The Riemann Notebook PDF Download
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Author: Andrew Robinson
Publisher: Troubador Publishing Ltd
ISBN: 1838595724
Category : Fiction
Languages : en
Pages : 178
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Book Description
Did the 19th century German mathematician Bernhard Riemann discover more about the intricacies of prime numbers than he published? Did a notebook survive the clear-out of his papers following his sudden death in Italy? Could this notebook enable the breaking of 21st century internet security?
Author: Andrew Robinson
Publisher: Troubador Publishing Ltd
ISBN: 1838595724
Category : Fiction
Languages : en
Pages : 178
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Book Description
Did the 19th century German mathematician Bernhard Riemann discover more about the intricacies of prime numbers than he published? Did a notebook survive the clear-out of his papers following his sudden death in Italy? Could this notebook enable the breaking of 21st century internet security?
Author: David I. Ketcheson
Publisher: SIAM
ISBN: 1611976219
Category : Mathematics
Languages : en
Pages : 178
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Book Description
This book addresses an important class of mathematical problems (the Riemann problem) for first-order hyperbolic partial differential equations (PDEs), which arise when modeling wave propagation in applications such as fluid dynamics, traffic flow, acoustics, and elasticity. The solution of the Riemann problem captures essential information about these models and is the key ingredient in modern numerical methods for their solution. This book covers the fundamental ideas related to classical Riemann solutions, including their special structure and the types of waves that arise, as well as the ideas behind fast approximate solvers for the Riemann problem. The emphasis is on the general ideas, but each chapter delves into a particular application. Riemann Problems and Jupyter Solutions is available in electronic form as a collection of Jupyter notebooks that contain executable computer code and interactive figures and animations, allowing readers to grasp how the concepts presented are affected by important parameters and to experiment by varying those parameters themselves. The only interactive book focused entirely on the Riemann problem, it develops each concept in the context of a specific physical application, helping readers apply physical intuition in learning mathematical concepts. Graduate students and researchers working in the analysis and/or numerical solution of hyperbolic PDEs will find this book of interest. This includes mathematicians, as well as scientists and engineers, working on wave propagation problems. Educators interested in developing instructional materials using Jupyter notebooks will also find this book useful. The book is appropriate for courses in Numerical Methods for Hyperbolic PDEs and Analysis of Hyperbolic PDEs, and it can be a great supplement for courses in computational fluid dynamics, acoustics, and gas dynamics.
Author: Bruce C. Berndt
Publisher: Springer Science & Business Media
ISBN: 1461208793
Category : Mathematics
Languages : en
Pages : 459
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Book Description
During the years 1903-1914, Ramanujan worked in almost complete isolation in India. During this time, he recorded most of his mathematical discoveries without proofs in notebooks. Although many of his results were already found in the literature, most were not. Almost a decade after Ramanujan's death in 1920, G.N. Watson and B.M. Wilson began to edit Ramanujan's notebooks, but they never completed the task. A photostat edition, with no editing, was published by the Tata Institute of Fundamental Research in Bombay in 1957. This book is the fourth of five volumes devoted to the editing of Ramanujan's notebooks. Parts I, II, and III, published in 1985, 1989, and 1991, contain accounts of Chapters 1-21 in Ramanujan's second notebook as well as a description of his quarterly reports. This is the first of two volumes devoted to proving the results found in the unorganized portions of the second notebook and in the third notebook. The author also proves those results in the first notebook that are not found in the second or third notebooks. For those results that are known, references in the literature are provided. Otherwise, complete proofs are given. Over 1/2 of the results in the notebooks are new. Many of them are so startling and different that there are no results akin to them in the literature.
Author: Aleksandar Ivic
Publisher: Courier Corporation
ISBN: 0486140040
Category : Mathematics
Languages : en
Pages : 548
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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: K V Vidyasagar
Publisher: K V Vidyasagar
ISBN:
Category :
Languages : en
Pages : 11
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Book Description
Title: Riemann Integration: Exploring Fundamental Principles Author: KUPARALA VENKATA VIDYASAGAR Dive into the world of Riemann integration with this comprehensive guide. This book offers a detailed exploration of the fundamental concepts, techniques, and applications of Riemann integration in the realm of mathematical analysis. From its inception by Bernhard Riemann to its modern interpretations and implications in various branches of mathematics and beyond, this text provides a clear and concise elucidation of this crucial mathematical tool. Inside these pages, readers will find: A rigorous yet accessible presentation of the Riemann integral, covering its definition, properties, and theorems. Practical examples and illustrative explanations aiding in the understanding of Riemann integration and its applications in calculus and beyond. Discussions on the convergence of Riemann sums, the Riemann integrability of functions, and connections to other areas of mathematics, including differential equations and complex analysis. Insightful exercises and problems to reinforce understanding and encourage further exploration. Whether you're a student delving into real analysis, a mathematician seeking a deeper comprehension of integration principles, or an enthusiast curious about the foundations of calculus, this book serves as an invaluable resource, offering a comprehensive and insightful journey into the world of Riemann integration.
Author: I. Grattan-Guinness
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 216
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Book Description
Author: Harold M. Edwards
Publisher: Courier Corporation
ISBN: 9780486417400
Category : Mathematics
Languages : en
Pages : 338
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Book Description
Superb high-level study of one of the most influential classics in mathematics examines landmark 1859 publication entitled “On the Number of Primes Less Than a Given Magnitude,” and traces developments in theory inspired by it. Topics include Riemann's main formula, the prime number theorem, the Riemann-Siegel formula, large-scale computations, Fourier analysis, and other related topics. English translation of Riemann's original document appears in the Appendix.
Author: John Derbyshire
Publisher: Joseph Henry Press
ISBN: 0309141257
Category : Science
Languages : en
Pages : 447
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Book Description
In August 1859 Bernhard Riemann, a little-known 32-year old mathematician, presented a paper to the Berlin Academy titled: "On the Number of Prime Numbers Less Than a Given Quantity." In the middle of that paper, Riemann made an incidental remark â€" a guess, a hypothesis. What he tossed out to the assembled mathematicians that day has proven to be almost cruelly compelling to countless scholars in the ensuing years. Today, after 150 years of careful research and exhaustive study, the question remains. Is the hypothesis true or false? Riemann's basic inquiry, the primary topic of his paper, concerned a straightforward but nevertheless important matter of arithmetic â€" defining a precise formula to track and identify the occurrence of prime numbers. But it is that incidental remark â€" the Riemann Hypothesis â€" that is the truly astonishing legacy of his 1859 paper. Because Riemann was able to see beyond the pattern of the primes to discern traces of something mysterious and mathematically elegant shrouded in the shadows â€" subtle variations in the distribution of those prime numbers. Brilliant for its clarity, astounding for its potential consequences, the Hypothesis took on enormous importance in mathematics. Indeed, the successful solution to this puzzle would herald a revolution in prime number theory. Proving or disproving it became the greatest challenge of the age. It has become clear that the Riemann Hypothesis, whose resolution seems to hang tantalizingly just beyond our grasp, holds the key to a variety of scientific and mathematical investigations. The making and breaking of modern codes, which depend on the properties of the prime numbers, have roots in the Hypothesis. In a series of extraordinary developments during the 1970s, it emerged that even the physics of the atomic nucleus is connected in ways not yet fully understood to this strange conundrum. Hunting down the solution to the Riemann Hypothesis has become an obsession for many â€" the veritable "great white whale" of mathematical research. Yet despite determined efforts by generations of mathematicians, the Riemann Hypothesis defies resolution. Alternating passages of extraordinarily lucid mathematical exposition with chapters of elegantly composed biography and history, Prime Obsession is a fascinating and fluent account of an epic mathematical mystery that continues to challenge and excite the world. Posited a century and a half ago, the Riemann Hypothesis is an intellectual feast for the cognoscenti and the curious alike. Not just a story of numbers and calculations, Prime Obsession is the engrossing tale of a relentless hunt for an elusive proof â€" and those who have been consumed by it.
Author: Barry Mazur
Publisher: Cambridge University Press
ISBN: 1107101921
Category : Mathematics
Languages : en
Pages : 155
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Book Description
This book introduces prime numbers and explains the famous unsolved Riemann hypothesis.
Author: Jürgen Renn
Publisher: Springer Science & Business Media
ISBN: 1402039999
Category : Science
Languages : en
Pages : 2072
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Book Description
This four-volume work represents the most comprehensive documentation and study of the creation of general relativity. Einstein’s 1912 Zurich notebook is published for the first time in facsimile and transcript and commented on by today’s major historians of science. Additional sources from Einstein and others, who from the late 19th to the early 20th century contributed to this monumental development, are presented here in translation for the first time. The volumes offer detailed commentaries and analyses of these sources that are based on a close reading of these documents supplemented by interpretations by the leading historians of relativity.
