Simply Riemann

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Simply Riemann

Author : Jeremy Gray
Publisher : Simply Charly
ISBN 13 : 1943657785
Total Pages : 169 pages
Book Rating : 4.9/5 (436 download)

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Book Synopsis Simply Riemann by : Jeremy Gray

Download or read book Simply Riemann written by Jeremy Gray and published by Simply Charly. This book was released on 2019-12-19 with total page 169 pages. Available in PDF, EPUB and Kindle. Book excerpt: “Jeremy Gray is one of the world’s leading historians of mathematics, and an accomplished author of popular science. In Simply Riemann he combines both talents to give us clear and accessible insights into the astonishing discoveries of Bernhard Riemann—a brilliant but enigmatic mathematician who laid the foundations for several major areas of today’s mathematics, and for Albert Einstein’s General Theory of Relativity. Readable, organized—and simple. Highly recommended.” —Ian Stewart, Emeritus Professor of Mathematics at Warwick University and author of Significant Figures Born to a poor Lutheran pastor in what is today the Federal Republic of Germany, Bernhard Riemann (1826-1866) was a child math prodigy who began studying for a degree in theology before formally committing to mathematics in 1846, at the age of 20. Though he would live for only another 20 years (he died of pleurisy during a trip to Italy), his seminal work in a number of key areas—several of which now bear his name—had a decisive impact on the shape of mathematics in the succeeding century and a half. In Simply Riemann, author Jeremy Gray provides a comprehensive and intellectually stimulating introduction to Riemann’s life and paradigm-defining work. Beginning with his early influences—in particular, his relationship with his renowned predecessor Carl Friedrich Gauss—Gray goes on to explore Riemann’s specific contributions to geometry, functions of a complex variable, prime numbers, and functions of a real variable, which opened the way to discovering the limits of the calculus. He shows how without Riemannian geometry, cosmology after Einstein would be unthinkable, and he illuminates the famous Riemann hypothesis, which many regard as the most important unsolved problem in mathematics today. With admirable concision and clarity, Simply Riemann opens the door on one of the most profound and original thinkers of the 19th century—a man who pioneered the concept of a multidimensional reality and who always saw his work as another way to serve God.

Prime Numbers and the Riemann Hypothesis

Author : Barry Mazur
Publisher : Cambridge University Press
ISBN 13 : 1107101921
Total Pages : 155 pages
Book Rating : 4.1/5 (71 download)

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Book Synopsis Prime Numbers and the Riemann Hypothesis by : Barry Mazur

Download or read book Prime Numbers and the Riemann Hypothesis written by Barry Mazur and published by Cambridge University Press. This book was released on 2016-04-11 with total page 155 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces prime numbers and explains the famous unsolved Riemann hypothesis.

The Riemann Hypothesis

Author : Peter Borwein
Publisher : Springer Science & Business Media
ISBN 13 : 0387721266
Total Pages : 541 pages
Book Rating : 4.3/5 (877 download)

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Book Synopsis The Riemann Hypothesis by : Peter Borwein

Download or read book The Riemann Hypothesis written by Peter Borwein and published by Springer Science & Business Media. This book was released on 2007-11-21 with total page 541 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the Riemann Hypothesis, connected problems, and a taste of the body of theory developed towards its solution. It is targeted at the educated non-expert. Almost all the material is accessible to any senior mathematics student, and much is accessible to anyone with some university mathematics. The appendices include a selection of original papers that encompass the most important milestones in the evolution of theory connected to the Riemann Hypothesis. The appendices also include some authoritative expository papers. These are the “expert witnesses” whose insight into this field is both invaluable and irreplaceable.

Prime Obsession

Author : John Derbyshire
Publisher : Joseph Henry Press
ISBN 13 : 0309141257
Total Pages : 447 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Prime Obsession by : John Derbyshire

Download or read book Prime Obsession written by John Derbyshire and published by Joseph Henry Press. This book was released on 2003-04-15 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

From Riemann to Differential Geometry and Relativity

Author : Lizhen Ji
Publisher : Springer
ISBN 13 : 3319600397
Total Pages : 664 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis From Riemann to Differential Geometry and Relativity by : Lizhen Ji

Download or read book From Riemann to Differential Geometry and Relativity written by Lizhen Ji and published by Springer. This book was released on 2017-10-03 with total page 664 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores the work of Bernhard Riemann and its impact on mathematics, philosophy and physics. It features contributions from a range of fields, historical expositions, and selected research articles that were motivated by Riemann’s ideas and demonstrate their timelessness. The editors are convinced of the tremendous value of going into Riemann’s work in depth, investigating his original ideas, integrating them into a broader perspective, and establishing ties with modern science and philosophy. Accordingly, the contributors to this volume are mathematicians, physicists, philosophers and historians of science. The book offers a unique resource for students and researchers in the fields of mathematics, physics and philosophy, historians of science, and more generally to a wide range of readers interested in the history of ideas.

Bernhard Riemann 1826–1866

Author : Detlef Laugwitz
Publisher : Springer Science & Business Media
ISBN 13 : 0817647775
Total Pages : 372 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Bernhard Riemann 1826–1866 by : Detlef Laugwitz

Download or read book Bernhard Riemann 1826–1866 written by Detlef Laugwitz and published by Springer Science & Business Media. This book was released on 2009-06-08 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: The name of Bernard Riemann is well known to mathematicians and physicists around the world. His name is indelibly stamped on the literature of mathematics and physics. This remarkable work, rich in insight and scholarship, is addressed to mathematicians, physicists, and philosophers interested in mathematics. It seeks to draw those readers closer to the underlying ideas of Riemann’s work and to the development of them in their historical context. This illuminating English-language version of the original German edition will be an important contribution to the literature of the history of mathematics.

Simply Wittgenstein

Author : James C. Klagge
Publisher : Simply Charly
ISBN 13 : 1943657041
Total Pages : 114 pages
Book Rating : 4.9/5 (436 download)

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Book Synopsis Simply Wittgenstein by : James C. Klagge

Download or read book Simply Wittgenstein written by James C. Klagge and published by Simply Charly. This book was released on 2016-06-17 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: "There are many introductions to the life and work of Ludwig Wittgenstein, but I think James Klagge has produced the very best. Taking as his premise that his reader may know nothing about Wittgenstein or, for that matter, about philosophy, Klagge gives a lucid, charming, and wholly convincing account of Wittgenstein’s basic ideas, his way of thinking, his views on religion, culture, ethical behavior, and so on. He is especially good at explaining the root concepts like “language game,” "form of life,” and “private language.” But perhaps the highlight of this book is its set of applications: that is, how do Wittgenstein’s concepts and writings help us to understand the events of our time from courtroom cases to the bombing of the Twin Towers on 9/11. Wittgenstein, Klagge shows, literally helps us to live our lives: he is the philosopher par excellence of the twentieth—and now the twenty-first—centuries. Klagge’s own clarity is exemplary: he never condescends to the reader and yet makes Wittgenstein’s thought wonderfully clear." —Marjorie Perloff, Sadie Dernham Patek Emerita Professor of Humanities at Stanford University Born in Vienna into an extremely wealthy and highly cultured family, Ludwig Wittgenstein (1889-1951) grew up surrounded by art, music, and a disturbing amount of dysfunctional behavior. After studying mechanical engineering and developing an interest in aeronautics, he became obsessed with mathematics and logic, which led to his life’s work exploring the relationship between language, philosophy, and reality. In Simply Wittgenstein, James Klagge presents a fascinating portrait of this brilliant and troubled man, while exploring his two extraordinary books—the Tractatus Logico-Philosophicus and Philosophical Investigations—in which he gave concrete form to his singular and perplexing ideas. Drawing on 30 years of teaching about Wittgenstein at both the undergraduate and graduate level, Klagge provides a clear and accessible introduction to these seminal works, helping the reader understand the revolutionary nature of Wittgenstein’s insights and the reason they continue to resonate in our own time. Though Wittgenstein himself was convinced that he would never be properly understood, Simply Wittgenstein shows, with brevity and lucidity, that his ideas have had a profound and enduring effect on how we think about language and life.

Classification Theory of Riemann Surfaces

Author : Leo Sario
Publisher : Springer Science & Business Media
ISBN 13 : 3642482694
Total Pages : 469 pages
Book Rating : 4.6/5 (424 download)

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Book Synopsis Classification Theory of Riemann Surfaces by : Leo Sario

Download or read book Classification Theory of Riemann Surfaces written by Leo Sario and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of the present monograph is to systematically develop a classification theory of Riemann surfaces. Some first steps will also be taken toward a classification of Riemannian spaces. Four phases can be distinguished in the chronological background: the type problem; general classification; compactifications; and extension to higher dimensions. The type problem evolved in the following somewhat overlapping steps: the Riemann mapping theorem, the classical type problem, and the existence of Green's functions. The Riemann mapping theorem laid the foundation to classification theory: there are only two conformal equivalence classes of (noncompact) simply connected regions. Over half a century of efforts by leading mathematicians went into giving a rigorous proof of the theorem: RIEMANN, WEIERSTRASS, SCHWARZ, NEUMANN, POINCARE, HILBERT, WEYL, COURANT, OSGOOD, KOEBE, CARATHEODORY, MONTEL. The classical type problem was to determine whether a given simply connected covering surface of the plane is conformally equivalent to the plane or the disko The problem was in the center of interest in the thirties and early forties, with AHLFORS, KAKUTANI, KOBAYASHI, P. MYRBERG, NEVANLINNA, SPEISER, TEICHMÜLLER and others obtaining incisive specific results. The main problem of finding necessary and sufficient conditions remains, however, unsolved.

From Special Relativity to Feynman Diagrams

Author : Riccardo D'Auria
Publisher : Springer
ISBN 13 : 3319220144
Total Pages : 609 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis From Special Relativity to Feynman Diagrams by : Riccardo D'Auria

Download or read book From Special Relativity to Feynman Diagrams written by Riccardo D'Auria and published by Springer. This book was released on 2015-10-06 with total page 609 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, now in its second edition, provides an introductory course on theoretical particle physics with the aim of filling the gap that exists between basic courses of classical and quantum mechanics and advanced courses of (relativistic) quantum mechanics and field theory. After a concise but comprehensive introduction to special relativity, key aspects of relativistic dynamics are covered and some elementary concepts of general relativity introduced. Basics of the theory of groups and Lie algebras are explained, with discussion of the group of rotations and the Lorentz and Poincaré groups. In addition, a concise account of representation theory and of tensor calculus is provided. Quantization of the electromagnetic field in the radiation range is fully discussed. The essentials of the Lagrangian and Hamiltonian formalisms are reviewed, proceeding from systems with a finite number of degrees of freedom and extending the discussion to fields. The final four chapters are devoted to development of the quantum field theory, ultimately introducing the graphical description of interaction processes by means of Feynman diagrams. The book will be of value for students seeking to understand the main concepts that form the basis of contemporary theoretical particle physics and also for engineers and lecturers. An Appendix on some special relativity effects is added.

The Conformal Mapping of Simply-connected Riemann Surfaces. II

Author : Maurice Heins
Publisher :
ISBN 13 :
Total Pages : 16 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis The Conformal Mapping of Simply-connected Riemann Surfaces. II by : Maurice Heins

Download or read book The Conformal Mapping of Simply-connected Riemann Surfaces. II written by Maurice Heins and published by . This book was released on 1957 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Encyclopaedia of Mathematics

Author : M. Hazewinkel
Publisher : Springer
ISBN 13 : 1489937919
Total Pages : 932 pages
Book Rating : 4.4/5 (899 download)

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Book Synopsis Encyclopaedia of Mathematics by : M. Hazewinkel

Download or read book Encyclopaedia of Mathematics written by M. Hazewinkel and published by Springer. This book was released on 2013-12-01 with total page 932 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Complex Analysis

Author : Joseph Bak
Publisher : Springer Science & Business Media
ISBN 13 : 1441972889
Total Pages : 332 pages
Book Rating : 4.4/5 (419 download)

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Book Synopsis Complex Analysis by : Joseph Bak

Download or read book Complex Analysis written by Joseph Bak and published by Springer Science & Business Media. This book was released on 2010-08-02 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unusual and lively textbook offers a clear and intuitive approach to the classical and beautiful theory of complex variables. With very little dependence on advanced concepts from several-variable calculus and topology, the text focuses on the authentic complex-variable ideas and techniques. Accessible to students at their early stages of mathematical study, this full first year course in complex analysis offers new and interesting motivations for classical results and introduces related topics stressing motivation and technique. Numerous illustrations, examples, and now 300 exercises, enrich the text. Students who master this textbook will emerge with an excellent grounding in complex analysis, and a solid understanding of its wide applicability.

Riemann, Topology, and Physics

Author : Michael I. Monastyrsky
Publisher : Springer Science & Business Media
ISBN 13 : 0817647791
Total Pages : 220 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Riemann, Topology, and Physics by : Michael I. Monastyrsky

Download or read book Riemann, Topology, and Physics written by Michael I. Monastyrsky and published by Springer Science & Business Media. This book was released on 2009-06-08 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: The significantly expanded second edition of this book combines a fascinating account of the life and work of Bernhard Riemann with a lucid discussion of current interaction between topology and physics. The author, a distinguished mathematical physicist, takes into account his own research at the Riemann archives of Göttingen University and developments over the last decade that connect Riemann with numerous significant ideas and methods reflected throughout contemporary mathematics and physics. Special attention is paid in part one to results on the Riemann–Hilbert problem and, in part two, to discoveries in field theory and condensed matter.

Geometric Function Theory

Author : Steven G. Krantz
Publisher : Springer Science & Business Media
ISBN 13 : 0817644407
Total Pages : 311 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Geometric Function Theory by : Steven G. Krantz

Download or read book Geometric Function Theory written by Steven G. Krantz and published by Springer Science & Business Media. This book was released on 2007-09-19 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: * Presented from a geometric analytical viewpoint, this work addresses advanced topics in complex analysis that verge on modern areas of research * Methodically designed with individual chapters containing a rich collection of exercises, examples, and illustrations

Linear Differential Equations and Group Theory from Riemann to Poincare

Author : Jeremy Gray
Publisher : Springer Science & Business Media
ISBN 13 : 0817647732
Total Pages : 357 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Linear Differential Equations and Group Theory from Riemann to Poincare by : Jeremy Gray

Download or read book Linear Differential Equations and Group Theory from Riemann to Poincare written by Jeremy Gray and published by Springer Science & Business Media. This book was released on 2010-01-07 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a study of how a particular vision of the unity of mathematics, often called geometric function theory, was created in the 19th century. The central focus is on the convergence of three mathematical topics: the hypergeometric and related linear differential equations, group theory, and on-Euclidean geometry. The text for this second edition has been greatly expanded and revised, and the existing appendices enriched. The exercises have been retained, making it possible to use the book as a companion to mathematics courses at the graduate level.

The Concept of a Riemann Surface

Author : Hermann Weyl
Publisher : Courier Corporation
ISBN 13 : 0486470040
Total Pages : 210 pages
Book Rating : 4.4/5 (864 download)

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Book Synopsis The Concept of a Riemann Surface by : Hermann Weyl

Download or read book The Concept of a Riemann Surface written by Hermann Weyl and published by Courier Corporation. This book was released on 2009-03-26 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: This classic on the general history of functions was written by one of the 20th century's best-known mathematicians. Weyl combined function theory and geometry in this high-level landmark work, forming a new branch of mathematics and the basis of the modern approach to analysis, geometry, and topology. 1955 edition.

Essentials of Integration Theory for Analysis

Author : Daniel W. Stroock
Publisher : Springer Science & Business Media
ISBN 13 : 1461411351
Total Pages : 254 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Essentials of Integration Theory for Analysis by : Daniel W. Stroock

Download or read book Essentials of Integration Theory for Analysis written by Daniel W. Stroock and published by Springer Science & Business Media. This book was released on 2011-08-02 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: ‘A Concise Introduction to the Theory of Integration’ was once a best-selling Birkhäuser title which published 3 editions. This manuscript is a substantial revision of the material. Chapter one now includes a section about the rate of convergence of Riemann sums. The second chapter now covers both Lebesgue and Bernoulli measures, whose relation to one another is discussed. The third chapter now includes a proof of Lebesgue's differential theorem for all monotone functions. This is a beautiful topic which is not often covered. The treatment of surface measure and the divergence theorem in the fifth chapter has been improved. Loose ends from the discussion of the Euler-MacLauren in Chapter I are tied together in Chapter seven. Chapter eight has been expanded to include a proof of Carathéory's method for constructing measures; his result is applied to the construction of Hausdorff measures. The new material is complemented by the addition of several new problems based on that material.