on the Real Line
Author: R. Kannan,Carole K. Krueger
Publisher: Springer Science & Business Media
ISBN: 1461384745
Category: Mathematics
Page: 260
View: 9121
-on the Real Line
Author: R. Kannan,Carole K. Krueger
Publisher: Springer Science & Business Media
ISBN: 1461384745
Category: Mathematics
Page: 260
View: 9121
-An Introduction
Author: Fernando Gouvea
Publisher: Springer Science & Business Media
ISBN: 9783540629115
Category: Mathematics
Page: 306
View: 6996
There are numbers of all kinds: rational, real, complex, p-adic. The p-adic numbers are less well known than the others, but they play a fundamental role in number theory and in other parts of mathematics. This elementary introduction offers a broad understanding of p-adic numbers. From the reviews: "It is perhaps the most suitable text for beginners, and I shall definitely recommend it to anyone who asks me what a p-adic number is." --THE MATHEMATICAL GAZETTEEine Einführung in die Theorie reeller Funktionen
Author: Jürgen Appell
Publisher: Springer-Verlag
ISBN: 3540889035
Category: Mathematics
Page: 470
View: 9496
Das Buch führt in die Theorie der reellen Funktionen einer und mehrerer Variablen ein. Im Vordergrund stehen weniger abstrakte Ergebnisse als vielmehr die zahlreichen Beispiele und Gegenbeispiele, anhand derer die Bedeutung mathematischer Sätze deutlich gemacht wird. Kapitel 1 – 3 sind den wesentlichen Ergebnissen über stetige, differenzierbare und integrierbare Funktionen gewidmet, Kapitel 4 geht mit „merkwürdigen" Teilmengen der reellen Achse etwas über den üblichen Stoff hinaus. Funktionen mehrerer Variablen werden in Kapitel 5 bzw. 6 behandelt.
Author: Vladimir I. Bogachev
Publisher: Springer Science & Business Media
ISBN: 3540345140
Category: Mathematics
Page: 1075
View: 5234
This book giving an exposition of the foundations of modern measure theory offers three levels of presentation: a standard university graduate course, an advanced study containing some complements to the basic course, and, finally, more specialized topics partly covered by more than 850 exercises with detailed hints and references. Bibliographical comments and an extensive bibliography with 2000 works covering more than a century are provided.Mathematical Analysis
Author: Elimhan Mahmudov
Publisher: Springer Science & Business Media
ISBN: 9491216864
Category: Mathematics
Page: 373
View: 5538
The book “Single variable Differential and Integral Calculus” is an interesting text book for students of mathematics and physics programs, and a reference book for graduate students in any engineering field. This book is unique in the field of mathematical analysis in content and in style. It aims to define, compare and discuss topics in single variable differential and integral calculus, as well as giving application examples in important business fields. Some elementary concepts such as the power of a set, cardinality, measure theory, measurable functions are introduced. It also covers real and complex numbers, vector spaces, topological properties of sets, series and sequences of functions (including complex-valued functions and functions of a complex variable), polynomials and interpolation and extrema of functions. Although analysis is based on the single variable models and applications, theorems and examples are all set to be converted to multi variable extensions. For example, Newton, Riemann, Stieltjes and Lebesque integrals are studied together and compared.
Author: N.A
Publisher: N.A
ISBN: N.A
Category: Mathematical statistics
Page: N.A
View: 5308
An Introduction to Set Theory and Analysis
Author: John Stillwell
Publisher: Springer Science & Business Media
ISBN: 331901577X
Category: Mathematics
Page: 244
View: 4755
While most texts on real analysis are content to assume the real numbers, or to treat them only briefly, this text makes a serious study of the real number system and the issues it brings to light. Analysis needs the real numbers to model the line, and to support the concepts of continuity and measure. But these seemingly simple requirements lead to deep issues of set theory—uncountability, the axiom of choice, and large cardinals. In fact, virtually all the concepts of infinite set theory are needed for a proper understanding of the real numbers, and hence of analysis itself. By focusing on the set-theoretic aspects of analysis, this text makes the best of two worlds: it combines a down-to-earth introduction to set theory with an exposition of the essence of analysis—the study of infinite processes on the real numbers. It is intended for senior undergraduates, but it will also be attractive to graduate students and professional mathematicians who, until now, have been content to "assume" the real numbers. Its prerequisites are calculus and basic mathematics. Mathematical history is woven into the text, explaining how the concepts of real number and infinity developed to meet the needs of analysis from ancient times to the late twentieth century. This rich presentation of history, along with a background of proofs, examples, exercises, and explanatory remarks, will help motivate the reader. The material covered includes classic topics from both set theory and real analysis courses, such as countable and uncountable sets, countable ordinals, the continuum problem, the Cantor–Schröder–Bernstein theorem, continuous functions, uniform convergence, Zorn's lemma, Borel sets, Baire functions, Lebesgue measure, and Riemann integrable functions.
Author: Winfried Schirotzek
Publisher: Springer
ISBN: 9783540713326
Category: Mathematics
Page: 378
View: 9560
This book treats various concepts of generalized derivatives and subdifferentials in normed spaces, their geometric counterparts and their application to optimization problems. It starts with the subdifferential of convex analysis, passes to corresponding concepts for locally Lipschitz continuous functions and then presents subdifferentials for general lower semicontinuous functions. All basic tools are presented where they are needed: this concerns separation theorems, variational and extremal principles as well as relevant parts of multifunction theory. Each chapter ends with bibliographic notes and exercises.
Author: Jürgen Jost
Publisher: Surendra Kumar
ISBN: 9783540636540
Category: Mathematics
Page: 455
View: 1348
An Introduction
Author: Daniel Perrin
Publisher: N.A
ISBN: N.A
Category: Geometry, Algebraic
Page: 258
View: 6746
Aimed primarily at graduate students and beginning researchers, this book provides an introduction to algebraic geometry that is particularly suitable for those with no previous contact with the subject; it assumes only the standard background of undergraduate algebra. The book starts with easily-formulated problems with non-trivial solutions and uses these problems to introduce the fundamental tools of modern algebraic geometry: dimension; singularities; sheaves; varieties; and cohomology. A range of exercises is provided for each topic discussed, and a selection of problems and exam papers are collected in an appendix to provide material for further study.
Author: Ján Borsík,Ján Haluška
Publisher: N.A
ISBN: N.A
Category: Functions of real variables
Page: 188
View: 5629
Advanced Calculus on the Real Axis
Author: Teodora-Liliana Radulescu,Vicentiu D. Radulescu,Titu Andreescu
Publisher: Springer Science & Business Media
ISBN: 0387773789
Category: Mathematics
Page: 452
View: 2796
Problems in Real Analysis: Advanced Calculus on the Real Axis features a comprehensive collection of challenging problems in mathematical analysis that aim to promote creative, non-standard techniques for solving problems. This self-contained text offers a host of new mathematical tools and strategies which develop a connection between analysis and other mathematical disciplines, such as physics and engineering. A broad view of mathematics is presented throughout; the text is excellent for the classroom or self-study. It is intended for undergraduate and graduate students in mathematics, as well as for researchers engaged in the interplay between applied analysis, mathematical physics, and numerical analysis.
Author: Karel Hrbacek,Olivier Lessmann,Richard O'Donovan
Publisher: CRC Press
ISBN: 149870266X
Category: Mathematics
Page: 316
View: 2352
Analysis with Ultrasmall Numbers presents an intuitive treatment of mathematics using ultrasmall numbers. With this modern approach to infinitesimals, proofs become simpler and more focused on the combinatorial heart of arguments, unlike traditional treatments that use epsilon–delta methods. Students can fully prove fundamental results, such as the Extreme Value Theorem, from the axioms immediately, without needing to master notions of supremum or compactness. The book is suitable for a calculus course at the undergraduate or high school level or for self-study with an emphasis on nonstandard methods. The first part of the text offers material for an elementary calculus course while the second part covers more advanced calculus topics. The text provides straightforward definitions of basic concepts, enabling students to form good intuition and actually prove things by themselves. It does not require any additional "black boxes" once the initial axioms have been presented. The text also includes numerous exercises throughout and at the end of each chapter.
Author: Feng Dai,Yuan Xu
Publisher: Birkhäuser
ISBN: 3034808879
Category: Mathematics
Page: 118
View: 3338
This book provides an introduction to h-harmonics and Dunkl transforms. These are extensions of the ordinary spherical harmonics and Fourier transforms, in which the usual Lebesgue measure is replaced by a reflection-invariant weighted measure. The authors’ focus is on the analysis side of both h-harmonics and Dunkl transforms. Graduate students and researchers working in approximation theory, harmonic analysis, and functional analysis will benefit from this book.With an Invitation to Functional Analysis
Author: Matthew A. Pons
Publisher: Springer Science & Business Media
ISBN: 1461496381
Category: Mathematics
Page: 409
View: 2497
This undergraduate textbook introduces students to the basics of real analysis, provides an introduction to more advanced topics including measure theory and Lebesgue integration, and offers an invitation to functional analysis. While these advanced topics are not typically encountered until graduate study, the text is designed for the beginner. The author’s engaging style makes advanced topics approachable without sacrificing rigor. The text also consistently encourages the reader to pick up a pencil and take an active part in the learning process. Key features include: - examples to reinforce theory; - thorough explanations preceding definitions, theorems and formal proofs; - illustrations to support intuition; - over 450 exercises designed to develop connections between the concrete and abstract. This text takes students on a journey through the basics of real analysis and provides those who wish to delve deeper the opportunity to experience mathematical ideas that are beyond the standard undergraduate curriculum.
Author: Douglas Smith,Maurice Eggen,Richard St. Andre
Publisher: Cengage Learning
ISBN: 1305177193
Category: Mathematics
Page: 448
View: 3076
A TRANSITION TO ADVANCED MATHEMATICS helps students to bridge the gap between calculus and advanced math courses. The most successful text of its kind, the 8th edition continues to provide a firm foundation in major concepts needed for continued study and guides students to think and express themselves mathematically—to analyze a situation, extract pertinent facts, and draw appropriate conclusions. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.