The Theory Of Singularities And Its Applications
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| Author | : Vladimir Igorevich Arnolʹd |
| Publisher | : Cambridge University Press |
| Total Pages | : 88 |
| Release | : 1991-05-31 |
| Genre | : Mathematics |
| ISBN | : 9780521422802 |
In this book, which is based on lectures given in Pisa under the auspices of the Accademia Nazionale dei Lincei, the distinguished mathematician Vladimir Arnold describes those singularities encountered in different branches of mathematics. He avoids giving difficult proofs of all the results in order to provide the reader with a concise and accessible overview of the many guises and areas in which singularities appear, such as geometry and optics; optimal control theory and algebraic geometry; reflection groups and dynamical systems and many more. This will be an excellent companion for final year undergraduates and graduates whose area of study brings them into contact with singularities.
| Author | : Vladimir Arnold |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 271 |
| Release | : 2013-12-01 |
| Genre | : Mathematics |
| ISBN | : 9401133301 |
One service mathematics has rendered the 'Et moi ...) si j'avait su comment en revenir, human race. It has put common sense back je n'y serais point aile.' Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non The series is divergent; therefore we may be sense'. ErieT. Bell able to do something with it. O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.
| Author | : Vladimir Igorevich Arnold |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 264 |
| Release | : 1993 |
| Genre | : Celestial mechanics |
| ISBN | : 9783540505839 |
'EMS 6' is the latest volume in the sub series 'Dynamical Systems of the Encyclopaedia'. It is the first of two volumes covering Singularity Theory, which, besides its fundamental use in Dynamical Systems and Bifurcation Theory, is an important part of other fields such as algebraic geometry, differential geometry and geometric optics.
| Author | : Gert-Martin Greuel |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 482 |
| Release | : 2007-02-23 |
| Genre | : Mathematics |
| ISBN | : 3540284192 |
Singularity theory is a young, rapidly-growing topic with connections to algebraic geometry, complex analysis, commutative algebra, representations theory, Lie groups theory and topology, and many applications in the natural and technical sciences. This book presents the basic singularity theory of analytic spaces, including local deformation theory and the theory of plane curve singularities. It includes complete proofs.
| Author | : Franz-Viktor Kuhlmann |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 472 |
| Release | : 2002 |
| Genre | : Mathematics |
| ISBN | : |
This book is the first of two proceedings volumes stemming from the International Conference and Workshop on Valuation Theory held at the University of Saskatchewan (Saskatoon, SK, Canada). The special feature of this book is its focus on current applications of valuation theory to a broad range of topics. This first volume contains research and survey papers on a variety of valuation-theoretic topics, including rigid analytic geometry, real algebraic geometry, resolution of singularities, noncommutative valuation theory, valuations on fields, and Galois theory. Also included is a paper on the history of valuation theory. The book is suitable for graduate students and research mathematicians working in algebra, algebraic geometry, number theory, and mathematical logic.
| Author | : Craig Huneke |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 152 |
| Release | : 1996 |
| Genre | : Mathematics |
| ISBN | : 082180412X |
This monograph deals with the theory of tight closure and its applications. The contents are based on ten talks given at a CBMS conference held at North Dakota State University in June 1995.
| Author | : Wolfgang Ebeling |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 334 |
| Release | : 2007 |
| Genre | : Mathematics |
| ISBN | : 0821833197 |
The book provides an introduction to the theory of functions of several complex variables and their singularities, with special emphasis on topological aspects. The topics include Riemann surfaces, holomorphic functions of several variables, classification and deformation of singularities, fundamentals of differential topology, and the topology of singularities. The aim of the book is to guide the reader from the fundamentals to more advanced topics of recent research. All the necessary prerequisites are specified and carefully explained. The general theory is illustrated by various examples and applications.
| Author | : SENTHILKUMARAN |
| Publisher | : IOP Publishing Limited |
| Total Pages | : 0 |
| Release | : 2024-01-25 |
| Genre | : Mathematics |
| ISBN | : 9780750349802 |
The book gives a thorough introduction to singularities and their development. It explains in detail important topics such as the types of singularities, their properties, detection and application, and emerging research trends.
| Author | : William K. Allard |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 482 |
| Release | : 1986 |
| Genre | : Mathematics |
| ISBN | : 0821814702 |
Includes twenty-six papers that survey a cross section of work in modern geometric measure theory and its applications in the calculus of variations. This title provides an access to the material, including introductions and summaries of many of the authors' much longer works and a section containing 80 open problems in the field.
| Author | : José Luis Cisneros Molina |
| Publisher | : Springer Nature |
| Total Pages | : 616 |
| Release | : 2020-10-24 |
| Genre | : Mathematics |
| ISBN | : 3030530612 |
This volume consists of ten articles which provide an in-depth and reader-friendly survey of some of the foundational aspects of singularity theory. Authored by world experts, the various contributions deal with both classical material and modern developments, covering a wide range of topics which are linked to each other in fundamental ways. Singularities are ubiquitous in mathematics and science in general. Singularity theory interacts energetically with the rest of mathematics, acting as a crucible where different types of mathematical problems interact, surprising connections are born and simple questions lead to ideas which resonate in other parts of the subject. This is the first volume in a series which aims to provide an accessible account of the state-of-the-art of the subject, its frontiers, and its interactions with other areas of research. The book is addressed to graduate students and newcomers to the theory, as well as to specialists who can use it as a guidebook.
