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Title David Hilbert s Lectures on the Foundations of Geometry 1891 1902
Author Michael Hallett
Publisher Springer Science & Business Media
Release 2004-05-17
Category Mathematics
Total Pages 661
ISBN 9783540643739
Language English, Spanish, and French
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Book Summary:

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.

Handbook of Differential Geometry by Franki J.E. Dillen

Title Handbook of Differential Geometry
Author Franki J.E. Dillen
Publisher Elsevier
Release 2005-11-29
Category Mathematics
Total Pages 574
ISBN 9780080461205
Language English, Spanish, and French
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Book Summary:

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

Title Lectures on Classical Differential Geometry
Author Dirk Jan Struik
Publisher Courier Corporation
Release 1961-01-01
Category Mathematics
Total Pages 232
ISBN 9780486656090
Language English, Spanish, and French
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Book Summary:

Elementary, yet authoritative and scholarly, this book offers an excellent brief introduction to the classical theory of differential geometry. It is aimed at advanced undergraduate and graduate students who will find it not only highly readable but replete with illustrations carefully selected to help stimulate the student's visual understanding of geometry. The text features an abundance of problems, most of which are simple enough for class use, and often convey an interesting geometrical fact. A selection of more difficult problems has been included to challenge the ambitious student. Written by a noted mathematician and historian of mathematics, this volume presents the fundamental conceptions of the theory of curves and surfaces and applies them to a number of examples. Dr. Struik has enhanced the treatment with copious historical, biographical, and bibliographical references that place the theory in context and encourage the student to consult original sources and discover additional important ideas there. For this second edition, Professor Struik made some corrections and added an appendix with a sketch of the application of Cartan's method of Pfaffians to curve and surface theory. The result was to further increase the merit of this stimulating, thought-provoking text — ideal for classroom use, but also perfectly suited for self-study. In this attractive, inexpensive paperback edition, it belongs in the library of any mathematician or student of mathematics interested in differential geometry.

Stochastic Geometry by David Coupier

Title Stochastic Geometry
Author David Coupier
Publisher Springer
Release 2019-04-09
Category Mathematics
Total Pages 232
ISBN 3030135470
Language English, Spanish, and French
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Book Summary:

This volume offers a unique and accessible overview of the most active fields in Stochastic Geometry, up to the frontiers of recent research. Since 2014, the yearly meeting of the French research structure GDR GeoSto has been preceded by two introductory courses. This book contains five of these introductory lectures. The first chapter is a historically motivated introduction to Stochastic Geometry which relates four classical problems (the Buffon needle problem, the Bertrand paradox, the Sylvester four-point problem and the bicycle wheel problem) to current topics. The remaining chapters give an application motivated introduction to contemporary Stochastic Geometry, each one devoted to a particular branch of the subject: understanding spatial point patterns through intensity and conditional intensities; stochastic methods for image analysis; random fields and scale invariance; and the theory of Gibbs point processes. Exposing readers to a rich theory, this book will encourage further exploration of the subject and its wide applications.

New Developments in Differential Geometry Budapest 1996 by Conference on Differential Geometry

Title New Developments in Differential Geometry Budapest 1996
Author Conference on Differential Geometry
Publisher Springer Science & Business Media
Release 1999
Category Mathematics
Total Pages 519
ISBN 9780792353072
Language English, Spanish, and French
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Book Summary:

Proceedings of the Conference on Differential Geometry, Budapest, Hungary, July 27-30, 1996

Nonlinear Computational Geometry by Ioannis Z. Emiris

Title Nonlinear Computational Geometry
Author Ioannis Z. Emiris
Publisher Springer Science & Business Media
Release 2009-10-28
Category Mathematics
Total Pages 239
ISBN 1441909990
Language English, Spanish, and French
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Book Summary:

An original motivation for algebraic geometry was to understand curves and surfaces in three dimensions. Recent theoretical and technological advances in areas such as robotics, computer vision, computer-aided geometric design and molecular biology, together with the increased availability of computational resources, have brought these original questions once more into the forefront of research. One particular challenge is to combine applicable methods from algebraic geometry with proven techniques from piecewise-linear computational geometry (such as Voronoi diagrams and hyperplane arrangements) to develop tools for treating curved objects. These research efforts may be summarized under the term nonlinear computational geometry. This volume grew out of an IMA workshop on Nonlinear Computational Geometry in May/June 2007 (organized by I.Z. Emiris, R. Goldman, F. Sottile, T. Theobald) which gathered leading experts in this emerging field. The research and expository articles in the volume are intended to provide an overview of nonlinear computational geometry. Since the topic involves computational geometry, algebraic geometry, and geometric modeling, the volume has contributions from all of these areas. By addressing a broad range of issues from purely theoretical and algorithmic problems, to implementation and practical applications this volume conveys the spirit of the IMA workshop.

Algebraic Geometry and Singularities by Antonio Campillo Lopez

Title Algebraic Geometry and Singularities
Author Antonio Campillo Lopez
Publisher Springer Science & Business Media
Release 1995-01-26
Category Mathematics
Total Pages 407
ISBN 9783764353346
Language English, Spanish, and French
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Book Summary:

The volume contains both general and research papers. Among the first ones are papers showing recent and original developments or methods in subjects such as resolution of singularities, D-module theory, singularities of maps and geometry of curves. The research papers deal on topics related to, or close to, those listed_above. The contributions are organized in three parts according to their contents. Part I presents a set of papers on resolution of singularities, a topic of renewed activity. It deals with important topics of current interest, such as canonical, algorithmic, combinatorial and graphical procedures (Villamayor, Oka, Marijmin), as well as special results on desingularization in characteristic p (Cossart, Moh), and connections between resolution and structure of the space of arcs through a singularity (Gonz81ez-Sprinberg-Lejeune-Jalabert). Part II contains a series of papers on the study~of singularities and its connections with differential systems and deformation or perturbation theo­ ries. Two expository papers (Maisonobe-Briam;on, :'vlebkhout) describe, in an algebro-geometric way, the interaction between singularities and D-module t.he­ ory including recent progress on Bernstein polynomials and Newton polygon techniques. Geometry of foliations (Henaut, Garcfa-Reguera), polar varieties and stratifications (Hajto) are also topics treated here. Two other papers (Wall, Greuel-Pfister) deal with quasihomogeneous singularities in the contexts of per­ turbations and moduli spaces. Globalization of deformations of singularities (de Jong) and determination of complex topology from the real one (~10nd) com­ plete this series of papers. Part III consists of papers on algebraic geometry of curves and surfaces.

Title Foundations of Three Dimensional Euclidean Geometry
Author Izu Vaisman
Publisher CRC Press
Release 2020-11-25
Category Mathematics
Total Pages 288
ISBN 1000110494
Language English, Spanish, and French
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Book Summary:

This book presents to the reader a modern axiomatic construction of three-dimensional Euclidean geometry in a rigorous and accessible form. It is helpful for high school teachers who are interested in the modernization of the teaching of geometry.

Combinatorial Algebraic Geometry by Gregory G. Smith

Title Combinatorial Algebraic Geometry
Author Gregory G. Smith
Publisher Springer
Release 2017-11-17
Category Mathematics
Total Pages 390
ISBN 1493974866
Language English, Spanish, and French
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Book Summary:

This volume consolidates selected articles from the 2016 Apprenticeship Program at the Fields Institute, part of the larger program on Combinatorial Algebraic Geometry that ran from July through December of 2016. Written primarily by junior mathematicians, the articles cover a range of topics in combinatorial algebraic geometry including curves, surfaces, Grassmannians, convexity, abelian varieties, and moduli spaces. This book bridges the gap between graduate courses and cutting-edge research by connecting historical sources, computation, explicit examples, and new results.

Title An Invitation To Noncommutative Geometry
Author Matilde Marcolli
Publisher World Scientific
Release 2008-02-11
Category Science
Total Pages 516
ISBN 9814475629
Language English, Spanish, and French
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Book Summary:

This is the first existing volume that collects lectures on this important and fast developing subject in mathematics. The lectures are given by leading experts in the field and the range of topics is kept as broad as possible by including both the algebraic and the differential aspects of noncommutative geometry as well as recent applications to theoretical physics and number theory.