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Author : Mathieu Anel,Gabriel Catren
Publisher : Cambridge University Press
Page : 601 pages
File Size : 44,5 Mb
Release : 2021-04
Category : Mathematics
ISBN : 9781108490634
In this graduate-level book, leading researchers explore various new notions of 'space' in mathematics.
Author : Mathieu Anel,Gabriel Catren
Publisher : Unknown
Page : 900 pages
File Size : 45,9 Mb
Release : 2020-11-30
Category : Mathematics
ISBN : 1108854362
Author : Mathieu Anel,Gabriel Catren
Publisher : Cambridge University Press
Page : 437 pages
File Size : 48,6 Mb
Release : 2021-04
Category : Mathematics
ISBN : 9781108490627
In this graduate-level book, leading researchers explore various new notions of 'space' in mathematical physics.
Author : Tim Maudlin
Publisher : Oxford University Press
Page : 374 pages
File Size : 44,7 Mb
Release : 2014-02
Category : Mathematics
ISBN : 9780198701309
Tim Maudlin sets out a completely new method for describing the geometrical structure of spaces, and thus a better mathematical tool for describing and understanding space-time. He presents a historical review of the development of geometry and topology, and then his original Theory of Linear Structures.
Author : Max Dickmann,Niels Schwartz,Marcus Tressl
Publisher : Cambridge University Press
Page : 652 pages
File Size : 45,6 Mb
Release : 2019-03-21
Category : Mathematics
ISBN : 9781107146723
Offers a comprehensive presentation of spectral spaces focussing on their topology and close connections with algebra, ordered structures, and logic.
Author : Garret Sobczyk
Publisher : Springer Science & Business Media
Page : 373 pages
File Size : 40,7 Mb
Release : 2012-10-26
Category : Mathematics
ISBN : 9780817683856
The first book of its kind, New Foundations in Mathematics: The Geometric Concept of Number uses geometric algebra to present an innovative approach to elementary and advanced mathematics. Geometric algebra offers a simple and robust means of expressing a wide range of ideas in mathematics, physics, and engineering. In particular, geometric algebra extends the real number system to include the concept of direction, which underpins much of modern mathematics and physics. Much of the material presented has been developed from undergraduate courses taught by the author over the years in linear algebra, theory of numbers, advanced calculus and vector calculus, numerical analysis, modern abstract algebra, and differential geometry. The principal aim of this book is to present these ideas in a freshly coherent and accessible manner. New Foundations in Mathematics will be of interest to undergraduate and graduate students of mathematics and physics who are looking for a unified treatment of many important geometric ideas arising in these subjects at all levels. The material can also serve as a supplemental textbook in some or all of the areas mentioned above and as a reference book for professionals who apply mathematics to engineering and computational areas of mathematics and physics.
Author : Gerard Buskes,Arnoud van Rooij
Publisher : Springer Science & Business Media
Page : 321 pages
File Size : 55,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461206651
gentle introduction to the subject, leading the reader to understand the notion of what is important in topology with regard to geometry. Divided into three sections - The line and the plane, Metric spaces and Topological spaces -, the book eases the move into higher levels of abstraction. Students are thereby informally assisted in learning new ideas while remaining on familiar territory. The authors do not assume previous knowledge of axiomatic approach or set theory. Similarly, they have restricted the mathematical vocabulary in the book so as to avoid overwhelming the reader, and the concept of convergence is employed to allow students to focus on a central theme while moving to a natural understanding of the notion of topology. The pace of the book is relaxed with gradual acceleration: the first nine sections form a balanced course in metric spaces for undergraduates while also containing ample material for a two-semester graduate course. Finally, the book illustrates the many connections between topology and other subjects, such as analysis and set theory, via the inclusion of "Extras" at the end of each chapter presenting a brief foray outside topology.
Author : Hakan Hedenmalm,Boris Korenblum,Kehe Zhu
Publisher : Springer Science & Business Media
Page : 299 pages
File Size : 52,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461204978
Fifteen years ago, most mathematicians who worked in the intersection of function theory and operator theory thought that progress on the Bergman spaces was unlikely, yet today the situation has completely changed. For several years, research interest and activity have expanded in this area and there are now rich theories describing the Bergman spaces and their operators. This book is a timely treatment of the theory, written by three of the major players in the field.
Author : Jeffrey R. Weeks
Publisher : CRC Press
Page : 405 pages
File Size : 44,7 Mb
Release : 2001-12-12
Category : Mathematics
ISBN : 9780203912669
Maintaining the standard of excellence set by the previous edition, this textbook covers the basic geometry of two- and three-dimensional spaces Written by a master expositor, leading researcher in the field, and MacArthur Fellow, it includes experiments to determine the true shape of the universe and contains illustrated examples and engaging exercises that teach mind-expanding ideas in an intuitive and informal way. Bridging the gap from geometry to the latest work in observational cosmology, the book illustrates the connection between geometry and the behavior of the physical universe and explains how radiation remaining from the big bang may reveal the actual shape of the universe.
Author : Melvin Hausner
Publisher : Courier Dover Publications
Page : 417 pages
File Size : 52,9 Mb
Release : 2018-10-17
Category : Mathematics
ISBN : 9780486835396
A fascinating exploration of the correlation between geometry and linear algebra, this text portrays the former as a subject better understood by the use and development of the latter rather than as an independent field. The treatment offers elementary explanations of the role of geometry in other branches of math and science — including physics, analysis, and group theory — as well as its value in understanding probability, determinant theory, and function spaces. Outstanding features of this volume include discussions of systematic geometric motivations in vector space theory and matrix theory; the use of the center of mass in geometry, with an introduction to barycentric coordinates; axiomatic development of determinants in a chapter dealing with area and volume; and a careful consideration of the particle problem. Students and other mathematically inclined readers will find that this inquiry into the interplay between geometry and other areas offers an enriched appreciation of both subjects.
Author : Haim Brezis
Publisher : Springer Science & Business Media
Page : 600 pages
File Size : 51,5 Mb
Release : 2010-11-02
Category : Mathematics
ISBN : 9780387709147
This textbook is a completely revised, updated, and expanded English edition of the important Analyse fonctionnelle (1983). In addition, it contains a wealth of problems and exercises (with solutions) to guide the reader. Uniquely, this book presents in a coherent, concise and unified way the main results from functional analysis together with the main results from the theory of partial differential equations (PDEs). Although there are many books on functional analysis and many on PDEs, this is the first to cover both of these closely connected topics. Since the French book was first published, it has been translated into Spanish, Italian, Japanese, Korean, Romanian, Greek and Chinese. The English edition makes a welcome addition to this list.
Author : Robert M. Thrall,Leonard Tornheim
Publisher : Courier Corporation
Page : 336 pages
File Size : 44,5 Mb
Release : 2014-01-15
Category : Mathematics
ISBN : 9780486321059
Students receive the benefits of axiom-based mathematical reasoning as well as a grasp of concrete formulations. Suitable as a primary or supplementary text for college-level courses in linear algebra. 1957 edition.
Author : Patrick Iglesias-Zemmour
Publisher : American Mathematical Soc.
Page : 467 pages
File Size : 42,7 Mb
Release : 2013-04-09
Category : Mathematics
ISBN : 9780821891315
Diffeology is an extension of differential geometry. With a minimal set of axioms, diffeology allows us to deal simply but rigorously with objects which do not fall within the usual field of differential geometry: quotients of manifolds (even non-Hausdorff), spaces of functions, groups of diffeomorphisms, etc. The category of diffeology objects is stable under standard set-theoretic operations, such as quotients, products, co-products, subsets, limits, and co-limits. With its right balance between rigor and simplicity, diffeology can be a good framework for many problems that appear in various areas of physics. Actually, the book lays the foundations of the main fields of differential geometry used in theoretical physics: differentiability, Cartan differential calculus, homology and cohomology, diffeological groups, fiber bundles, and connections. The book ends with an open program on symplectic diffeology, a rich field of application of the theory. Many exercises with solutions make this book appropriate for learning the subject.
Author : P.R. Halmos
Publisher : Springer Science & Business Media
Page : 385 pages
File Size : 40,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781468493306
From the Preface: "This book was written for the active reader. The first part consists of problems, frequently preceded by definitions and motivation, and sometimes followed by corollaries and historical remarks... The second part, a very short one, consists of hints... The third part, the longest, consists of solutions: proofs, answers, or contructions, depending on the nature of the problem.... This is not an introduction to Hilbert space theory. Some knowledge of that subject is a prerequisite: at the very least, a study of the elements of Hilbert space theory should proceed concurrently with the reading of this book."
Author : Hossein Abbaspour,Matilde Marcolli,Thomas Tradler
Publisher : Springer Science & Business Media
Page : 174 pages
File Size : 54,6 Mb
Release : 2010-04-21
Category : Mathematics
ISBN : 9783834896803
The first instances of deformation theory were given by Kodaira and Spencer for complex structures and by Gerstenhaber for associative algebras. Since then, deformation theory has been applied as a useful tool in the study of many other mathematical structures, and even today it plays an important role in many developments of modern mathematics. This volume collects a few self-contained and peer-reviewed papers by experts which present up-to-date research topics in algebraic and motivic topology, quantum field theory, algebraic geometry, noncommutative geometry and the deformation theory of Poisson algebras. They originate from activities at the Max-Planck-Institute for Mathematics and the Hausdorff Center for Mathematics in Bonn.