Geometry from a Differentiable Viewpoint

Author: John McCleary

Publisher: Cambridge University Press

ISBN: 9780521424806

Category: Mathematics

Page: 308

View: 2642

This book offers a new treatment of the topic, one which is designed to make differential geometry an approachable subject for advanced undergraduates. Professor McCleary considers the historical development of non-Euclidean geometry, placing differential geometry in the context of geometry students will be familiar with from high school. The text serves as both an introduction to the classical differential geometry of curves and surfaces and as a history of a particular surface, the non-Euclidean or hyperbolic plane. The main theorems of non-Euclidean geometry are presented along with their historical development. The author then introduces the methods of differential geometry and develops them toward the goal of constructing models of the hyperbolic plane. While interesting diversions are offered, such as Huygen's pendulum clock and mathematical cartography, the book thoroughly treats the models of non-Euclidean geometry and the modern ideas of abstract surfaces and manifolds.

Classical Geometry

Euclidean, Transformational, Inversive, and Projective

Author: I. E. Leonard,J. E. Lewis,A. C. F. Liu,G. W. Tokarsky

Publisher: John Wiley & Sons

ISBN: 1118679148

Category: Mathematics

Page: 496

View: 5363

Features the classical themes of geometry with plentiful applications in mathematics, education, engineering, and science Accessible and reader-friendly, Classical Geometry: Euclidean, Transformational, Inversive, and Projective introduces readers to a valuable discipline that is crucial to understanding bothspatial relationships and logical reasoning. Focusing on the development of geometric intuitionwhile avoiding the axiomatic method, a problem solving approach is encouraged throughout. The book is strategically divided into three sections: Part One focuses on Euclidean geometry, which provides the foundation for the rest of the material covered throughout; Part Two discusses Euclidean transformations of the plane, as well as groups and their use in studying transformations; and Part Three covers inversive and projective geometry as natural extensions of Euclidean geometry. In addition to featuring real-world applications throughout, Classical Geometry: Euclidean, Transformational, Inversive, and Projective includes: Multiple entertaining and elegant geometry problems at the end of each section for every level of study Fully worked examples with exercises to facilitate comprehension and retention Unique topical coverage, such as the theorems of Ceva and Menalaus and their applications An approach that prepares readers for the art of logical reasoning, modeling, and proofs The book is an excellent textbook for courses in introductory geometry, elementary geometry, modern geometry, and history of mathematics at the undergraduate level for mathematics majors, as well as for engineering and secondary education majors. The book is also ideal for anyone who would like to learn the various applications of elementary geometry.

Topics in Geometry

In Memory of Joseph D’Atri

Author: Simon Gindikin

Publisher: Springer Science & Business Media

ISBN: 1461224322

Category: Mathematics

Page: 370

View: 1812

This collection of articles serves to commemorate the legacy of Joseph D'Atri, who passed away on April 29, 1993, a few days after his 55th birthday. Joe D' Atri is credited with several fundamental discoveries in ge ometry. In the beginning of his mathematical career, Joe was interested in the generalization of symmetrical spaces in the E. Cart an sense. Symmetric spaces, differentiated from other homogeneous manifolds by their geomet rical richness, allows the development of a deep analysis. Geometers have been constantly interested and challenged by the problem of extending the class of symmetric spaces so as to preserve their geometrical and analytical abundance. The name of D'Atri is tied to one of the most successful gen eralizations: Riemann manifolds in which (local) geodesic symmetries are volume-preserving (up to sign). In time, it turned out that the majority of interesting generalizations of symmetrical spaces are D'Atri spaces: natu ral reductive homogeneous spaces, Riemann manifolds whose geodesics are orbits of one-parameter subgroups, etc. The central place in D'Atri's research is occupied by homogeneous bounded domains in en, which are not symmetric. Such domains were discovered by Piatetskii-Shapiro in 1959, and given Joe's strong interest in the generalization of symmetric spaces, it was very natural for him to direct his research along this path.

Selected Papers on Probability and Statistics

Author: N.A

Publisher: American Mathematical Soc.

ISBN: 0821848216

Category: Mathematics

Page: 231

View: 2946

This volume contains translations of papers that originally appeared in the Japanese journal Sugaku. The papers range over a variety of topics in probability theory, statistics, and applications. This volume is suitable for graduate students and research mathematicians interested in probability and statistics.

Selected Papers on Differential Equations and Analysis

Author: N.A

Publisher: American Mathematical Soc.

ISBN: 9780821839270

Category: Mathematics

Page: 145

View: 4482

This volume contains translations of papers that originally appeared in the Japanese journal ""Sugaku"". The papers range over a variety of topics, including differential equations with free boundary, singular integral operators, operator algebras, and relations between the Brownian motion on a manifold with function theory. The volume is suitable for graduate students and research mathematicians interested in analysis and differential equations.

Selected Papers on Analysis, Probability, and Statistics

Author: Katsumi Nomizu

Publisher: American Mathematical Soc.

ISBN: 9780821875124

Category: Mathematics

Page: 151

View: 5523

This book presents papers that originally appeared in the Japanese journal ""Sugaku"". The papers fall into the general area of mathematical analysis as it pertains to probability and statistics, dynamical systems, differential equations and analytic function theory. Among the topics discussed are: stochastic differential equations, spectra of the Laplacian and Schrodinger operators, nonlinear partial differential equations which generate dissipative dynamical systems, fractal analysis on self-similar sets and their global structure of analytic functions.

Selected Papers of Freeman Dyson with Commentary

Author: Freeman J. Dyson,Professor of Physics Institute for Advanced Study Freeman J Dyson

Publisher: American Mathematical Soc.

ISBN: 9780821805619

Category: Science

Page: 601

View: 2787

This book offers a unique compilation of papers in mathematics and physics from Freeman Dyson's 50 years of activity and research. These are the papers that Dyson considers most worthy of preserving, and many of them are classics. The papers are accompanied by commentary explaining the context from which they originated and the subsequent history of the problems that either were solved or left unsolved. This collection offers a connected narrative of the developments in mathematics and physics in which the author was involved, beginning with his professional life as a student of G. H. Hardy.

Selected Topics in Algebraic Geometry

Author: National Research Council (U.S.). Committee on Rational Transformations,Virgil Snyder

Publisher: American Mathematical Soc.

ISBN: 9780828401890

Category: Mathematics

Page: 487

View: 5198

This book resulted from two reports (published in 1928 and 1932) of the Committee on Rational Transformations, established by the National Research Council. The purpose of the reports was to give a comprehensive survey of the literature on the subject. Each chapter is regarded as a separate unit that can be read independently.

Russell's Unknown Logicism

A Study in the History and Philosophy of Mathematics

Author: S. Gandon

Publisher: Springer

ISBN: 1137024658

Category: Mathematics

Page: 263

View: 3718

In this excellent book Sebastien Gandon focuses mainly on Russell's two major texts, Principa Mathematica and Principle of Mathematics , meticulously unpicking the details of these texts and bringing a new interpretation of both the mathematical and the philosophical content. Winner of The Bertrand Russell Society Book Award 2013.

Landmark Papers on Photorefractive Nonlinear Optics

Author: Pochi Yeh

Publisher: World Scientific

ISBN: 9789810214432

Category: Science

Page: 605

View: 4843

This book, intended for students, researchers and engineers, is a collection of classic papers on photorefractive nonlinear optics. Included are landmark papers on fundamental photorefractive phenomena, two-wave mixing, four-wave mixing, phase conjugators and resonators, material growth and physics, and applications in image processing, optical storage and optical computing.

Geometry of Foliations

Author: Philippe Tondeur

Publisher: Springer Science & Business Media

ISBN: 9783764357412

Category: Mathematics

Page: 305

View: 670

This volume describes research on the differential geometry of foliations, in particular Riemannian foliations, done over the last few years. It can be read by graduate students and researchers with a background in differential geometry and Riemannian geometry. Of particular interest will be the Hodge theory for the transversal Laplacian, and applications of the heat equation method to Riemannian foliations. There are chapters on the spectral theory for Riemannian foliations, on Connes' point of view of foliations as examples of noncommutative spaces, and a chapter on infinite-dimensional examples of Riemannian foliations.

Optical Engineering

The Journal of the Society of Photo-optical Instrumentation Engineers

Author: N.A

Publisher: N.A


Category: Optical instruments

Page: N.A

View: 9713


Menahem Max Schiffer: Selected Papers

Author: Peter Duren,Lawrence Zalcman

Publisher: Springer Science & Business Media

ISBN: 0817680853

Category: Mathematics

Page: 564

View: 7199

This two volume set presents over 50 of the most groundbreaking contributions of Menahem M Schiffer. All of the reprints of Schiffer’s works herein have extensive annotation and invited commentaries, giving new clarity and insight into the impact and legacy of Schiffer's work. A complete bibliography and brief biography make this a rounded and invaluable reference.

Discrete and Computational Geometry and Graphs

16th Japanese Conference, JCDCGG 2013, Tokyo, Japan, September 17-19, 2013, Revised Selected Papers

Author: Jin Akiyama,Hiro Ito,Toshinori Sakai

Publisher: Springer

ISBN: 3319132873

Category: Computers

Page: 191

View: 6945

This book constitutes the thoroughly refereed post-conference proceedings of the 16th Japanese Conference on Discrete and computational Geometry and Graphs, JDCDGG 2013, held in Tokyo, Japan, in September 2013. The total of 16 papers included in this volume was carefully reviewed and selected from 58 submissions. The papers feature advances made in the field of computational geometry and focus on emerging technologies, new methodology and applications, graph theory and dynamics.

Collected Mathematical Papers

Vol. 1 I Determinants II Linear Algebra III Algebraic Equations

Author: A. Ostrowski

Publisher: Springer Science & Business Media

ISBN: 9783764315061

Category: Mathematics

Page: 904

View: 8738

This publication was made possible through a bequest from my beloved late wife. United together in this present collection are those works by the author which have not previously appeared in book form. The following are excepted: Vorlesungen tiber Differential und Integralrechnung (Lectures on Differential and Integral Calculus) Vols 1-3, Birkhiiuser Verlag, Basel (1965-1968); Aufgabensammlung zur Infinitesimalrechnung (Exercises in Infinitesimal Calculus) Vols 1, 2a, 2b, and 3, Birkhiiuser Verlag, Basel (1967-1977); two issues from Memorial des Sciences on Conformal Mapping (written together with C. Gattegno), Gauthier-Villars, Paris (1949); Solution of Equations in Euclidean and Banach Spaces, Academic Press, New York (1973); and Stu­ dien tiber den Schottkyschen Satz (Studies on Schottky's Theorem), Wepf & Co., Basel (1931). Where corrections have had to be implemented in the text of certain papers, references to these are made at the conclusion of each paper. In the few instances where this system does not, for technical reasons, seem appropriate, an asterisk in the page margin indicates wherever a correction is necessary and this is then given at the end of the paper. (There is one exception: the correc­ tions to the paper on page 561 are presented on page 722. The works are published in 6 volumes and are arranged under 16 topic headings. Within each heading, the papers are ordered chronologically according to the date of original publication.

Michael Atiyah Collected Works


Author: Michael Atiyah

Publisher: Oxford University Press, USA

ISBN: 0199689261

Category: Mathematics

Page: 442

View: 7017

Professor Atiyah is one of the greatest living mathematicians and is renowned in the mathematical world. He is a recipient of the Fields Medal, the mathematical equivalent of the Nobel Prize, and is still actively involved in the mathematics community. His huge number of published papers, focusing on the areas of algebraic geometry and topology, have here been collected into seven volumes, with the first five volumes divided thematically and the sixth and seventh arranged by date. This seventh volume in Michael Atiyah's Collected Works contains a selection of his publications between 2002 and 2013, including his work on skyrmions; K-theory and cohomology; geometric models of matter; curvature, cones and characteristic numbers; and reflections on the work of Riemann, Einstein and Bott.