Surprises And Counterexamples In Real Function Theory
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Surprises And Counterexamples In Real Function Theory
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Author : A. R. Rajwade
language : en
Publisher: Springer
Release Date : 2007-01-15
Surprises And Counterexamples In Real Function Theory written by A. R. Rajwade and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-01-15 with Mathematics categories.
This book presents a variety of intriguing, surprising and appealing topics and nonroutine theorems in real function theory. It is a reference book to which one can turn for finding that arise while studying or teaching analysis.Chapter 1 is an introduction to algebraic, irrational and transcendental numbers and contains the Cantor ternary set. Chapter 2 contains functions with extraordinary properties; functions that are continuous at each point but differentiable at no point. Chapters 4 and intermediate value property, periodic functions, Rolle's theorem, Taylor's theorem, points of tangents. Chapter 6 discusses sequences and series. It includes the restricted harmonic series, of alternating harmonic series and some number theoretic aspects. In Chapter 7, the infinite peculiar range of convergence is studied. Appendix I deal with some specialized topics. Exercises at the end of chapters and their solutions are provided in Appendix II.This book will be useful for students and teachers alike.
Surprise And Counterexamples In Real Function Theory
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Author : A. R Rajwade
language : en
Publisher:
Release Date : 2013-09
Surprise And Counterexamples In Real Function Theory written by A. R Rajwade and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-09 with categories.
Introduction To Game Theory
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Author : Stef Tijs
language : en
Publisher: Springer
Release Date : 2003-01-01
Introduction To Game Theory written by Stef Tijs and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-01-01 with Mathematics categories.
A Course On Integration Theory
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Author : K. Chandrasekharan
language : en
Publisher: Springer
Release Date : 1996-01-01
A Course On Integration Theory written by K. Chandrasekharan and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-01-01 with Mathematics categories.
A First Course In Graph Theory And Combinatorics
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Author : Sebastian M. Cioabă
language : en
Publisher: Springer
Release Date : 2009-05-15
A First Course In Graph Theory And Combinatorics written by Sebastian M. Cioabă and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-05-15 with Mathematics categories.
The concept of a graph is fundamental in mathematics since it conveniently encodes diverse relations and facilitates combinatorial analysis of many complicated counting problems. In this book, the authors have traced the origins of graph theory from its humble beginnings of recreational mathematics to its modern setting for modeling communication networks as is evidenced by the World Wide Web graph used by many Internet search engines. This book is an introduction to graph theory and combinatorial analysis. It is based on courses given by the second author at Queen's University at Kingston, Ontario, Canada between 2002 and 2008. The courses were aimed at students in their final year of their undergraduate program.
Measure And Integration
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Author : S. Kesavan
language : en
Publisher: Springer
Release Date : 2019-02-25
Measure And Integration written by S. Kesavan and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-02-25 with Mathematics categories.
This book deals with topics on the theory of measure and integration. It starts with discussion on the Riemann integral and points out certain shortcomings, which motivate the theory of measure and the Lebesgue integral. Most of the material in this book can be covered in a one-semester introductory course. An awareness of basic real analysis and elementary topological notions, with special emphasis on the topology of the n-dimensional Euclidean space, is the pre-requisite for this book. Each chapter is provided with a variety of exercises for the students. The book is targeted to students of graduate- and advanced-graduate-level courses on the theory of measure and integration.
Analysis Ii
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Author : Terence Tao
language : en
Publisher: Springer
Release Date : 2016-08-22
Analysis Ii written by Terence Tao and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-08-22 with Mathematics categories.
This is part two of a two-volume book on real analysis and is intended for senior undergraduate students of mathematics who have already been exposed to calculus. The emphasis is on rigour and foundations of analysis. Beginning with the construction of the number systems and set theory, the book discusses the basics of analysis (limits, series, continuity, differentiation, Riemann integration), through to power series, several variable calculus and Fourier analysis, and then finally the Lebesgue integral. These are almost entirely set in the concrete setting of the real line and Euclidean spaces, although there is some material on abstract metric and topological spaces. The book also has appendices on mathematical logic and the decimal system. The entire text (omitting some less central topics) can be taught in two quarters of 25–30 lectures each. The course material is deeply intertwined with the exercises, as it is intended that the student actively learn the material (and practice thinking and writing rigorously) by proving several of the key results in the theory.
Atiyah Singer Index Theorem An Introduction
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Author : Amiya Mukherjee
language : en
Publisher: Springer
Release Date : 2013-10-30
Atiyah Singer Index Theorem An Introduction written by Amiya Mukherjee and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-30 with Mathematics categories.
This monograph is a thorough introduction to the Atiyah-Singer index theorem for elliptic operators on compact manifolds without boundary. The main theme is only the classical index theorem and some of its applications, but not the subsequent developments and simplifications of the theory. The book is designed for a complete proof of the K -theoretic index theorem and its representation in terms of cohomological characteristic classes. In an effort to make the demands on the reader's knowledge of background materials as modest as possible, the author supplies the proofs of almost every result. The applications include Hirzebruch signature theorem, Riemann-Roch-Hirzebruch theorem, and the Atiyah-Segal-Singer fixed point theorem, etc.
Analysis I
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Author : Terence Tao
language : en
Publisher: Springer
Release Date : 2016-08-29
Analysis I written by Terence Tao and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-08-29 with Mathematics categories.
This is part one of a two-volume book on real analysis and is intended for senior undergraduate students of mathematics who have already been exposed to calculus. The emphasis is on rigour and foundations of analysis. Beginning with the construction of the number systems and set theory, the book discusses the basics of analysis (limits, series, continuity, differentiation, Riemann integration), through to power series, several variable calculus and Fourier analysis, and then finally the Lebesgue integral. These are almost entirely set in the concrete setting of the real line and Euclidean spaces, although there is some material on abstract metric and topological spaces. The book also has appendices on mathematical logic and the decimal system. The entire text (omitting some less central topics) can be taught in two quarters of 25–30 lectures each. The course material is deeply intertwined with the exercises, as it is intended that the student actively learn the material (and practice thinking and writing rigorously) by proving several of the key results in the theory.
Operators On Hilbert Space
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Author : V. S. Sunder
language : en
Publisher: Springer
Release Date : 2016-08-05
Operators On Hilbert Space written by V. S. Sunder and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-08-05 with Mathematics categories.
The primarily objective of the book is to serve as a primer on the theory of bounded linear operators on separable Hilbert space. The book presents the spectral theorem as a statement on the existence of a unique continuous and measurable functional calculus. It discusses a proof without digressing into a course on the Gelfand theory of commutative Banach algebras. The book also introduces the reader to the basic facts concerning the various von Neumann–Schatten ideals, the compact operators, the trace-class operators and all bounded operators.