Plueckers Line Geometry And Lies Sphere Geometry An Example Of Generalized Duality

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Geometry of Algebraic Curves

Author : Enrico Arbarello
Publisher : Springer
ISBN 13 : 9781475753240
Total Pages : 387 pages
Book Rating : 4.7/5 (532 download)

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Book Synopsis Geometry of Algebraic Curves by : Enrico Arbarello

Download or read book Geometry of Algebraic Curves written by Enrico Arbarello and published by Springer. This book was released on 2013-08-30 with total page 387 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years there has been enormous activity in the theory of algebraic curves. Many long-standing problems have been solved using the general techniques developed in algebraic geometry during the 1950's and 1960's. Additionally, unexpected and deep connections between algebraic curves and differential equations have been uncovered, and these in turn shed light on other classical problems in curve theory. It seems fair to say that the theory of algebraic curves looks completely different now from how it appeared 15 years ago; in particular, our current state of knowledge repre sents a significant advance beyond the legacy left by the classical geometers such as Noether, Castelnuovo, Enriques, and Severi. These books give a presentation of one of the central areas of this recent activity; namely, the study of linear series on both a fixed curve (Volume I) and on a variable curve (Volume II). Our goal is to give a comprehensive and self-contained account of the extrinsic geometry of algebraic curves, which in our opinion constitutes the main geometric core of the recent advances in curve theory. Along the way we shall, of course, discuss appli cations of the theory of linear series to a number of classical topics (e.g., the geometry of the Riemann theta divisor) as well as to some of the current research (e.g., the Kodaira dimension of the moduli space of curves).

Twistor Geometry and Field Theory

Author : R. S. Ward
Publisher : Cambridge University Press
ISBN 13 : 9780521422680
Total Pages : 534 pages
Book Rating : 4.4/5 (226 download)

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Book Synopsis Twistor Geometry and Field Theory by : R. S. Ward

Download or read book Twistor Geometry and Field Theory written by R. S. Ward and published by Cambridge University Press. This book was released on 1990 with total page 534 pages. Available in PDF, EPUB and Kindle. Book excerpt: Deals with the twistor treatment of certain linear and non-linear partial differential equations. The description in terms of twistors involves algebraic and differential geometry, and several complex variables.

Thermodynamics and an Introduction to Thermostatistics

Author : Herbert B. Callen
Publisher : John Wiley & Sons
ISBN 13 : 0471862568
Total Pages : 518 pages
Book Rating : 4.4/5 (718 download)

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Book Synopsis Thermodynamics and an Introduction to Thermostatistics by : Herbert B. Callen

Download or read book Thermodynamics and an Introduction to Thermostatistics written by Herbert B. Callen and published by John Wiley & Sons. This book was released on 1991-01-16 with total page 518 pages. Available in PDF, EPUB and Kindle. Book excerpt: The only text to cover both thermodynamic and statistical mechanics--allowing students to fully master thermodynamics at the macroscopic level. Presents essential ideas on critical phenomena developed over the last decade in simple, qualitative terms. This new edition maintains the simple structure of the first and puts new emphasis on pedagogical considerations. Thermostatistics is incorporated into the text without eclipsing macroscopic thermodynamics, and is integrated into the conceptual framework of physical theory.

Geometry II

Author : E.B. Vinberg
Publisher : Springer Science & Business Media
ISBN 13 : 3662029014
Total Pages : 263 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Geometry II by : E.B. Vinberg

Download or read book Geometry II written by E.B. Vinberg and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: A very clear account of the subject from the viewpoints of elementary geometry, Riemannian geometry and group theory – a book with no rival in the literature. Mostly accessible to first-year students in mathematics, the book also includes very recent results which will be of interest to researchers in this field.

Introduction to Tropical Geometry

Author : Diane Maclagan
Publisher : American Mathematical Society
ISBN 13 : 1470468565
Total Pages : 363 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Introduction to Tropical Geometry by : Diane Maclagan

Download or read book Introduction to Tropical Geometry written by Diane Maclagan and published by American Mathematical Society. This book was released on 2021-12-13 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tropical geometry is a combinatorial shadow of algebraic geometry, offering new polyhedral tools to compute invariants of algebraic varieties. It is based on tropical algebra, where the sum of two numbers is their minimum and the product is their sum. This turns polynomials into piecewise-linear functions, and their zero sets into polyhedral complexes. These tropical varieties retain a surprising amount of information about their classical counterparts. Tropical geometry is a young subject that has undergone a rapid development since the beginning of the 21st century. While establishing itself as an area in its own right, deep connections have been made to many branches of pure and applied mathematics. This book offers a self-contained introduction to tropical geometry, suitable as a course text for beginning graduate students. Proofs are provided for the main results, such as the Fundamental Theorem and the Structure Theorem. Numerous examples and explicit computations illustrate the main concepts. Each of the six chapters concludes with problems that will help the readers to practice their tropical skills, and to gain access to the research literature. This wonderful book will appeal to students and researchers of all stripes: it begins at an undergraduate level and ends with deep connections to toric varieties, compactifications, and degenerations. In between, the authors provide the first complete proofs in book form of many fundamental results in the subject. The pages are sprinkled with illuminating examples, applications, and exercises, and the writing is lucid and meticulous throughout. It is that rare kind of book which will be used equally as an introductory text by students and as a reference for experts. —Matt Baker, Georgia Institute of Technology Tropical geometry is an exciting new field, which requires tools from various parts of mathematics and has connections with many areas. A short definition is given by Maclagan and Sturmfels: “Tropical geometry is a marriage between algebraic and polyhedral geometry”. This wonderful book is a pleasant and rewarding journey through different landscapes, inviting the readers from a day at a beach to the hills of modern algebraic geometry. The authors present building blocks, examples and exercises as well as recent results in tropical geometry, with ingredients from algebra, combinatorics, symbolic computation, polyhedral geometry and algebraic geometry. The volume will appeal both to beginning graduate students willing to enter the field and to researchers, including experts. —Alicia Dickenstein, University of Buenos Aires, Argentina

Linear Algebra and Geometry

Author : Igor R. Shafarevich
Publisher : Springer Science & Business Media
ISBN 13 : 3642309941
Total Pages : 536 pages
Book Rating : 4.6/5 (423 download)

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Book Synopsis Linear Algebra and Geometry by : Igor R. Shafarevich

Download or read book Linear Algebra and Geometry written by Igor R. Shafarevich and published by Springer Science & Business Media. This book was released on 2012-08-23 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book on linear algebra and geometry is based on a course given by renowned academician I.R. Shafarevich at Moscow State University. The book begins with the theory of linear algebraic equations and the basic elements of matrix theory and continues with vector spaces, linear transformations, inner product spaces, and the theory of affine and projective spaces. The book also includes some subjects that are naturally related to linear algebra but are usually not covered in such courses: exterior algebras, non-Euclidean geometry, topological properties of projective spaces, theory of quadrics (in affine and projective spaces), decomposition of finite abelian groups, and finitely generated periodic modules (similar to Jordan normal forms of linear operators). Mathematical reasoning, theorems, and concepts are illustrated with numerous examples from various fields of mathematics, including differential equations and differential geometry, as well as from mechanics and physics.

Canonical Duality Theory

Author : David Yang Gao
Publisher : Springer
ISBN 13 : 3319580175
Total Pages : 374 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Canonical Duality Theory by : David Yang Gao

Download or read book Canonical Duality Theory written by David Yang Gao and published by Springer. This book was released on 2017-10-09 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book on canonical duality theory provides a comprehensive review of its philosophical origin, physics foundation, and mathematical statements in both finite- and infinite-dimensional spaces. A ground-breaking methodological theory, canonical duality theory can be used for modeling complex systems within a unified framework and for solving a large class of challenging problems in multidisciplinary fields in engineering, mathematics, and the sciences. This volume places a particular emphasis on canonical duality theory’s role in bridging the gap between non-convex analysis/mechanics and global optimization. With 18 total chapters written by experts in their fields, this volume provides a nonconventional theory for unified understanding of the fundamental difficulties in large deformation mechanics, bifurcation/chaos in nonlinear science, and the NP-hard problems in global optimization. Additionally, readers will find a unified methodology and powerful algorithms for solving challenging problems in complex systems with real-world applications in non-convex analysis, non-monotone variational inequalities, integer programming, topology optimization, post-buckling of large deformed structures, etc. Researchers and graduate students will find explanation and potential applications in multidisciplinary fields.

Multiple View Geometry in Computer Vision

Author : Richard Hartley
Publisher : Cambridge University Press
ISBN 13 : 1139449141
Total Pages : 676 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Multiple View Geometry in Computer Vision by : Richard Hartley

Download or read book Multiple View Geometry in Computer Vision written by Richard Hartley and published by Cambridge University Press. This book was released on 2004-03-25 with total page 676 pages. Available in PDF, EPUB and Kindle. Book excerpt: A basic problem in computer vision is to understand the structure of a real world scene given several images of it. Techniques for solving this problem are taken from projective geometry and photogrammetry. Here, the authors cover the geometric principles and their algebraic representation in terms of camera projection matrices, the fundamental matrix and the trifocal tensor. The theory and methods of computation of these entities are discussed with real examples, as is their use in the reconstruction of scenes from multiple images. The new edition features an extended introduction covering the key ideas in the book (which itself has been updated with additional examples and appendices) and significant new results which have appeared since the first edition. Comprehensive background material is provided, so readers familiar with linear algebra and basic numerical methods can understand the projective geometry and estimation algorithms presented, and implement the algorithms directly from the book.

Sexistence

Author : Jean-Luc Nancy
Publisher : Fordham University Press
ISBN 13 : 0823294013
Total Pages : 113 pages
Book Rating : 4.8/5 (232 download)

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Book Synopsis Sexistence by : Jean-Luc Nancy

Download or read book Sexistence written by Jean-Luc Nancy and published by Fordham University Press. This book was released on 2021-05-04 with total page 113 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sex, more than just a part of our experience, troubles our conceptions of existence. Drawing on a fascinating array of sources, ancient and modern, philosophical and literary, Jean-Luc Nancy explores and upholds the form-giving thrust of the drive. Nancy reminds us that we are more comfortable with the drama of prohibitions, ideals, repression, transgression, and destruction, which often hamper thinking about sex and gender, than with the affirmation of an originary trouble at the limits of language that divides being and opens the world. Sexistence develops a new philosophical account of sexuality that resonates with contemporary research on gender and biopolitics. Without attempting to be comprehensive, the book ranges from the ancient world through psychoanalysis to discover the turbulence of the drive at the heart of existence.

Symbolic-Numeric Computation

Author : Dongming Wang
Publisher : Springer Science & Business Media
ISBN 13 : 3764379839
Total Pages : 391 pages
Book Rating : 4.7/5 (643 download)

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Book Synopsis Symbolic-Numeric Computation by : Dongming Wang

Download or read book Symbolic-Numeric Computation written by Dongming Wang and published by Springer Science & Business Media. This book was released on 2007-01-22 with total page 391 pages. Available in PDF, EPUB and Kindle. Book excerpt: The growing demand of speed, accuracy, and reliability in scientific and engineering computing has been accelerating the merging of symbolic and numeric computations. These two types of computation coexist in mathematics yet are separated in traditional research of mathematical computation. This book presents 27 research articles on the integration and interaction of symbolic and numeric computation.

Geometry of Algebraic Curves

Author : Enrico Arbarello
Publisher : Springer Science & Business Media
ISBN 13 : 1475753233
Total Pages : 402 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Geometry of Algebraic Curves by : Enrico Arbarello

Download or read book Geometry of Algebraic Curves written by Enrico Arbarello and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years there has been enormous activity in the theory of algebraic curves. Many long-standing problems have been solved using the general techniques developed in algebraic geometry during the 1950's and 1960's. Additionally, unexpected and deep connections between algebraic curves and differential equations have been uncovered, and these in turn shed light on other classical problems in curve theory. It seems fair to say that the theory of algebraic curves looks completely different now from how it appeared 15 years ago; in particular, our current state of knowledge repre sents a significant advance beyond the legacy left by the classical geometers such as Noether, Castelnuovo, Enriques, and Severi. These books give a presentation of one of the central areas of this recent activity; namely, the study of linear series on both a fixed curve (Volume I) and on a variable curve (Volume II). Our goal is to give a comprehensive and self-contained account of the extrinsic geometry of algebraic curves, which in our opinion constitutes the main geometric core of the recent advances in curve theory. Along the way we shall, of course, discuss appli cations of the theory of linear series to a number of classical topics (e.g., the geometry of the Riemann theta divisor) as well as to some of the current research (e.g., the Kodaira dimension of the moduli space of curves).

Methods of Algebraic Geometry: Volume 3

Author : W. V. D. Hodge
Publisher : Cambridge University Press
ISBN 13 : 0521467756
Total Pages : 350 pages
Book Rating : 4.5/5 (214 download)

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Book Synopsis Methods of Algebraic Geometry: Volume 3 by : W. V. D. Hodge

Download or read book Methods of Algebraic Geometry: Volume 3 written by W. V. D. Hodge and published by Cambridge University Press. This book was released on 1994-05-19 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: All three volumes of Hodge and Pedoe's classic work have now been reissued. Together, these books give an insight into algebraic geometry that is unique and unsurpassed.

Solutions Manual for Thermodynamics and an Introduction to Thermostatistics, Second Edition

Author : Herbert B. Callen
Publisher :
ISBN 13 : 9780471819936
Total Pages : 132 pages
Book Rating : 4.8/5 (199 download)

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Book Synopsis Solutions Manual for Thermodynamics and an Introduction to Thermostatistics, Second Edition by : Herbert B. Callen

Download or read book Solutions Manual for Thermodynamics and an Introduction to Thermostatistics, Second Edition written by Herbert B. Callen and published by . This book was released on 1986 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Essentials of Tropical Combinatorics

Author : Michael Joswig
Publisher : American Mathematical Society
ISBN 13 : 1470466538
Total Pages : 398 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Essentials of Tropical Combinatorics by : Michael Joswig

Download or read book Essentials of Tropical Combinatorics written by Michael Joswig and published by American Mathematical Society. This book was released on 2021-12-08 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of this book is to explain, at the graduate student level, connections between tropical geometry and optimization. Building bridges between these two subject areas is fruitful in two ways. Through tropical geometry optimization algorithms become applicable to questions in algebraic geometry. Conversely, looking at topics in optimization through the tropical geometry lens adds an additional layer of structure. The author covers contemporary research topics that are relevant for applications such as phylogenetics, neural networks, combinatorial auctions, game theory, and computational complexity. This self-contained book grew out of several courses given at Technische Universität Berlin and elsewhere, and the main prerequisite for the reader is a basic knowledge in polytope theory. It contains a good number of exercises, many examples, beautiful figures, as well as explicit tools for computations using $texttt{polymake}$.

Introduction to the Mori Program

Author : Kenji Matsuki
Publisher : Springer Science & Business Media
ISBN 13 : 147575602X
Total Pages : 502 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Introduction to the Mori Program by : Kenji Matsuki

Download or read book Introduction to the Mori Program written by Kenji Matsuki and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 502 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mori's Program is a fusion of the so-called Minimal Model Program and the IItaka Program toward the biregular and/or birational classification of higher dimensional algebraic varieties. The author presents this theory in an easy and understandable way with lots of background motivation. Prerequisites are those covered in Hartshorne's book "Algebraic Geometry." This is the first book in this extremely important and active field of research and will become a key resource for graduate students wanting to get into the area.

The Calabi–Yau Landscape

Author : Yang-Hui He
Publisher : Springer Nature
ISBN 13 : 3030775623
Total Pages : 214 pages
Book Rating : 4.0/5 (37 download)

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Book Synopsis The Calabi–Yau Landscape by : Yang-Hui He

Download or read book The Calabi–Yau Landscape written by Yang-Hui He and published by Springer Nature. This book was released on 2021-07-31 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: Can artificial intelligence learn mathematics? The question is at the heart of this original monograph bringing together theoretical physics, modern geometry, and data science. The study of Calabi–Yau manifolds lies at an exciting intersection between physics and mathematics. Recently, there has been much activity in applying machine learning to solve otherwise intractable problems, to conjecture new formulae, or to understand the underlying structure of mathematics. In this book, insights from string and quantum field theory are combined with powerful techniques from complex and algebraic geometry, then translated into algorithms with the ultimate aim of deriving new information about Calabi–Yau manifolds. While the motivation comes from mathematical physics, the techniques are purely mathematical and the theme is that of explicit calculations. The reader is guided through the theory and provided with explicit computer code in standard software such as SageMath, Python and Mathematica to gain hands-on experience in applications of artificial intelligence to geometry. Driven by data and written in an informal style, The Calabi–Yau Landscape makes cutting-edge topics in mathematical physics, geometry and machine learning readily accessible to graduate students and beyond. The overriding ambition is to introduce some modern mathematics to the physicist, some modern physics to the mathematician, and machine learning to both.

Changing Difference

Author : Catherine Malabou
Publisher : Polity
ISBN 13 : 0745651089
Total Pages : 176 pages
Book Rating : 4.7/5 (456 download)

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Book Synopsis Changing Difference by : Catherine Malabou

Download or read book Changing Difference written by Catherine Malabou and published by Polity. This book was released on 2011-09-19 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: Translated by CAROLYN SHREAD In the post-feminist age the fact that ‘woman' finds herself deprived of her ‘essence' only confirms, paradoxically, a very ancient state of affairs: ‘woman' has never been able to define herself in any other way than in terms of the violence done to her. Violence alone confers her being - whether it is domestic and social violence or theoretical violence. The critique of ‘essentialism' (i.e. there is no specifically feminine essence) proposed by both gender theory and deconstruction is just one more twist in the ontological negation of the feminine. Contrary to all expectations, however, this ever more radical hollowing out of woman within intellectual movements supposed to protect her, this assimilation of woman to a ‘being nothing', clears the way for a new beginning. Let us now assume the thought of ‘woman' as an empty but resistant essence, an essence that is resistant precisely because it is empty, a resistance that strikes down the impossibility of its own disappearance once and for all. To ask what remains of woman after the sacrifice of her being is to signal a new era in the feminist struggle, changing the terms of the battle to go beyond both essentialism and anti-essentialism. In this path-breaking work Catherine Malabou begins with philosophy, asking: what is the life of a woman philosopher?