Geometry Of Mobius Transformations Elliptic Parabolic And Hyperbolic Actions Of Sl2 R With Dvd Rom
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Geometry Of Mobius Transformations Elliptic Parabolic And Hyperbolic Actions Of Sl2 R With Dvd Rom
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Author : Vladimir V Kisil
language : en
Publisher: World Scientific
Release Date : 2012-06-19
Geometry Of Mobius Transformations Elliptic Parabolic And Hyperbolic Actions Of Sl2 R With Dvd Rom written by Vladimir V Kisil and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-06-19 with Mathematics categories.
This book is a unique exposition of rich and inspiring geometries associated with Möbius transformations of the hypercomplex plane. The presentation is self-contained and based on the structural properties of the group SL2(R). Starting from elementary facts in group theory, the author unveils surprising new results about the geometry of circles, parabolas and hyperbolas, using an approach based on the Erlangen programme of F Klein, who defined geometry as a study of invariants under a transitive group action.The treatment of elliptic, parabolic and hyperbolic Möbius transformations is provided in a uniform way. This is possible due to an appropriate usage of complex, dual and double numbers which represent all non-isomorphic commutative associative two-dimensional algebras with unit. The hypercomplex numbers are in perfect correspondence with the three types of geometries concerned. Furthermore, connections with the physics of Minkowski and Galilean space-time are considered./a
Geometry Of M Bius Transformations
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Author : Vladimir V. Kisil
language : en
Publisher: World Scientific
Release Date : 2012
Geometry Of M Bius Transformations written by Vladimir V. Kisil and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.
This book is a unique exposition of rich and inspiring geometries associated with Möbius transformations of the hypercomplex plane. The presentation is self-contained and based on the structural properties of the group SL2(R). Starting from elementary facts in group theory, the author unveils surprising new results about the geometry of circles, parabolas and hyperbolas, using an approach based on the Erlangen programme of F Klein, who defined geometry as a study of invariants under a transitive group action.The treatment of elliptic, parabolic and hyperbolic Möbius transformations is provided in a uniform way. This is possible due to an appropriate usage of complex, dual and double numbers which represent all non-isomorphic commutative associative two-dimensional algebras with unit. The hypercomplex numbers are in perfect correspondence with the three types of geometries concerned. Furthermore, connections with the physics of Minkowski and Galilean space-time are considered.
Topics In Clifford Analysis
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Author : Swanhild Bernstein
language : en
Publisher: Springer Nature
Release Date : 2019-10-15
Topics In Clifford Analysis written by Swanhild Bernstein and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-15 with Mathematics categories.
Quaternionic and Clifford analysis are an extension of complex analysis into higher dimensions. The unique starting point of Wolfgang Sprößig’s work was the application of quaternionic analysis to elliptic differential equations and boundary value problems. Over the years, Clifford analysis has become a broad-based theory with a variety of applications both inside and outside of mathematics, such as higher-dimensional function theory, algebraic structures, generalized polynomials, applications of elliptic boundary value problems, wavelets, image processing, numerical and discrete analysis. The aim of this volume is to provide an essential overview of modern topics in Clifford analysis, presented by specialists in the field, and to honor the valued contributions to Clifford analysis made by Wolfgang Sprößig throughout his career.
Expansion In Finite Simple Groups Of Lie Type
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Author : Terence Tao
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-04-16
Expansion In Finite Simple Groups Of Lie Type written by Terence Tao and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-04-16 with Mathematics categories.
Expander graphs are an important tool in theoretical computer science, geometric group theory, probability, and number theory. Furthermore, the techniques used to rigorously establish the expansion property of a graph draw from such diverse areas of mathematics as representation theory, algebraic geometry, and arithmetic combinatorics. This text focuses on the latter topic in the important case of Cayley graphs on finite groups of Lie type, developing tools such as Kazhdan's property (T), quasirandomness, product estimates, escape from subvarieties, and the Balog-Szemerédi-Gowers lemma. Applications to the affine sieve of Bourgain, Gamburd, and Sarnak are also given. The material is largely self-contained, with additional sections on the general theory of expanders, spectral theory, Lie theory, and the Lang-Weil bound, as well as numerous exercises and other optional material.
A Primer Of Infinitesimal Analysis
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Author : John L. Bell
language : en
Publisher: Cambridge University Press
Release Date : 2008-04-07
A Primer Of Infinitesimal Analysis written by John L. Bell and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-04-07 with Mathematics categories.
A rigorous, axiomatically formulated presentation of the 'zero-square', or 'nilpotent' infinitesimal.
Disquisitiones Arithmeticae
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Author : Carl F. Gauss
language : en
Publisher: Springer
Release Date : 1986-05-01
Disquisitiones Arithmeticae written by Carl F. Gauss and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986-05-01 with Mathematics categories.
The Analytical Theory Of Heat
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Author : Jean-Baptiste-Joseph Fourier
language : en
Publisher:
Release Date : 1878
The Analytical Theory Of Heat written by Jean-Baptiste-Joseph Fourier and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1878 with Heat categories.
Dynamical Systems With Applications Using Maple
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Author : Stephen Lynch
language : en
Publisher: Springer Science & Business Media
Release Date : 2001
Dynamical Systems With Applications Using Maple written by Stephen Lynch and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Computers categories.
"The text treats a remarkable spectrum of topics and has a little for everyone. It can serve as an introduction to many of the topics of dynamical systems, and will help even the most jaded reader, such as this reviewer, enjoy some of the interactive aspects of studying dynamics using Maple." --UK Nonlinear News (Review of First Edition) "The book will be useful for all kinds of dynamical systems courses.... [It] shows the power of using a computer algebra program to study dynamical systems, and, by giving so many worked examples, provides ample opportunity for experiments. ... [It] is well written and a pleasure to read, which is helped by its attention to historical background." --Mathematical Reviews (Review of First Edition) Since the first edition of this book was published in 2001, MapleTM has evolved from Maple V into Maple 13. Accordingly, this new edition has been thoroughly updated and expanded to include more applications, examples, and exercises, all with solutions; two new chapters on neural networks and simulation have also been added. There are also new sections on perturbation methods, normal forms, Gröbner bases, and chaos synchronization. The work provides an introduction to the theory of dynamical systems with the aid of Maple. The author has emphasized breadth of coverage rather than fine detail, and theorems with proof are kept to a minimum. Some of the topics treated are scarcely covered elsewhere. Common themes such as bifurcation, bistability, chaos, instability, multistability, and periodicity run through several chapters. The book has a hands-on approach, using Maple as a pedagogical tool throughout. Maple worksheet files are listed at the end of each chapter, and along with commands, programs, and output may be viewed in color at the author's website. Additional applications and further links of interest may be found at Maplesoft's Application Center. Dynamical Systems with Applications using Maple is aimed at senior undergraduates, graduate students, and working scientists in various branches of applied mathematics, the natural sciences, and engineering. ISBN 978-0-8176-4389-8 § Also by the author: Dynamical Systems with Applications using MATLAB®, ISBN 978-0-8176-4321-8 Dynamical Systems with Applications using Mathematica®, ISBN 978-0-8176-4482-6.
Combinatorial Convexity
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Author : Imre Bárány
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-11-04
Combinatorial Convexity written by Imre Bárány and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-04 with Education categories.
This book is about the combinatorial properties of convex sets, families of convex sets in finite dimensional Euclidean spaces, and finite points sets related to convexity. This area is classic, with theorems of Helly, Carathéodory, and Radon that go back more than a hundred years. At the same time, it is a modern and active field of research with recent results like Tverberg's theorem, the colourful versions of Helly and Carathéodory, and the (p,q) (p,q) theorem of Alon and Kleitman. As the title indicates, the topic is convexity and geometry, and is close to discrete mathematics. The questions considered are frequently of a combinatorial nature, and the proofs use ideas from geometry and are often combined with graph and hypergraph theory. The book is intended for students (graduate and undergraduate alike), but postdocs and research mathematicians will also find it useful. It can be used as a textbook with short chapters, each suitable for a one- or two-hour lecture. Not much background is needed: basic linear algebra and elements of (hyper)graph theory as well as some mathematical maturity should suffice.
Math On Trial
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Author : Leila Schneps
language : en
Publisher: Basic Books
Release Date : 2013-03-12
Math On Trial written by Leila Schneps and has been published by Basic Books this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-12 with Mathematics categories.
In the wrong hands, math can be deadly. Even the simplest numbers can become powerful forces when manipulated by politicians or the media, but in the case of the law, your liberty -- and your life -- can depend on the right calculation. In Math on Trial, mathematicians Leila Schneps and Coralie Colmez describe ten trials spanning from the nineteenth century to today, in which mathematical arguments were used -- and disastrously misused -- as evidence. They tell the stories of Sally Clark, who was accused of murdering her children by a doctor with a faulty sense of calculation; of nineteenth-century tycoon Hetty Green, whose dispute over her aunt's will became a signal case in the forensic use of mathematics; and of the case of Amanda Knox, in which a judge's misunderstanding of probability led him to discount critical evidence -- which might have kept her in jail. Offering a fresh angle on cases from the nineteenth-century Dreyfus affair to the murder trial of Dutch nurse Lucia de Berk, Schneps and Colmez show how the improper application of mathematical concepts can mean the difference between walking free and life in prison. A colorful narrative of mathematical abuse, Math on Trial blends courtroom drama, history, and math to show that legal expertise isn't't always enough to prove a person innocent.