs-Lyche, Kaare Aksnes, Anton Skulberg, Bernt Øksendal, Odd-Bjørn Fure, Inge Lønning, Mahmood Amiry-Moghaddam, Sigmund Skard, Ernst Håkon Jahr, Lars Vegard, Even Lange, Toril Moi, Ole Henrik Magga, Idun Reiten, Kjell Aartun, Ottar Brox, Geir Kjetsaa, Sigmund Grønmo, Knut Einar Eriksen, Knut Kjeldstadli, Einar Thomassen, Christian Torber Hegge Geelmuyden, Erik Alfsen, Hans Fredrik Dahl, Øyvind S. Bruland, Leiv Kristen Sydnes, Geir Ellingsrud, Peter Sjøholt, Jarle Simensen, Jan Mangerud, Helge Dahl, Lucy Smith, Dagfinn Føllesdal, Helge Pharo, Sivert Langholm, Edgeir Benum, Jan Eivind Myhre, T...More: http://booksllc.net/?id=275564 ... Read more

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"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.

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Was ist die Natur mathematischer Objekte? Existieren sieunabh{ngig vom Gehirn des Menschen oder sind sie das Produktder Gehirnaktivit{t? Kann schlie~lich echte k}nstlicheIntelligenz aus unbelebter Materie entstehen?Diese undweitere bis hin zur Ethik auftretende Fragen werden inDialogform dynamisch von zwei hervorragenden FachleutenderMathematik und der Neurowissenschaften in diesem Buchdiskutiert. Diese Darstellungsform soll den Leser anregen,selbst zu dem bis auf Platozur}ckgehenden Problemkreisnachzudenken. Daf}r relevante Erkenntnisse dermodernenmathematischen und neurobiologischen Hirnforschung werdenkompetent und allgemeinverst{ndlich bereitgestellt. ... Read more

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.