Fundamental Theorems Concerning Point Sets
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Handbook Of Topological Fixed Point Theory
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Author : Robert F. Brown
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-12-05
Handbook Of Topological Fixed Point Theory written by Robert F. Brown 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 2005-12-05 with Mathematics categories.
This book is the first in the world literature presenting all new trends in topological fixed point theory. Until now all books connected to the topological fixed point theory were devoted only to some parts of this theory. This book will be especially useful for post-graduate students and researchers interested in the fixed point theory, particularly in topological methods in nonlinear analysis, differential equations and dynamical systems. The content is also likely to stimulate the interest of mathematical economists, population dynamics experts as well as theoretical physicists exploring the topological dynamics.
Foundations Of Point Set Theory
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Author : Robert Lee Moore
language : en
Publisher: American Mathematical Soc.
Release Date : 1932-12-31
Foundations Of Point Set Theory written by Robert Lee Moore 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 1932-12-31 with Mathematics categories.
Elements Of Point Set Topology
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Author : John D. Baum
language : en
Publisher: Courier Corporation
Release Date : 1991-01-01
Elements Of Point Set Topology written by John D. Baum and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-01-01 with Mathematics categories.
Topology continues to be a topic of prime importance in contemporary mathematics, but until the publication of this book there were few if any introductions to topology for undergraduates. This book remedied that need by offering a carefully thought-out, graduated approach to point set topology at the undergraduate level. To make the book as accessible as possible, the author approaches topology from a geometric and axiomatic standpoint; geometric, because most students come to the subject with a good deal of geometry behind them, enabling them to use their geometric intuition; axiomatic, because it parallels the student's experience with modern algebra, and keeps the book in harmony with current trends in mathematics. After a discussion of such preliminary topics as the algebra of sets, Euler-Venn diagrams and infinite sets, the author takes up basic definitions and theorems regarding topological spaces (Chapter 1). The second chapter deals with continuous functions (mappings) and homeomorphisms, followed by two chapters on special types of topological spaces (varieties of compactness and varieties of connectedness). Chapter 5 covers metric spaces. Since basic point set topology serves as a foundation not only for functional analysis but also for more advanced work in point set topology and algebraic topology, the author has included topics aimed at students with interests other than analysis. Moreover, Dr. Baum has supplied quite detailed proofs in the beginning to help students approaching this type of axiomatic mathematics for the first time. Similarly, in the first part of the book problems are elementary, but they become progressively more difficult toward the end of the book. References have been supplied to suggest further reading to the interested student.
Contributions To The Theory Of Games Am 24 Volume I
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Author : Harold William Kuhn
language : en
Publisher: Princeton University Press
Release Date : 2016-03-02
Contributions To The Theory Of Games Am 24 Volume I written by Harold William Kuhn and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-02 with Mathematics categories.
The description for this book, Contributions to the Theory of Games (AM-24), Volume I, will be forthcoming.
Point Set Theory
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Author : Morgan
language : en
Publisher: Routledge
Release Date : 2018-04-27
Point Set Theory written by Morgan and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-04-27 with Mathematics categories.
Investigations by Baire, Lebesgue, Hausdorff, Marczewski, and othes have culminated invarious schemes for classifying point sets. This important reference/text bringstogether in a single theoretical framework the properties common to these classifications.Providing a clear, thorough overview and analysis of the field, Point Set Theoryutilizes the axiomatically determined notion of a category base for extending generaltopological theorems to a higher level of abstraction ... axiomatically unifies analogiesbetween Baire category and Lebesgue measure . .. enhances understanding of thematerial with numerous examples and discussions of abstract concepts ... and more.Imparting a solid foundation for the modem theory of real functions and associated areas,this authoritative resource is a vital reference for set theorists, logicians, analysts, andresearch mathematicians involved in topology, measure theory, or real analysis. It is anideal text for graduate mathematics students in the above disciplines who havecompleted undergraduate courses in set theory and real analysis.
The New Era In American Mathematics 1920 1950
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Author : Karen Hunger Parshall
language : en
Publisher: Princeton University Press
Release Date : 2022-02-22
The New Era In American Mathematics 1920 1950 written by Karen Hunger Parshall and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-22 with Mathematics categories.
A meticulously researched history on the development of American mathematics in the three decades following World War I As the Roaring Twenties lurched into the Great Depression, to be followed by the scourge of Nazi Germany and World War II, American mathematicians pursued their research, positioned themselves collectively within American science, and rose to global mathematical hegemony. How did they do it? The New Era in American Mathematics, 1920–1950 explores the institutional, financial, social, and political forces that shaped and supported this community in the first half of the twentieth century. In doing so, Karen Hunger Parshall debunks the widely held view that American mathematics only thrived after European émigrés fled to the shores of the United States. Drawing from extensive archival and primary-source research, Parshall uncovers the key players in American mathematics who worked together to effect change and she looks at their research output over the course of three decades. She highlights the educational, professional, philanthropic, and governmental entities that bolstered progress. And she uncovers the strategies implemented by American mathematicians in their quest for the advancement of knowledge. Throughout, she considers how geopolitical circumstances shifted the course of the discipline. Examining how the American mathematical community asserted itself on the international stage, The New Era in American Mathematics, 1920–1950 shows the way one nation became the focal point for the field.
Fundamental Principles Of Classical Mechanics A Geometrical Perspective
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Author : Kai S Lam
language : en
Publisher: World Scientific Publishing Company
Release Date : 2014-07-07
Fundamental Principles Of Classical Mechanics A Geometrical Perspective written by Kai S Lam and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-07 with Science categories.
This book is written with the belief that classical mechanics, as a theoretical discipline, possesses an inherent beauty, depth, and richness that far transcends its immediate applications in mechanical systems. These properties are manifested, by and large, through the coherence and elegance of the mathematical structure underlying the discipline, and are eminently worthy of being communicated to physics students at the earliest stage possible. This volume is therefore addressed mainly to advanced undergraduate and beginning graduate physics students who are interested in the application of modern mathematical methods in classical mechanics, in particular, those derived from the fields of topology and differential geometry, and also to the occasional mathematics student who is interested in important physics applications of these areas of mathematics. Its main purpose is to offer an introductory and broad glimpse of the majestic edifice of the mathematical theory of classical dynamics, not only in the time-honored analytical tradition of Newton, Laplace, Lagrange, Hamilton, Jacobi, and Whittaker, but also the more topological/geometrical one established by Poincare, and enriched by Birkhoff, Lyapunov, Smale, Siegel, Kolmogorov, Arnold, and Moser (as well as many others).
The Fundamental Theorem Of Algebra
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Author : Benjamin Fine
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
The Fundamental Theorem Of Algebra written by Benjamin Fine 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 2012-12-06 with Mathematics categories.
The fundamental theorem of algebra states that any complex polynomial must have a complex root. This book examines three pairs of proofs of the theorem from three different areas of mathematics: abstract algebra, complex analysis and topology. The first proof in each pair is fairly straightforward and depends only on what could be considered elementary mathematics. However, each of these first proofs leads to more general results from which the fundamental theorem can be deduced as a direct consequence. These general results constitute the second proof in each pair. To arrive at each of the proofs, enough of the general theory of each relevant area is developed to understand the proof. In addition to the proofs and techniques themselves, many applications such as the insolvability of the quintic and the transcendence of e and pi are presented. Finally, a series of appendices give six additional proofs including a version of Gauss'original first proof. The book is intended for junior/senior level undergraduate mathematics students or first year graduate students, and would make an ideal "capstone" course in mathematics.
Elements Of Real Analysis
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Author : M.D.Raisinghania
language : en
Publisher: S. Chand Publishing
Release Date : 2003-06
Elements Of Real Analysis written by M.D.Raisinghania and has been published by S. Chand Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-06 with Science categories.
This book is an attempt to make presentation of Elements of Real Analysis more lucid. The book contains examples and exercises meant to help a proper understanding of the text. For B.A., B.Sc. and Honours (Mathematics and Physics), M.A. and M.Sc. (Mathematics) students of various Universities/ Institutions.As per UGC Model Curriculum and for I.A.S. and Various other competitive exams.
The Genesis Of Point Set Topology
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Author : Jerome Henry Mahneim
language : en
Publisher:
Release Date : 1962
The Genesis Of Point Set Topology written by Jerome Henry Mahneim and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1962 with Mathematics categories.