Poincare's Legacies, Part I

Poincare's Legacies, Part I
Author: Terence Tao
Publisher: American Mathematical Soc.
Total Pages: 306
Release: 2009
Genre: Mathematics
ISBN: 0821848836

Focuses on ergodic theory, combinatorics, and number theory. This book discusses a variety of topics, ranging from developments in additive prime number theory to expository articles on individual mathematical topics such as the law of large numbers and the Lucas-Lehmer test for Mersenne primes.

Poincare's Legacies, Part II

Poincare's Legacies, Part II
Author: Terence Tao
Publisher: American Mathematical Soc.
Total Pages: 305
Release: 2009
Genre: Mathematics
ISBN: 0821848852

Focuses on geometry, topology, and partial differential equations. This book discusses a variety of topics, including expository articles on topics such as gauge theory, the Kakeya needle problem, and the Black-Scholes equation. It is suitable for graduate students and research mathematicians interested in broad exposure to mathematical topics.

The Scientific Legacy of Poincare

The Scientific Legacy of Poincare
Author: Éric Charpentier
Publisher: American Mathematical Soc.
Total Pages: 410
Release: 2010
Genre: Biography & Autobiography
ISBN: 082184718X

Henri Poincare (1854-1912) was one of the greatest scientists of his time, perhaps the last one to have mastered and expanded almost all areas in mathematics and theoretical physics. In this book, twenty world experts present one part of Poincare's extraordinary work. Each chapter treats one theme, presenting Poincare's approach, and achievements.

Poincaré's Legacies

Poincaré's Legacies
Author: Terence Tao
Publisher: American Mathematical Soc.
Total Pages: 305
Release: 2009-01-01
Genre: Mathematics
ISBN: 0821886347

Poincaré's Legacies, Part I

Poincaré's Legacies, Part I
Author: Terence Tao
Publisher:
Total Pages: 306
Release: 2009
Genre: Differential equations, Partial
ISBN: 9781470416010

There are many bits and pieces of folklore in mathematics that are passed down from advisor to student, or from collaborator to collaborator, but which are too fuzzy and non-rigorous to be discussed in the formal literature. Traditionally, it was a matter of luck and location as to who learned such folklore mathematics. But today, such bits and pieces can be communicated effectively and efficiently via the semiformal medium of research blogging. This book grew from such a blog. In 2007, Terry Tao began a mathematical blog to cover a variety of topics, ranging from his own research and other re.

Einstein's Clocks and Poincare's Maps: Empires of Time

Einstein's Clocks and Poincare's Maps: Empires of Time
Author: Peter Galison
Publisher: W. W. Norton & Company
Total Pages: 393
Release: 2004-09-17
Genre: Science
ISBN: 0393243869

"More than a history of science; it is a tour de force in the genre." —New York Times Book Review A dramatic new account of the parallel quests to harness time that culminated in the revolutionary science of relativity, Einstein's Clocks, Poincaré's Maps is "part history, part science, part adventure, part biography, part meditation on the meaning of modernity....In Galison's telling of science, the meters and wires and epoxy and solder come alive as characters, along with physicists, engineers, technicians and others.…Galison has unearthed fascinating material" (New York Times). Clocks and trains, telegraphs and colonial conquest: the challenges of the late nineteenth century were an indispensable real-world background to the enormous theoretical breakthrough of relativity. And two giants at the foundations of modern science were converging, step-by-step, on the answer: Albert Einstein, an young, obscure German physicist experimenting with measuring time using telegraph networks and with the coordination of clocks at train stations; and the renowned mathematician Henri Poincaré, president of the French Bureau of Longitude, mapping time coordinates across continents. Each found that to understand the newly global world, he had to determine whether there existed a pure time in which simultaneity was absolute or whether time was relative. Esteemed historian of science Peter Galison has culled new information from rarely seen photographs, forgotten patents, and unexplored archives to tell the fascinating story of two scientists whose concrete, professional preoccupations engaged them in a silent race toward a theory that would conquer the empire of time.

Kam Story, The: A Friendly Introduction To The Content, History, And Significance Of Classical Kolmogorov-arnold-moser Theory

Kam Story, The: A Friendly Introduction To The Content, History, And Significance Of Classical Kolmogorov-arnold-moser Theory
Author: H Scott Dumas
Publisher: World Scientific Publishing Company
Total Pages: 378
Release: 2014-02-28
Genre: Mathematics
ISBN: 9814556602

This is a semi-popular mathematics book aimed at a broad readership of mathematically literate scientists, especially mathematicians and physicists who are not experts in classical mechanics or KAM theory, and scientific-minded readers. Parts of the book should also appeal to less mathematically trained readers with an interest in the history or philosophy of science.The scope of the book is broad: it not only describes KAM theory in some detail, but also presents its historical context (thus showing why it was a “breakthrough”). Also discussed are applications of KAM theory (especially to celestial mechanics and statistical mechanics) and the parts of mathematics and physics in which KAM theory resides (dynamical systems, classical mechanics, and Hamiltonian perturbation theory).Although a number of sources on KAM theory are now available for experts, this book attempts to fill a long-standing gap at a more descriptive level. It stands out very clearly from existing publications on KAM theory because it leads the reader through an accessible account of the theory and places it in its proper context in mathematics, physics, and the history of science.

The Riemann Legacy

The Riemann Legacy
Author: Krzysztof Maurin
Publisher: Springer Science & Business Media
Total Pages: 732
Release: 2013-04-17
Genre: Mathematics
ISBN: 9401589399

very small domain (environment) affects through analytic continuation the whole of Riemann surface, or analytic manifold . Riemann was a master at applying this principle and also the first who noticed and emphasized that a meromorphic function is determined by its 'singularities'. Therefore he is rightly regarded as the father of the huge 'theory of singularities' which is developing so quickly and whose importance (also for physics) can hardly be overe~timated. Amazing and mysterious for our cognition is the role of Euclidean space. Even today many philosophers believe (following Kant) that 'real space' is Euclidean and other spaces being 'abstract constructs of mathematicians, should not be called spaces'. The thesis is no longer tenable - the whole of physics testifies to that. Nevertheless, there is a grain of truth in the 3 'prejudice': E (three-dimensional Euclidean space) is special in a particular way pleasantly familiar to us - in it we (also we mathematicians!) feel particularly 'confident' and move with a sense of greater 'safety' than in non-Euclidean spaces. For this reason perhaps, Riemann space M stands out among the multitude of 'interesting geometries'. For it is: 1. Locally Euclidean, i. e. , M is a differentiable manifold whose tangent spaces TxM are equipped with Euclidean metric Uxi 2. Every submanifold M of Euclidean space E is equipped with Riemann natural metric (inherited from the metric of E) and it is well known how often such submanifolds are used in mechanics (e. g. , the spherical pendulum).

The Poincare Conjecture

The Poincare Conjecture
Author: Donal O'Shea
Publisher: Bloomsbury Publishing USA
Total Pages: 306
Release: 2009-05-26
Genre: Mathematics
ISBN: 0802718949

Henri Poincaré was one of the greatest mathematicians of the late nineteenth and early twentieth century. He revolutionized the field of topology, which studies properties of geometric configurations that are unchanged by stretching or twisting. The Poincaré conjecture lies at the heart of modern geometry and topology, and even pertains to the possible shape of the universe. The conjecture states that there is only one shape possible for a finite universe in which every loop can be contracted to a single point. Poincaré's conjecture is one of the seven "millennium problems" that bring a one-million-dollar award for a solution. Grigory Perelman, a Russian mathematician, has offered a proof that is likely to win the Fields Medal, the mathematical equivalent of a Nobel prize, in August 2006. He also will almost certainly share a Clay Institute millennium award. In telling the vibrant story of The Poincaré Conjecture, Donal O'Shea makes accessible to general readers for the first time the meaning of the conjecture, and brings alive the field of mathematics and the achievements of generations of mathematicians whose work have led to Perelman's proof of this famous conjecture.