A Primer Of Real Functions Fourth Edition
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A Primer Of Real Functions Fourth Edition
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Author : Ralph P. Boas
language : en
Publisher: American Mathematical Soc.
Release Date : 1996-12-31
A Primer Of Real Functions Fourth Edition written by Ralph P. Boas 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 1996-12-31 with Mathematics categories.
This is a revised, updated, and significantly augmented edition of a classic Carus Monograph (a bestseller for over 25 years) on the theory of functions of a real variable. Earlier editions of this classic Carus Monograph covered sets, metric spaces, continuous functions, and differentiable functions. The fourth edition adds sections on measurable sets and functions, the Lebesgue and Stieltjes integrals, and applications. The book retains the informal chatty style of the previous editions, remaining accessible to readers with some mathematical sophistication and a background in calculus. The book is, thus, suitable either for self-study or for supplemental reading in a course on advanced calculus or real analysis. Not intended as a systematic treatise, this book has more the character of a sequence of lectures on a variety of interesting topics connected with real functions. Many of these topics are not commonly encountered in undergraduate textbooks: e.g., the existence of continuous everywhere-oscillating functions (via the Baire category theorem); the universal chord theorem; two functions having equal derivatives, yet not differing by a constant; and application of Stieltjes integration to the speed of convergence of infinite series. This book recaptures the sense of wonder that was associated with the subject in its early days. It is a must for mathematics libraries.
A Primer Of Real Analytic Functions
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Author : Steven G. Krantz
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-09-08
A Primer Of Real Analytic Functions written by Steven G. Krantz 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 2012-09-08 with Mathematics categories.
It is a pleasure and a privilege to write this new edition of A Primer 0/ Real Ana lytic Functions. The theory of real analytic functions is the wellspring of mathe matical analysis. It is remarkable that this is the first book on the subject, and we want to keep it up to date and as correct as possible. With these thoughts in mind, we have utilized helpful remarks and criticisms from many readers and have thereby made numerous emendations. We have also added material. There is a now a treatment of the Weierstrass preparation theorem, a new argument to establish Hensel's lemma and Puiseux's theorem, a new treat ment of Faa di Bruno's forrnula, a thorough discussion of topologies on spaces of real analytic functions, and a second independent argument for the implicit func tion theorem. We trust that these new topics will make the book more complete, and hence a more useful reference. It is a pleasure to thank our editor, Ann Kostant of Birkhäuser Boston, for mak ing the publishing process as smooth and trouble-free as possible. We are grateful for useful communications from the readers of our first edition, and we look for ward to further constructive feedback.
Real Analysis And Foundations Fourth Edition
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Author : Steven G. Krantz
language : en
Publisher: CRC Press
Release Date : 2016-12-12
Real Analysis And Foundations Fourth Edition written by Steven G. Krantz and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-12-12 with Mathematics categories.
A Readable yet Rigorous Approach to an Essential Part of Mathematical Thinking Back by popular demand, Real Analysis and Foundations, Third Edition bridges the gap between classic theoretical texts and less rigorous ones, providing a smooth transition from logic and proofs to real analysis. Along with the basic material, the text covers Riemann-Stieltjes integrals, Fourier analysis, metric spaces and applications, and differential equations. New to the Third Edition Offering a more streamlined presentation, this edition moves elementary number systems and set theory and logic to appendices and removes the material on wavelet theory, measure theory, differential forms, and the method of characteristics. It also adds a chapter on normed linear spaces and includes more examples and varying levels of exercises. Extensive Examples and Thorough Explanations Cultivate an In-Depth Understanding This best-selling book continues to give students a solid foundation in mathematical analysis and its applications. It prepares them for further exploration of measure theory, functional analysis, harmonic analysis, and beyond.
Invitation To Complex Analysis
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Author : Ralph P. Boas
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-05-05
Invitation To Complex Analysis written by Ralph P. Boas 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 2020-05-05 with Mathematics categories.
Ideal for a first course in complex analysis, this book can be used either as a classroom text or for independent study. Written at a level accessible to advanced undergraduates and beginning graduate students, the book is suitable for readers acquainted with advanced calculus or introductory real analysis. The treatment goes beyond the standard material of power series, Cauchy's theorem, residues, conformal mapping, and harmonic functions by including accessible discussions of intriguing topics that are uncommon in a book at this level. The flexibility afforded by the supplementary topics and applications makes the book adaptable either to a short, one-term course or to a comprehensive, full-year course. Detailed solutions of the exercises both serve as models for students and facilitate independent study. Supplementary exercises, not solved in the book, provide an additional teaching tool. This second edition has been painstakingly revised by the author's son, himself an award-winning mathematical expositor.
Computable Foundations For Economics
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Author : K. Vela Velupillai
language : en
Publisher: Routledge
Release Date : 2012-07-26
Computable Foundations For Economics written by K. Vela Velupillai and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-07-26 with Business & Economics categories.
Computable Foundations for Economics is a unified collection of essays, some of which are published here for the first time and all of which have been updated for this book, on an approach to economic theory from the point of view of algorithmic mathematics. By algorithmic mathematics the author means computability theory and constructive mathematics. This is in contrast to orthodox mathematical economics and game theory, which are formalised with the mathematics of real analysis, underpinned by what is called the ZFC formalism, i.e., set theory with the axiom of choice. This reliance on ordinary real analysis and the ZFC system makes economic theory in its current mathematical mode completely non-algorithmic, which means it is numerically meaningless. The book provides a systematic attempt to dissect and expose the non-algorithmic content of orthodox mathematical economics and game theory and suggests a reformalization on the basis of a strictly rigorous algorithmic mathematics. This removes the current schizophrenia in mathematical economics and game theory, where theory is entirely divorced from algorithmic applicability – for experimental and computational exercises. The chapters demonstrate the uncomputability and non-constructivity of core areas of general equilibrium theory, game theory and recursive macroeconomics. The book also provides a fresh look at the kind of behavioural economics that lies behind Herbert Simon’s work, and resurrects a role for the noble classical traditions of induction and verification, viewed and formalised, now, algorithmically. It will therefore be of particular interest to postgraduate students and researchers in algorithmic economics, game theory and classical behavioural economics.
The Stieltjes Integral
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Author : Gregory Convertito
language : en
Publisher: CRC Press
Release Date : 2023-02-28
The Stieltjes Integral written by Gregory Convertito and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-02-28 with Mathematics categories.
The Stieltjes Integral provides a detailed, rigorous treatment of the Stieltjes integral. This integral is a generalization of the Riemann and Darboux integrals of calculus and undergraduate analysis, and can serve as a bridge between classical and modern analysis. It has applications in many areas, including number theory, statistics, physics, and finance. It begins with the Darboux integral, builds the theory of functions of bounded variation, and then develops the Stieltjes integral. It culminates with a proof of the Riesz representation theorem as an application of the Stieltjes integral. For much of the 20th century the Stjeltjes integral was a standard part of the undergraduate or beginning graduate student sequence in analysis. However, the typical mathematics curriculum has changed at many institutions, and the Stieltjes integral has become less common in undergraduate textbooks and analysis courses. This book seeks to address this by offering an accessible treatment of the subject to students who have had a one semester course in analysis. This book is suitable for a second semester course in analysis, and also for independent study or as the foundation for a senior thesis or Masters project. Features: Written to be rigorous without sacrificing readability. Accessible to undergraduate students who have taken a one-semester course on real analysis. Contains a large number of exercises from routine to challenging.
Statistical Independence In Probability Analysis And Number Theory
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Author : Mark Kac
language : en
Publisher: American Mathematical Soc.
Release Date : 1959-12-31
Statistical Independence In Probability Analysis And Number Theory written by Mark Kac 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 1959-12-31 with Mathematics categories.
Professor Kac's monograph is designed to illustrate how simple observations can be made the starting point of rich and fruitful theories and how the same theme recurs in seemingly unrelated disciplines. An elementary but thorough discussion of the game of "heads or tails," including the normal law and the laws of large numbers, is presented in a setting in which a variety of purely analytic results appear natural and inevitable. The chapter "Primes Play a Game of Chance" uses the same setting in dealing with problems of the distribution of values of arithmetic functions. The final chapter "From Kinetic Theory to Continued Fractions" deals with a spectacular application of the ergodic theorems to continued fractions. Mark Kac conveyed his infectious enthusiasm for mathematics and its applications in his lectures, papers, and books. Two of his papers won Chauvenet awards for expository excellence.
An Introduction To Modern Analysis
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Author : Vicente Montesinos
language : en
Publisher: Springer
Release Date : 2015-05-04
An Introduction To Modern Analysis written by Vicente Montesinos and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-05-04 with Mathematics categories.
Examining the basic principles in real analysis and their applications, this text provides a self-contained resource for graduate and advanced undergraduate courses. It contains independent chapters aimed at various fields of application, enhanced by highly advanced graphics and results explained and supplemented with practical and theoretical exercises. The presentation of the book is meant to provide natural connections to classical fields of applications such as Fourier analysis or statistics. However, the book also covers modern areas of research, including new and seminal results in the area of functional analysis.
Irrational Numbers
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Author : Ivan Niven
language : en
Publisher: Cambridge University Press
Release Date : 2005-08-18
Irrational Numbers written by Ivan Niven 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 2005-08-18 with Mathematics categories.
In this monograph, Ivan Niven provides a masterful exposition of some central results on irrational, transcendental, and normal numbers. He gives a complete treatment by elementary methods of the irrationality of the exponential, logarithmic, and trigonometric functions with rational arguments. The approximation of irrational numbers by rationals, up to such results as the best possible approximation of Hurwitz, is also given with elementary technique. The last third of the monograph treats normal and transcendental numbers, including the Lindemann theorem, and the Gelfond-Schneider theorem. The book is wholly self-contained. The results needed from analysis and algebra are central. Well-known theorems, and complete references to standard works are given to help the beginner. The chapters are for the most part independent. There are notes at the end of each chapter citing the main sources used by the author and suggesting further reading.
Noncommutative Rings
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Author : I. N. Herstein
language : en
Publisher: Cambridge University Press
Release Date : 2005-09-08
Noncommutative Rings written by I. N. Herstein 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 2005-09-08 with Mathematics categories.
A cross-section of ideas, techniques and results that give the reader an unparalleled introductory overview of the subject.