Foundations Of Mathematics And Physics One Century After Hilbert

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Foundations of Mathematics and Physics One Century After Hilbert

Joseph Kouneiher
Foundations of Mathematics and Physics One Century After Hilbert Book PDF

Author : Joseph Kouneiher
Publisher : Springer
Page : 441 pages
File Size : 46,9 Mb
Release : 2018-05-26
Category : Science
ISBN : 9783319648132

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Foundations of Mathematics and Physics One Century After Hilbert by Joseph Kouneiher Pdf

This book explores the rich and deep interplay between mathematics and physics one century after David Hilbert’s works from 1891 to 1933, published by Springer in six volumes. The most prominent scientists in various domains of these disciplines contribute to this volume providing insight to their works, and analyzing the impact of the breakthrough and the perspectives of their own contributions. The result is a broad journey through the most recent developments in mathematical physics, such as string theory, quantum gravity, noncommutative geometry, twistor theory, Gauge and Quantum fields theories, just to mention a few. The reader, accompanied on this journey by some of the fathers of these theories, explores some far reaching interfaces where mathematics and theoretical physics interact profoundly and gets a broad and deep understanding of subjects which are at the core of recent developments in mathematical physics. The journey is not confined to the present state of the art, but sheds light on future developments of the field, highlighting a list of open problems. Graduate students and researchers working in physics, mathematics and mathematical physics will find this journey extremely fascinating. All those who want to benefit from a comprehensive description of all the latest advances in mathematics and mathematical physics, will find this book very useful too.

David Hilbert's Lectures on the Foundations of Physics 1915-1927

Tilman Sauer,Ulrich Majer
David Hilbert s Lectures on the Foundations of Physics 1915 1927 Book PDF

Author : Tilman Sauer,Ulrich Majer
Publisher : Springer Science & Business Media
Page : 690 pages
File Size : 42,8 Mb
Release : 2009-08-06
Category : Mathematics
ISBN : 9783540682424

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David Hilbert's Lectures on the Foundations of Physics 1915-1927 by Tilman Sauer,Ulrich Majer Pdf

These documents do nothing less than bear witness to one of the most dramatic changes in the foundations of science. The book has three sections that cover general relativity, epistemological issues, and quantum mechanics. This fascinating work will be a vital text for historians and philosophers of physics, as well as researchers in related physical theories.

The Foundations of Geometry

David Hilbert
The Foundations of Geometry Book PDF

Author : David Hilbert
Publisher : Read Books Ltd
Page : 98 pages
File Size : 46,9 Mb
Release : 2014-07-07
Category : Mathematics
ISBN : 9781473395947

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The Foundations of Geometry by David Hilbert Pdf

This early work by David Hilbert was originally published in the early 20th century and we are now republishing it with a brand new introductory biography. David Hilbert was born on the 23rd January 1862, in a Province of Prussia. Hilbert is recognised as one of the most influential and universal mathematicians of the 19th and early 20th centuries. He discovered and developed a broad range of fundamental ideas in many areas, including invariant theory and the axiomatization of geometry. He also formulated the theory of Hilbert spaces, one of the foundations of functional analysis.

Methods of Mathematical Physics

Richard Courant,David Hilbert
Methods of Mathematical Physics Book PDF

Author : Richard Courant,David Hilbert
Publisher : John Wiley & Sons
Page : 575 pages
File Size : 52,9 Mb
Release : 2008-09-26
Category : Science
ISBN : 9783527617227

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Methods of Mathematical Physics by Richard Courant,David Hilbert Pdf

Since the first volume of this work came out in Germany in 1924, this book, together with its second volume, has remained standard in the field. Courant and Hilbert's treatment restores the historically deep connections between physical intuition and mathematical development, providing the reader with a unified approach to mathematical physics. The present volume represents Richard Courant's second and final revision of 1953.

Foundations of Geometry

David Hilbert,Paul Bernays
Foundations of Geometry Book PDF

Author : David Hilbert,Paul Bernays
Publisher : Open Court Publishing
Page : 244 pages
File Size : 45,6 Mb
Release : 1971
Category : Mathematics
ISBN : UOM:39015014352945

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Foundations of Geometry by David Hilbert,Paul Bernays Pdf

Along with the writings of Hilbert's friend and correspondent Frege, Hilbert's Grundlagen der Geometrie is the major prop that set the stage for Russell and Whitehead's Principia Mathematica. Hilbert presents a new axiomatization of geometry, the reduction of geometry to algebra, and introduces the distinction between mathematics and metamathematics, with a new theory of proof. This edition is translated from the tenth German edition, including all the improvements which Hilbert derived from his own reflections and the contributions of other writers. --Back cover.

David Hilbert's Lectures on the Foundations of Physics 1915-1927

Tilman Sauer,Ulrich Majer
David Hilbert s Lectures on the Foundations of Physics 1915 1927 Book PDF

Author : Tilman Sauer,Ulrich Majer
Publisher : Springer
Page : 690 pages
File Size : 46,9 Mb
Release : 2009-08-27
Category : Mathematics
ISBN : 354020606X

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David Hilbert's Lectures on the Foundations of Physics 1915-1927 by Tilman Sauer,Ulrich Majer Pdf

These documents do nothing less than bear witness to one of the most dramatic changes in the foundations of science. The book has three sections that cover general relativity, epistemological issues, and quantum mechanics. This fascinating work will be a vital text for historians and philosophers of physics, as well as researchers in related physical theories.

Methods of Mathematical Physics

Richard Courant,David Hilbert
Methods of Mathematical Physics Book PDF

Author : Richard Courant,David Hilbert
Publisher : Wiley-VCH
Page : 586 pages
File Size : 50,5 Mb
Release : 1989
Category : Science
ISBN : UCSC:32106006108424

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Methods of Mathematical Physics by Richard Courant,David Hilbert Pdf

Since the first volume of this work came out in Germany in 1924, this book, together with its second volume, has remained standard in the field. Courant and Hilbert's treatment restores the historically deep connections between physical intuition and mathematical development, providing the reader with a unified approach to mathematical physics. The present volume represents Richard Courant's second and final revision of 1953.

Theory of Algebraic Invariants

David Hilbert
Theory of Algebraic Invariants Book PDF

Author : David Hilbert
Publisher : Cambridge University Press
Page : 212 pages
File Size : 53,5 Mb
Release : 1993-11-26
Category : Mathematics
ISBN : 0521449030

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Theory of Algebraic Invariants by David Hilbert Pdf

An English translation of the notes from David Hilbert's course in 1897 on Invariant Theory at the University of Gottingen taken by his student Sophus Marxen.

David Hilbert and the Axiomatization of Physics (1898–1918)

L. Corry
David Hilbert and the Axiomatization of Physics 1898 1918 Book PDF

Author : L. Corry
Publisher : Springer Science & Business Media
Page : 513 pages
File Size : 51,7 Mb
Release : 2013-06-29
Category : Science
ISBN : 9781402027789

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David Hilbert and the Axiomatization of Physics (1898–1918) by L. Corry Pdf

David Hilbert (1862-1943) was the most influential mathematician of the early twentieth century and, together with Henri Poincaré, the last mathematical universalist. His main known areas of research and influence were in pure mathematics (algebra, number theory, geometry, integral equations and analysis, logic and foundations), but he was also known to have some interest in physical topics. The latter, however, was traditionally conceived as comprising only sporadic incursions into a scientific domain which was essentially foreign to his mainstream of activity and in which he only made scattered, if important, contributions. Based on an extensive use of mainly unpublished archival sources, the present book presents a totally fresh and comprehensive picture of Hilbert’s intense, original, well-informed, and highly influential involvement with physics, that spanned his entire career and that constituted a truly main focus of interest in his scientific horizon. His program for axiomatizing physical theories provides the connecting link with his research in more purely mathematical fields, especially geometry, and a unifying point of view from which to understand his physical activities in general. In particular, the now famous dialogue and interaction between Hilbert and Einstein, leading to the formulation in 1915 of the generally covariant field-equations of gravitation, is adequately explored here within the natural context of Hilbert’s overall scientific world-view. This book will be of interest to historians of physics and of mathematics, to historically-minded physicists and mathematicians, and to philosophers of science.

The Theory of Algebraic Number Fields

David Hilbert
The Theory of Algebraic Number Fields Book PDF

Author : David Hilbert
Publisher : Springer Science & Business Media
Page : 402 pages
File Size : 44,5 Mb
Release : 1998-08-20
Category : Mathematics
ISBN : 3540627790

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The Theory of Algebraic Number Fields by David Hilbert Pdf

A translation of Hilberts "Theorie der algebraischen Zahlkörper" best known as the "Zahlbericht", first published in 1897, in which he provides an elegantly integrated overview of the development of algebraic number theory up to the end of the nineteenth century. The Zahlbericht also provided a firm foundation for further research in the theory, and can be seen as the starting point for all twentieth century investigations into the subject, as well as reciprocity laws and class field theory. This English edition further contains an introduction by F. Lemmermeyer and N. Schappacher.

Geometry and the Imagination

David Hilbert,Stephan Cohn-Vossen
Geometry and the Imagination Book PDF

Author : David Hilbert,Stephan Cohn-Vossen
Publisher : American Mathematical Soc.
Page : 370 pages
File Size : 49,5 Mb
Release : 1999
Category : Mathematics
ISBN : 9780821819982

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Geometry and the Imagination by David Hilbert,Stephan Cohn-Vossen Pdf

This remarkable book endures as a true masterpiece of mathematical exposition. The book is overflowing with mathematical ideas, which are always explained clearly and elegantly, and above all, with penetrating insight. It is a joy to read, both for beginners and experienced mathematicians. Geometry and the Imagination is full of interesting facts, many of which you wish you had known before. The book begins with examples of the simplest curves and surfaces, including thread constructions of certain quadrics and other surfaces. The chapter on regular systems of points leads to the crystallographic groups and the regular polyhedra in $\mathbb{R}^3$. In this chapter, they also discuss plane lattices. By considering unit lattices, and throwing in a small amount of number theory when necessary, they effortlessly derive Leibniz's series: $\pi/4 = 1 - 1/3 + 1/5 - 1/7 + - \ldots$. In the section on lattices in three and more dimensions, the authors consider sphere-packing problems, including the famous Kepler problem. One of the most remarkable chapters is ``Projective Configurations''. In a short introductory section, Hilbert and Cohn-Vossen give perhaps the most concise and lucid description of why a general geometer would care about projective geometry and why such an ostensibly plain setup is truly rich in structure and ideas. The chapter on kinematics includes a nice discussion of linkages and the geometry of configurations of points and rods that are connected and, perhaps, constrained in some way. This topic in geometry has become increasingly important in recent times, especially in applications to robotics. This is another example of a simple situation that leads to a rich geometry. It would be hard to overestimate the continuing influence Hilbert-Cohn-Vossen's book has had on mathematicians of this century. It surely belongs in the pantheon of great mathematics books.

David Hilbert’s Lectures on the Foundations of Geometry 1891–1902

Michael Hallett,Ulrich Majer
David Hilbert s Lectures on the Foundations of Geometry 1891 1902 Book PDF

Author : Michael Hallett,Ulrich Majer
Publisher : Springer
Page : 0 pages
File Size : 52,7 Mb
Release : 2004-05-17
Category : Mathematics
ISBN : 3540643737

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David Hilbert’s Lectures on the Foundations of Geometry 1891–1902 by Michael Hallett,Ulrich Majer Pdf

This volume contains six sets of notes for lectures on the foundations of geometry held by Hilbert in the period 1891-1902. It also reprints the first edition of Hilbert’s celebrated Grundlagen der Geometrie of 1899, together with the important additions which appeared first in the French translation of 1900. The lectures document the emergence of a new approach to foundational study and contain many reflections and investigations which never found their way into print.

Logos and Alogon

Arkady Plotnitsky
Logos and Alogon Book PDF

Author : Arkady Plotnitsky
Publisher : Springer Nature
Page : 307 pages
File Size : 45,7 Mb
Release : 2023-01-16
Category : Mathematics
ISBN : 9783031136788

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Logos and Alogon by Arkady Plotnitsky Pdf

This book is a philosophical study of mathematics, pursued by considering and relating two aspects of mathematical thinking and practice, especially in modern mathematics, which, having emerged around 1800, consolidated around 1900 and extends to our own time, while also tracing both aspects to earlier periods, beginning with the ancient Greek mathematics. The first aspect is conceptual, which characterizes mathematics as the invention of and working with concepts, rather than only by its logical nature. The second, Pythagorean, aspect is grounded, first, in the interplay of geometry and algebra in modern mathematics, and secondly, in the epistemologically most radical form of modern mathematics, designated in this study as radical Pythagorean mathematics. This form of mathematics is defined by the role of that which beyond the limits of thought in mathematical thinking, or in ancient Greek terms, used in the book’s title, an alogon in the logos of mathematics. The outcome of this investigation is a new philosophical and historical understanding of the nature of modern mathematics and mathematics in general. The book is addressed to mathematicians, mathematical physicists, and philosophers and historians of mathematics, and graduate students in these fields.

The Oxford Handbook of the History of Quantum Interpretations

Guido Bacciagaluppi,Olivier Darrigol,Olival Freire Jr
The Oxford Handbook of the History of Quantum Interpretations Book PDF

Author : Guido Bacciagaluppi,Olivier Darrigol,Olival Freire Jr
Publisher : Oxford University Press
Page : 1311 pages
File Size : 44,7 Mb
Release : 2022
Category : Science
ISBN : 9780198844495

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The Oxford Handbook of the History of Quantum Interpretations by Guido Bacciagaluppi,Olivier Darrigol,Olival Freire Jr Pdf

Crucial to most research in physics, as well as leading to the development of inventions such as the transistor and the laser, quantum mechanics approaches its centenary with an impressive record. However, the field has also long been the subject of ongoing debates about the foundations and interpretation of the theory, referred to as the quantum controversy. This Oxford Handbook offers a historical overview of the contrasts which have been at the heart of quantum physics for the last 100 years. Drawing on the wide-ranging expertise of several contributors working across physics, history, and philosophy, the handbook outlines the main theories and interpretations of quantum physics. It goes on to tackle the key controversies surrounding the field, touching on issues such as determinism, realism, locality, classicality, information, measurements, mathematical foundations, and the links between quantum theory and gravity. This engaging introduction is an essential guide for all those interested in the history of scientific controversies and history of quantum physics. It also provides a fascinating examination of the potential of quantum physics to influence new discoveries and advances in fields such quantum information and computing.

Lie Theory and Its Applications in Physics

Vladimir Dobrev
Lie Theory and Its Applications in Physics Book PDF

Author : Vladimir Dobrev
Publisher : Springer Nature
Page : 552 pages
File Size : 43,9 Mb
Release : 2020-10-15
Category : Science
ISBN : 9789811577758

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Lie Theory and Its Applications in Physics by Vladimir Dobrev Pdf

This volume presents modern trends in the area of symmetries and their applications based on contributions to the workshop "Lie Theory and Its Applications in Physics" held near Varna (Bulgaria) in June 2019. Traditionally, Lie theory is a tool to build mathematical models for physical systems. Recently, the trend is towards geometrization of the mathematical description of physical systems and objects. A geometric approach to a system yields in general some notion of symmetry, which is very helpful in understanding its structure. Geometrization and symmetries are meant in their widest sense, i.e., representation theory, algebraic geometry, number theory, infinite-dimensional Lie algebras and groups, superalgebras and supergroups, groups and quantum groups, noncommutative geometry, symmetries of linear and nonlinear partial differential operators, special functions, and others. Furthermore, the necessary tools from functional analysis are included. This is a large interdisciplinary and interrelated field. The topics covered in this volume from the workshop represent the most modern trends in the field : Representation Theory, Symmetries in String Theories, Symmetries in Gravity Theories, Supergravity, Conformal Field Theory, Integrable Systems, Polylogarithms, and Supersymmetry. They also include Supersymmetric Calogero-type models, Quantum Groups, Deformations, Quantum Computing and Deep Learning, Entanglement, Applications to Quantum Theory, and Exceptional Quantum Algebra for the standard model of particle physics This book is suitable for a broad audience of mathematicians, mathematical physicists, and theoretical physicists, including researchers and graduate students interested in Lie Theory.