Simply Riemann

Simply Riemann
Author: Jeremy Gray
Publisher: Simply Charly
Total Pages: 169
Release: 2019-12-19
Genre: Biography & Autobiography
ISBN: 1943657785

“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

Prime Numbers and the Riemann Hypothesis
Author: Barry Mazur
Publisher: Cambridge University Press
Total Pages: 155
Release: 2016-04-11
Genre: Mathematics
ISBN: 1107101921

This book introduces prime numbers and explains the famous unsolved Riemann hypothesis.

From Riemann to Differential Geometry and Relativity

From Riemann to Differential Geometry and Relativity
Author: Lizhen Ji
Publisher: Springer
Total Pages: 664
Release: 2017-10-03
Genre: Mathematics
ISBN: 3319600397

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

Bernhard Riemann 1826–1866
Author: Detlef Laugwitz
Publisher: Springer Science & Business Media
Total Pages: 372
Release: 2009-06-08
Genre: Mathematics
ISBN: 0817647775

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.

Classification Theory of Riemann Surfaces

Classification Theory of Riemann Surfaces
Author: Leo Sario
Publisher: Springer Science & Business Media
Total Pages: 469
Release: 2012-12-06
Genre: Mathematics
ISBN: 3642482694

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

From Special Relativity to Feynman Diagrams
Author: Riccardo D'Auria
Publisher: Springer
Total Pages: 609
Release: 2015-10-06
Genre: Science
ISBN: 3319220144

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.

Complex Analysis

Complex Analysis
Author: Joseph Bak
Publisher: Springer Science & Business Media
Total Pages: 332
Release: 2010-08-02
Genre: Mathematics
ISBN: 1441972889

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.

Geometric Function Theory

Geometric Function Theory
Author: Steven G. Krantz
Publisher: Springer Science & Business Media
Total Pages: 311
Release: 2007-09-19
Genre: Mathematics
ISBN: 0817644407

* 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

Linear Differential Equations and Group Theory from Riemann to Poincare
Author: Jeremy Gray
Publisher: Springer Science & Business Media
Total Pages: 357
Release: 2010-01-07
Genre: Mathematics
ISBN: 0817647732

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.