Reassessing Riemann's Paper
Reassessing Riemann's Paper

Author: Walter Dittrich

Publisher: Springer Nature

Published: 2021-01-04

Total Pages: 110

ISBN-13: 3030610497

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In this book, the author pays tribute to Bernhard Riemann (1826-1866), a mathematician with revolutionary ideas, whose work on the theory of integration, the Fourier transform, the hypergeometric differential equation, etc. contributed immensely to mathematical physics. The text concentrates in particular on Riemann’s only work on prime numbers, including ideas – new at the time – such as analytical continuation into the complex plane and the product formula for entire functions. A detailed analysis of the zeros of the Riemann zeta-function is presented. The impact of Riemann’s ideas on regularizing infinite values in field theory is also emphasized. This revised and enhanced new edition contains three new chapters, two on the application of Riemann’s zeta-function regularization to obtain the partition function of a Bose (Fermi) oscillator and one on the zeta-function regularization in quantum electrodynamics. Appendix A2 has been re-written to make the calculations more transparent. A summary of Euler-Riemann formulae completes the book.

Laws Of Form: A Fiftieth Anniversary
Laws Of Form: A Fiftieth Anniversary

Author: Louis H Kauffman

Publisher: World Scientific

Published: 2023-01-09

Total Pages: 944

ISBN-13: 9811247447

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Laws of Form is a seminal work in foundations of logic, mathematics and philosophy published by G Spencer-Brown in 1969. The book provides a new point of view on form and the role of distinction, markedness and the absence of distinction (the unmarked state) in the construction of any universe. A conference was held August 8-10, 2019 at the Old Library, Liverpool University, 19 Abercromby Square, L697ZN, UK to celebrate the 50th anniversary of the publication of Laws of Form and to remember George Spencer-Brown, its author. The book is a collection of papers introducing and extending Laws of Form written primarily by people who attended the conference in 2019.

The History of Mathematics: A Source-Based Approach, Volume 2
The History of Mathematics: A Source-Based Approach, Volume 2

Author: June Barrow-Green

Publisher: American Mathematical Society

Published: 2022-05-26

Total Pages: 703

ISBN-13: 1470443821

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The History of Mathematics: A Source-Based Approach is a comprehensive history of the development of mathematics. This, the second volume of a two-volume set, takes the reader from the invention of the calculus to the beginning of the twentieth century. The initial discoverers of calculus are given thorough investigation, and special attention is also paid to Newton's Principia. The eighteenth century is presented as primarily a period of the development of calculus, particularly in differential equations and applications of mathematics. Mathematics blossomed in the nineteenth century and the book explores progress in geometry, analysis, foundations, algebra, and applied mathematics, especially celestial mechanics. The approach throughout is markedly historiographic: How do we know what we know? How do we read the original documents? What are the institutions supporting mathematics? Who are the people of mathematics? The reader learns not only the history of mathematics, but also how to think like a historian. The two-volume set was designed as a textbook for the authors' acclaimed year-long course at the Open University. It is, in addition to being an innovative and insightful textbook, an invaluable resource for students and scholars of the history of mathematics. The authors, each among the most distinguished mathematical historians in the world, have produced over fifty books and earned scholarly and expository prizes from the major mathematical societies of the English-speaking world.

Handbook of Differential Geometry
Handbook of Differential Geometry

Author: Franki J.E. Dillen

Publisher: Elsevier

Published: 2005-11-29

Total Pages: 575

ISBN-13: 0080461204

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In the series of volumes which together will constitute the "Handbook of Differential Geometry" we try to give a rather complete survey of the field of differential geometry. The different chapters will both deal with the basic material of differential geometry and with research results (old and recent).All chapters are written by experts in the area and contain a large bibliography. In this second volume a wide range of areas in the very broad field of differential geometry is discussed, as there are Riemannian geometry, Lorentzian geometry, Finsler geometry, symplectic geometry, contact geometry, complex geometry, Lagrange geometry and the geometry of foliations. Although this does not cover the whole of differential geometry, the reader will be provided with an overview of some its most important areas.. Written by experts and covering recent research. Extensive bibliography. Dealing with a diverse range of areas. Starting from the basics

Intermediate Dynamics for Engineers
Intermediate Dynamics for Engineers

Author: Oliver M. O'Reilly

Publisher: Cambridge University Press

Published: 2020-01-30

Total Pages: 545

ISBN-13: 1108494218

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A fully updated second edition providing a systematic treatment of engineering dynamics that covers Newton-Euler and Lagrangian approaches. It includes two completely revised chapters, a 350-page solutions manual for instructors, and numerous structured examples and exercises, and is suitable for both senior-level and first-year graduate courses.

Geometry
Geometry

Author: John Tabak

Publisher: Infobase Publishing

Published: 2014-05-14

Total Pages: 241

ISBN-13: 0816068763

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Greek ideas about geometry, straight-edge and compass constructions, and the nature of mathematical proof dominated mathematical thought for about 2,000 years.

The Philosophy of Mathematical Practice
The Philosophy of Mathematical Practice

Author: Paolo Mancosu

Publisher: Oxford University Press on Demand

Published: 2008-06-19

Total Pages: 460

ISBN-13: 0199296456

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There is an urgent need in philosophy of mathematics for new approaches which pay closer attention to mathematical practice. This book will blaze the trail: it offers philosophical analyses of important characteristics of contemporary mathematics and of many aspects of mathematical activity which escape purely formal logical treatment.

Model and Mathematics: From the 19th to the 21st Century
Model and Mathematics: From the 19th to the 21st Century

Author: Michael Friedman

Publisher: Springer Nature

Published: 2022-08-08

Total Pages: 441

ISBN-13: 3030978338

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This open access book collects the historical and medial perspectives of a systematic and epistemological analysis of the complicated, multifaceted relationship between model and mathematics, ranging from, for example, the physical mathematical models of the 19th century to the simulation and digital modelling of the 21st century. The aim of this anthology is to showcase the status of the mathematical model between abstraction and realization, presentation and representation, what is modeled and what models. This book is open access under a CC BY 4.0 license.

Unsteady Aerodynamics and Aeroelasticity of Turbomachines
Unsteady Aerodynamics and Aeroelasticity of Turbomachines

Author: Torsten H. Fransson

Publisher: Springer Science & Business Media

Published: 1998-06-30

Total Pages: 882

ISBN-13: 9780792350408

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Twenty-one years have passed since the first symposium in this series was held in Paris (1976). Since then there have been meetings in Lausanne (1980), Cambridge (1984), Aachen (1987), Beijing (1989), Notre Dame (1991) and Fukuoka (1994). During this period a tremendous development in the field of unsteady aerodynamics and aeroelasticity in turbomachines has taken place. As steady-state flow conditions become better known, and as blades in the turbomachine are constantly pushed towards lower weight, and higher load and efficiency, the importance of unsteady phenomena appear more clearly. th The 8 Symposium was, as the previous ones, of high quality. Furthermore, it presented the audience with the latest developments in experimental, numerical and theoretical research. More papers than ever before were submitted to the conference. As the organising committee wanted to preserve the uniqueness of the symposium by having single sessions, and thus mingle speakers and audience with different backgrounds in this interdisciplinary field, only a limited number of papers could be accepted. 54 papers were accepted and presented at the meeting, all of which are included in the present proceedings.