Lectures On The Hyperreals

Author : Robert Goldblatt
Publisher : Springer Science & Business Media
Page : 292 pages
File Size : 53,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461206156

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Lectures on the Hyperreals by Robert Goldblatt Pdf

An introduction to nonstandard analysis based on a course given by the author. It is suitable for beginning graduates or upper undergraduates, or for self-study by anyone familiar with elementary real analysis. It presents nonstandard analysis not just as a theory about infinitely small and large numbers, but as a radically different way of viewing many standard mathematical concepts and constructions. It is a source of new ideas, objects and proofs, and a wealth of powerful new principles of reasoning. The book begins with the ultrapower construction of hyperreal number systems, and proceeds to develop one-variable calculus, analysis and topology from the nonstandard perspective. It then sets out the theory of enlargements of fragments of the mathematical universe, providing a foundation for the full-scale development of the nonstandard methodology. The final chapters apply this to a number of topics, including Loeb measure theory and its relation to Lebesgue measure on the real line. Highlights include an early introduction of the ideas of internal, external and hyperfinite sets, and a more axiomatic set-theoretic approach to enlargements than is usual.

Author : Loukas Grafakos
Publisher : Springer Science & Business Media
Page : 517 pages
File Size : 45,5 Mb
Release : 2009-04-28
Category : Mathematics
ISBN : 9780387094342

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Modern Fourier Analysis by Loukas Grafakos Pdf

The great response to the publication of the book Classical and Modern Fourier Analysishasbeenverygratifying.IamdelightedthatSpringerhasofferedtopublish the second edition of this book in two volumes: Classical Fourier Analysis, 2nd Edition, and Modern Fourier Analysis, 2nd Edition. These volumes are mainly addressed to graduate students who wish to study Fourier analysis. This second volume is intended to serve as a text for a seco- semester course in the subject. It is designed to be a continuation of the rst v- ume. Chapters 1–5 in the rst volume contain Lebesgue spaces, Lorentz spaces and interpolation, maximal functions, Fourier transforms and distributions, an introd- tion to Fourier analysis on the n-torus, singular integrals of convolution type, and Littlewood–Paley theory. Armed with the knowledgeof this material, in this volume,the reader encounters more advanced topics in Fourier analysis whose development has led to important theorems. These theorems are proved in great detail and their proofs are organized to present the ow of ideas. The exercises at the end of each section enrich the material of the corresponding section and provide an opportunity to develop ad- tional intuition and deeper comprehension. The historical notes in each chapter are intended to provide an account of past research but also to suggest directions for further investigation. The auxiliary results referred to the appendix can be located in the rst volume.

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 47,8 Mb
Release : 2024-06-13
Category : Electronic
ISBN : 9789814466318

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Mathematical Mechanics by Anonim Pdf

Author : John B Conway
Publisher : Springer
Page : 416 pages
File Size : 41,7 Mb
Release : 2019-03-09
Category : Mathematics
ISBN : 9781475743838

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A Course in Functional Analysis by John B Conway Pdf

This book is an introductory text in functional analysis. Unlike many modern treatments, it begins with the particular and works its way to the more general. From the reviews: "This book is an excellent text for a first graduate course in functional analysis....Many interesting and important applications are included....It includes an abundance of exercises, and is written in the engaging and lucid style which we have come to expect from the author." --MATHEMATICAL REVIEWS

Author : Ross Geoghegan
Publisher : Springer Science & Business Media
Page : 473 pages
File Size : 51,9 Mb
Release : 2007-12-17
Category : Mathematics
ISBN : 9780387746111

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Topological Methods in Group Theory by Ross Geoghegan Pdf

This book is about the interplay between algebraic topology and the theory of infinite discrete groups. It is a hugely important contribution to the field of topological and geometric group theory, and is bound to become a standard reference in the field. To keep the length reasonable and the focus clear, the author assumes the reader knows or can easily learn the necessary algebra, but wants to see the topology done in detail. The central subject of the book is the theory of ends. Here the author adopts a new algebraic approach which is geometric in spirit.

Author : Steven Roman
Publisher : Springer Science & Business Media
Page : 525 pages
File Size : 52,8 Mb
Release : 2007-09-20
Category : Mathematics
ISBN : 9780387728315

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Advanced Linear Algebra by Steven Roman Pdf

This graduate level textbook covers an especially broad range of topics. The book first offers a careful discussion of the basics of linear algebra. It then proceeds to a discussion of modules, emphasizing a comparison with vector spaces, and presents a thorough discussion of inner product spaces, eigenvalues, eigenvectors, and finite dimensional spectral theory, culminating in the finite dimensional spectral theorem for normal operators. The new edition has been revised and contains a chapter on the QR decomposition, singular values and pseudoinverses, and a chapter on convexity, separation and positive solutions to linear systems.

Author : Jane P. Gilman,Irwin Kra,Rubí E. Rodríguez
Publisher : Springer Science & Business Media
Page : 220 pages
File Size : 42,8 Mb
Release : 2007-11-25
Category : Mathematics
ISBN : 9780387747156

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Complex Analysis by Jane P. Gilman,Irwin Kra,Rubí E. Rodríguez Pdf

The authors’ aim here is to present a precise and concise treatment of those parts of complex analysis that should be familiar to every research mathematician. They follow a path in the tradition of Ahlfors and Bers by dedicating the book to a very precise goal: the statement and proof of the Fundamental Theorem for functions of one complex variable. They discuss the many equivalent ways of understanding the concept of analyticity, and offer a leisure exploration of interesting consequences and applications. Readers should have had undergraduate courses in advanced calculus, linear algebra, and some abstract algebra. No background in complex analysis is required.

Author : Gerd Grubb
Publisher : Springer Science & Business Media
Page : 464 pages
File Size : 49,7 Mb
Release : 2008-10-10
Category : Mathematics
ISBN : 9780387848952

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Distributions and Operators by Gerd Grubb Pdf

This book gives an introduction to distribution theory, based on the work of Schwartz and of many other people. It is the first book to present distribution theory as a standard text. Each chapter has been enhanced with many exercises and examples.

Author : U.S.R. Murty
Publisher : Springer Science & Business Media
Page : 458 pages
File Size : 54,7 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9781475734416

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Problems in Analytic Number Theory by U.S.R. Murty Pdf

"In order to become proficient in mathematics, or in any subject," writes Andre Weil, "the student must realize that most topics in volve only a small number of basic ideas. " After learning these basic concepts and theorems, the student should "drill in routine exercises, by which the necessary reflexes in handling such concepts may be ac quired. . . . There can be no real understanding of the basic concepts of a mathematical theory without an ability to use them intelligently and apply them to specific problems. " Weil's insightfulobservation becomes especially important at the graduate and research level. It is the viewpoint of this book. Our goal is to acquaint the student with the methods of analytic number theory as rapidly as possible through examples and exercises. Any landmark theorem opens up a method of attacking other problems. Unless the student is able to sift out from the mass of theory the underlying techniques, his or her understanding will only be academic and not that of a participant in research. The prime number theorem has given rise to the rich Tauberian theory and a general method of Dirichlet series with which one can study the asymptotics of sequences. It has also motivated the development of sieve methods. We focus on this theme in the book. We also touch upon the emerging Selberg theory (in Chapter 8) and p-adic analytic number theory (in Chapter 10).

Author : Raymond O. Wells
Publisher : Springer Science & Business Media
Page : 315 pages
File Size : 49,6 Mb
Release : 2007-12-06
Category : Mathematics
ISBN : 9780387738925

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Differential Analysis on Complex Manifolds by Raymond O. Wells Pdf

A brand new appendix by Oscar Garcia-Prada graces this third edition of a classic work. In developing the tools necessary for the study of complex manifolds, this comprehensive, well-organized treatment presents in its opening chapters a detailed survey of recent progress in four areas: geometry (manifolds with vector bundles), algebraic topology, differential geometry, and partial differential equations. Wells’s superb analysis also gives details of the Hodge-Riemann bilinear relations on Kahler manifolds, Griffiths's period mapping, quadratic transformations, and Kodaira's vanishing and embedding theorems. Oscar Garcia-Prada’s appendix gives an overview of the developments in the field during the decades since the book appeared.

Author : Ezra Miller,Bernd Sturmfels
Publisher : Springer Science & Business Media
Page : 442 pages
File Size : 55,9 Mb
Release : 2005-06-21
Category : Mathematics
ISBN : 0387237070

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Combinatorial Commutative Algebra by Ezra Miller,Bernd Sturmfels Pdf

Recent developments are covered Contains over 100 figures and 250 exercises Includes complete proofs

Author : Ward Cheney
Publisher : Springer Science & Business Media
Page : 455 pages
File Size : 45,8 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9781475735598

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Analysis for Applied Mathematics by Ward Cheney Pdf

This well-written book contains the analytical tools, concepts, and viewpoints needed for modern applied mathematics. It treats various practical methods for solving problems such as differential equations, boundary value problems, and integral equations. Pragmatic approaches to difficult equations are presented, including the Galerkin method, the method of iteration, Newton’s method, projection techniques, and homotopy methods.

Author : Daniel Bump
Publisher : Springer Science & Business Media
Page : 462 pages
File Size : 46,8 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9781475740943

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Lie Groups by Daniel Bump Pdf

This book proceeds beyond the representation theory of compact Lie groups (which is the basis of many texts) and offers a carefully chosen range of material designed to give readers the bigger picture. It explores compact Lie groups through a number of proofs and culminates in a "topics" section that takes the Frobenius-Schur duality between the representation theory of the symmetric group and the unitary groups as unifying them.

Author : J.E. Humphreys
Publisher : Springer Science & Business Media
Page : 189 pages
File Size : 41,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461263982

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Introduction to Lie Algebras and Representation Theory by J.E. Humphreys Pdf

This book is designed to introduce the reader to the theory of semisimple Lie algebras over an algebraically closed field of characteristic 0, with emphasis on representations. A good knowledge of linear algebra (including eigenvalues, bilinear forms, euclidean spaces, and tensor products of vector spaces) is presupposed, as well as some acquaintance with the methods of abstract algebra. The first four chapters might well be read by a bright undergraduate; however, the remaining three chapters are admittedly a little more demanding. Besides being useful in many parts of mathematics and physics, the theory of semisimple Lie algebras is inherently attractive, combining as it does a certain amount of depth and a satisfying degree of completeness in its basic results. Since Jacobson's book appeared a decade ago, improvements have been made even in the classical parts of the theory. I have tried to incor porate some of them here and to provide easier access to the subject for non-specialists. For the specialist, the following features should be noted: (I) The Jordan-Chevalley decomposition of linear transformations is emphasized, with "toral" subalgebras replacing the more traditional Cartan subalgebras in the semisimple case. (2) The conjugacy theorem for Cartan subalgebras is proved (following D. J. Winter and G. D. Mostow) by elementary Lie algebra methods, avoiding the use of algebraic geometry.

Author : J.H. Silverman
Publisher : Springer Science & Business Media
Page : 518 pages
File Size : 43,5 Mb
Release : 2010-05-05
Category : Mathematics
ISBN : 9780387699042

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The Arithmetic of Dynamical Systems by J.H. Silverman Pdf

This book provides an introduction to the relatively new discipline of arithmetic dynamics. Whereas classical discrete dynamics is the study of iteration of self-maps of the complex plane or real line, arithmetic dynamics is the study of the number-theoretic properties of rational and algebraic points under repeated application of a polynomial or rational function. A principal theme of arithmetic dynamics is that many of the fundamental problems in the theory of Diophantine equations have dynamical analogs.This graduate-level text provides an entry for students into an active field of research and serves as a standard reference for researchers.