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Author: Dan Rockmore Publisher: Vintage ISBN: 0307427943 Category : Mathematics Languages : en Pages : 306
Book Description
For 150 years the Riemann hypothesis has been the holy grail of mathematics. Now, at a moment when mathematicians are finally moving in on a proof, Dartmouth professor Dan Rockmore tells the riveting history of the hunt for a solution.In 1859 German professor Bernhard Riemann postulated a law capable of describing with an amazing degree of accuracy the occurrence of the prime numbers. Rockmore takes us all the way from Euclid to the mysteries of quantum chaos to show how the Riemann hypothesis lies at the very heart of some of the most cutting-edge research going on today in physics and mathematics.
Author: Dan Rockmore Publisher: Vintage ISBN: 0307427943 Category : Mathematics Languages : en Pages : 306
Book Description
For 150 years the Riemann hypothesis has been the holy grail of mathematics. Now, at a moment when mathematicians are finally moving in on a proof, Dartmouth professor Dan Rockmore tells the riveting history of the hunt for a solution.In 1859 German professor Bernhard Riemann postulated a law capable of describing with an amazing degree of accuracy the occurrence of the prime numbers. Rockmore takes us all the way from Euclid to the mysteries of quantum chaos to show how the Riemann hypothesis lies at the very heart of some of the most cutting-edge research going on today in physics and mathematics.
Author: Dan Rockmore Publisher: Vintage ISBN: 9780099429944 Category : Number theory Languages : en Pages : 288
Book Description
Like a hunter who sees 'a bit of blood' on the trail, that's how Princeton mathematician Peter Sarnak describes the feeling of chasing an idea that seems to have a chance of success. If this is so, then the jungle of abstractions that is mathematics is full of frenzied hunters these days. They are out stalking big game: the resolution of 'The Riemann Hypothesis', seems to be in their sights. The Riemann Hypothesis is about the prime numbers, the fundamental numerical elements. Stated in 1859 by Professor Bernhard Riemann, it proposes a simple law which Riemann believed a 'very likely' explanation for the way in which the primes are distributed among the whole numbers, indivisible stars scattered without end throughout a boundless numerical universe. Just eight years later, at the tender age of thirty-nine Riemann would be dead from tuberculosis, cheated of the opportunity to settle his conjecture. For over a century, the Riemann Hypothesis has stumped the greatest of mathematical minds, but these days frustration has begun to give way to excitement. This unassuming comment is revealing astounding connections among nuclear physics, chaos and number theory, creating a frenzy of intellectual excitement amplified by the recent promise of a one million dollar bounty. The story of the quest to settle the Riemann Hypothesis is one of scientific exploration. It is peopled with solitary hermits and gregarious cheerleaders, cool calculators and wild-eyed visionaries, Nobel Prize-winners and Fields Medalists. To delve into the Riemann Hypothesis is to gain a window into the world of modern mathematics and the nature of mathematics research. Stalking the Riemann Hypothesis will open wide this window so that all may gaze through it in amazement.
Author: Peter B. Borwein Publisher: Springer Science & Business Media ISBN: 0387721258 Category : Mathematics Languages : en Pages : 543
Book Description
The Riemann Hypothesis has become the Holy Grail of mathematics in the century and a half since 1859 when Bernhard Riemann, one of the extraordinary mathematical talents of the 19th century, originally posed the problem. While the problem is notoriously difficult, and complicated even to state carefully, it can be loosely formulated as "the number of integers with an even number of prime factors is the same as the number of integers with an odd number of prime factors." The Hypothesis makes a very precise connection between two seemingly unrelated mathematical objects, namely prime numbers and the zeros of analytic functions. If solved, it would give us profound insight into number theory and, in particular, the nature of prime numbers. This book is an introduction to the theory surrounding the Riemann Hypothesis. Part I serves as a compendium of known results and as a primer for the material presented in the 20 original papers contained in Part II. The original papers place the material into historical context and illustrate the motivations for research on and around the Riemann Hypothesis. Several of these papers focus on computation of the zeta function, while others give proofs of the Prime Number Theorem, since the Prime Number Theorem is so closely connected to the Riemann Hypothesis. The text is suitable for a graduate course or seminar or simply as a reference for anyone interested in this extraordinary conjecture.
Author: Aleksandar Ivic Publisher: Courier Corporation ISBN: 0486140040 Category : Mathematics Languages : en Pages : 548
Book Description
This text covers exponential integrals and sums, 4th power moment, zero-free region, mean value estimates over short intervals, higher power moments, omega results, zeros on the critical line, zero-density estimates, and more. 1985 edition.
Author: Daniel M. Russell Publisher: MIT Press ISBN: 0262546078 Category : Computers Languages : en Pages : 337
Book Description
How to be a great online searcher, demonstrated with step-by-step searches for answers to a series of intriguing questions (for example, “Is that plant poisonous?”). We all know how to look up something online by typing words into a search engine. We do this so often that we have made the most famous search engine a verb: we Google it—“Japan population” or “Nobel Peace Prize” or “poison ivy” or whatever we want to know. But knowing how to Google something doesn't make us search experts; there's much more we can do to access the massive collective knowledge available online. In The Joy of Search, Daniel Russell shows us how to be great online researchers. We don't have to be computer geeks or a scholar searching out obscure facts; we just need to know some basic methods. Russell demonstrates these methods with step-by-step searches for answers to a series of intriguing questions—from “what is the wrong side of a towel?” to “what is the most likely way you will die?” Along the way, readers will discover essential tools for effective online searches—and learn some fascinating facts and interesting stories. Russell explains how to frame search queries so they will yield information and describes the best ways to use such resources as Google Earth, Google Scholar, Wikipedia, and Wikimedia. He shows when to put search terms in double quotes, how to use the operator (*), why metadata is important, and how to triangulate information from multiple sources. By the end of this engaging journey of discovering, readers will have the definitive answer to why the best online searches involve more than typing a few words into Google.
Author: Lisa Zunshine Publisher: MIT Press ISBN: 0262046334 Category : Science Languages : en Pages : 337
Book Description
An innovative account that brings together cognitive science, ethnography, and literary history to examine patterns of “mindreading” in a wide range of literary works. For over four thousand years, writers have been experimenting with what cognitive scientists call “mindreading”: constantly devising new social contexts for making their audiences imagine complex mental states of characters and narrators. In The Secret Life of Literature, Lisa Zunshine uncovers these mindreading patterns, which have, until now, remained invisible to both readers and critics, in works ranging from The Epic of Gilgamesh to Invisible Man. Bringing together cognitive science, ethnography, and literary studies, this engaging book transforms our understanding of literary history. Central to Zunshine’s argument is the exploration of mental states “embedded” within each other, as, for instance, when Ellison’s Invisible Man is aware of how his white Communist Party comrades pretend not to understand what he means, when they want to reassert their position of power. Paying special attention to how race, class, and gender inform literary embedments, Zunshine contrasts this dynamic with real-life patterns studied by cognitive and social psychologists. She also considers community-specific mindreading values and looks at the rise and migration of embedment patterns across genres and national literary traditions, noting particularly the use of deception, eavesdropping, and shame as plot devices. Finally, she investigates mindreading in children’s literature. Stories for children geared toward different stages of development, she shows, provide cultural scaffolding for initiating young readers into a long-term engagement with the secret life of literature.
Author: Joel R. Primack Publisher: Penguin ISBN: 1101126884 Category : Science Languages : en Pages : 401
Book Description
In this strikingly original book, a world-renowned cosmologist and an innovative writer of the history and philosophy of science uncover an astonishing truth: Humans actually are central to the universe. What does this mean for our culture and our personal lives? The answer is revolutionary: a science-based cosmology that allows us to understand the universe as a whole and our extraordinary place in it.
Author: Roger Highfield Publisher: Back Bay Books ISBN: 0316054518 Category : Science Languages : en Pages : 198
Book Description
Why might Rudolph's nose have been red? Why do we actually give Christmas gifts? Why has smell become an important component in the Christmas shopping experience? Roger Highfield, science editor of London's Daily Telegraph and co-author of the highly acclaimed The Arrow of Time, has taken a long-overdue look at our most cherished holiday from the rigorous (but highly entertaining) viewpoint of a scientist. What are the thermodynamics involved in cooking a turkey? What are the likely celestial candidates for the Star of Bethlehem? Is the concept of a virgin birth scientifically feasible? What happens to us physically when we overindulge in alcohol? How does snow form? Why are we always depressed after Christmas? How does Santa manage to deliver all those presents in one night? (He has, in fact, little over two ten- thousands of a second to get between each of the 842 million households he must visit.) The Physics of Christmas is that rare science book that manages to be as delightful as it is informative.
Author: Dan Rockmore
Author: Dan Rockmore
Author: Dan Rockmore
Author: Daniel Nahum Rockmore
Author: Barry Mazur
Author: Peter B. Borwein
Author: Aleksandar Ivic
Author: Daniel M. Russell
Author: Lisa Zunshine
Author: Joel R. Primack
Author: Roger Highfield