Modern Geometric Structures And Fields

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Modern Geometric Structures And Fields

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Author : Сергей Петрович Новиков
language : en
Publisher: American Mathematical Soc.
Release Date : 2006

Modern Geometric Structures And Fields written by Сергей Петрович Новиков 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 2006 with Mathematics categories.

Presents the basics of Riemannian geometry in its modern form as geometry of differentiable manifolds and the important structures on them. This book shows that Riemannian geometry has a great influence to several fundamental areas of modern mathematics and its applications.

Modern Geometric Structures And Fields

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Author : Sergei Petrovich Novikov
language : en
Publisher: American Mathematical Soc.
Release Date : 2006

Modern Geometric Structures And Fields written by Sergei Petrovich Novikov 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 2006 with categories.

Differential Geometric Structures

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Author : Walter A. Poor
language : en
Publisher: Courier Corporation
Release Date : 2015-04-27

Differential Geometric Structures written by Walter A. Poor and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-04-27 with Mathematics categories.

This introductory text defines geometric structure by specifying parallel transport in an appropriate fiber bundle and focusing on simplest cases of linear parallel transport in a vector bundle. 1981 edition.

Recent Progress In Differential Geometry And Its Related Fields

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Author : Toshiaki Adachi
language : en
Publisher: World Scientific
Release Date : 2012

Recent Progress In Differential Geometry And Its Related Fields written by Toshiaki Adachi 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 volume contains the contributions by the main participants of the 2nd International Colloquium on Differential Geometry and its Related Fields (ICDG2010), held in Veliko Tarnovo, Bulgaria to exchange information on current topics in differential geometry, information geometry and applications. These contributions from active specialists in differential geometry provide significant information on research papers which cover geometric structures, concrete Lie group theory and information geometry. This volume is invaluable not only for researchers in this special area but also for those who are interested in interdisciplinary areas in differential geometry, complex analysis, probability theory and mathematical physics. It also serves as a good guide to graduate students in the field of differential geometry.

A Guide To Lie Systems With Compatible Geometric Structures

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Author : Javier De Lucas Araujo
language : en
Publisher: World Scientific
Release Date : 2020-01-22

A Guide To Lie Systems With Compatible Geometric Structures written by Javier De Lucas Araujo and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-22 with Mathematics categories.

The book presents a comprehensive guide to the study of Lie systems from the fundamentals of differential geometry to the development of contemporary research topics. It embraces several basic topics on differential geometry and the study of geometric structures while developing known applications in the theory of Lie systems. The book also includes a brief exploration of the applications of Lie systems to superequations, discrete systems, and partial differential equations.Offering a complete overview from the topic's foundations to the present, this book is an ideal resource for Physics and Mathematics students, doctoral students and researchers.

Twenty Four Hours Of Local Cohomology

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Author : Srikanth B. Iyengar
language : en
Publisher: American Mathematical Society
Release Date : 2022-07-19

Twenty Four Hours Of Local Cohomology written by Srikanth B. Iyengar and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-07-19 with Mathematics categories.

This book is aimed to provide an introduction to local cohomology which takes cognizance of the breadth of its interactions with other areas of mathematics. It covers topics such as the number of defining equations of algebraic sets, connectedness properties of algebraic sets, connections to sheaf cohomology and to de Rham cohomology, Gröbner bases in the commutative setting as well as for $D$-modules, the Frobenius morphism and characteristic $p$ methods, finiteness properties of local cohomology modules, semigroup rings and polyhedral geometry, and hypergeometric systems arising from semigroups. The book begins with basic notions in geometry, sheaf theory, and homological algebra leading to the definition and basic properties of local cohomology. Then it develops the theory in a number of different directions, and draws connections with topology, geometry, combinatorics, and algorithmic aspects of the subject.

A Course In Minimal Surfaces

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Author : Tobias Holck Colding
language : en
Publisher: American Mathematical Society
Release Date : 2024-01-18

A Course In Minimal Surfaces written by Tobias Holck Colding and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-01-18 with Mathematics categories.

Minimal surfaces date back to Euler and Lagrange and the beginning of the calculus of variations. Many of the techniques developed have played key roles in geometry and partial differential equations. Examples include monotonicity and tangent cone analysis originating in the regularity theory for minimal surfaces, estimates for nonlinear equations based on the maximum principle arising in Bernstein's classical work, and even Lebesgue's definition of the integral that he developed in his thesis on the Plateau problem for minimal surfaces. This book starts with the classical theory of minimal surfaces and ends up with current research topics. Of the various ways of approaching minimal surfaces (from complex analysis, PDE, or geometric measure theory), the authors have chosen to focus on the PDE aspects of the theory. The book also contains some of the applications of minimal surfaces to other fields including low dimensional topology, general relativity, and materials science. The only prerequisites needed for this book are a basic knowledge of Riemannian geometry and some familiarity with the maximum principle.

Quantum Mechanics For Mathematicians

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Author : Leon Armenovich Takhtadzhi͡an
language : en
Publisher: American Mathematical Soc.
Release Date : 2008

Quantum Mechanics For Mathematicians written by Leon Armenovich Takhtadzhi͡an 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 2008 with Mathematics categories.

Presents a comprehensive treatment of quantum mechanics from a mathematics perspective. Including traditional topics, like classical mechanics, mathematical foundations of quantum mechanics, quantization, and the Schrodinger equation, this book gives a mathematical treatment of systems of identical particles with spin.

Elements Of Homology Theory

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Author : V. V. Prasolov
language : en
Publisher: American Mathematical Society
Release Date : 2025-02-04

Elements Of Homology Theory written by V. V. Prasolov and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-04 with Mathematics categories.

The book is a continuation of the previous book by the author (Elements of Combinatorial and Differential Topology, Graduate Studies in Mathematics, Volume 74, American Mathematical Society, 2006). It starts with the definition of simplicial homology and cohomology, with many examples and applications. Then the Kolmogorov–Alexander multiplication in cohomology is introduced. A significant part of the book is devoted to applications of simplicial homology and cohomology to obstruction theory, in particular, to characteristic classes of vector bundles. The later chapters are concerned with singular homology and cohomology, and Čech and de Rham cohomology. The book ends with various applications of homology to the topology of manifolds, some of which might be of interest to experts in the area. The book contains many problems; almost all of them are provided with hints or complete solutions.

Sage For Undergraduates

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Author : Gregory V. Bard
language : en
Publisher: American Mathematical Society
Release Date : 2022-09-26

Sage For Undergraduates written by Gregory V. Bard and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-09-26 with Mathematics categories.

As the open-source and free alternative to expensive software like Maple™, Mathematica®, and MATLAB®, Sage offers anyone with a web browser the ability to use cutting-edge mathematical software and share the results with others, often with stunning graphics. This book is a gentle introduction to Sage for undergraduate students during Calculus II, Multivariate Calculus, Differential Equations, Linear Algebra, Math Modeling, or Operations Research. This book assumes no background in programming, but the reader who finishes the book will have learned about 60 percent of a first semester computer science course, including much of the Python programming language. The audience is not only math majors, but also physics, engineering, environmental science, finance, chemistry, economics, data science, and computer science majors. Many of the book's examples are drawn from those fields. Filled with “challenges” for the students to test their progress, the book is also ideal for self-study. What's New in the Second Edition: In 2019, Sage transitioned from Python 2 to Python 3, which changed the syntax in several significant ways, including for the print command. All the examples in this book have been rewritten to be compatible with Python 3. Moreover, every code block longer than four lines has been placed in an archive on the book's website http://www.sage-for-undergraduates.org that is maintained by the author, so that the students won't have to retype the code! Other additions include… The number of “challenges” for the students to test their own progress in learning Sage has roughly doubled, which will be a great boon for self-study.There's approximately 150 pages of new content, including: New projects on Leontief Input-Output Analysis and on Environmental ScienceNew sections on Complex Numbers and Complex Analysis, on SageTex, and on solving problems via Monte-Carlo Simulations.The first three sections of Chapter 1 have been completely rewritten to give absolute beginners a smoother transition into Sage.