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Foundations of Modern Analysis

Foundations of Modern Analysis PDF Author: Avner Friedman
Publisher: Courier Corporation
ISBN: 9780486640624
Category : Mathematics
Languages : en
Pages : 276

Book Description
Measure and integration, metric spaces, the elements of functional analysis in Banach spaces, and spectral theory in Hilbert spaces — all in a single study. Only book of its kind. Unusual topics, detailed analyses. Problems. Excellent for first-year graduate students, almost any course on modern analysis. Preface. Bibliography. Index.

Foundations of Modern Analysis

Foundations of Modern Analysis PDF Author: Avner Friedman
Publisher: Courier Corporation
ISBN: 9780486640624
Category : Mathematics
Languages : en
Pages : 276

Book Description
Measure and integration, metric spaces, the elements of functional analysis in Banach spaces, and spectral theory in Hilbert spaces — all in a single study. Only book of its kind. Unusual topics, detailed analyses. Problems. Excellent for first-year graduate students, almost any course on modern analysis. Preface. Bibliography. Index.

Foundations of Modern Analysis

Foundations of Modern Analysis PDF Author: J. Dieudonne
Publisher: Hesperides Press
ISBN: 1443724262
Category : Mathematics
Languages : en
Pages : 412

Book Description
FOUNDATIONS OFMODERN ANALYSISEnlarged and Corrected PrintingJ. DIEUDONNEThis book is the first volume of a treatise which will eventually consist offour volumes. It is also an enlarged and corrected printing, essentiallywithout changes, of my Foundations of Modern Analysis, published in1960. Many readers, colleagues, and friends have urged me to write a sequelto that book, and in the end I became convinced that there was a place fora survey of modern analysis, somewhere between the minimum tool kitof an elementary nature which I had intended to write, and specialistmonographs leading to the frontiers of research. My experience of teachinghas also persuaded me that the mathematical apprentice, after taking the firststep of Foundations, needs further guidance and a kind of general birdseyeview of his subject before he is launched onto the ocean of mathematicalliterature or set on the narrow path of his own topic of research.Thus I have finally been led to attempt to write an equivalent, for themathematicians of 1970, of what the Cours dAnalyse of Jordan, Picard, and Goursat were for mathematical students between 1880 and 1920.It is manifestly out of the question to attempt encyclopedic coverage, andcertainly superfluous to rewrite the works of N. Bourbaki. I have thereforebeen obliged to cut ruthlessly in order to keep within limits comparable tothose of the classical treatises. I have opted for breadth rather than depth, inthe opinion that it is better to show the reader rudiments of many branchesof modern analysis rather than to provide him with a complete and detailedexposition of a small number of topics.Experience seems to show that the student usually finds a new theorydifficult tograsp at a first reading. He needs to return to it several times beforehe becomes really familiar with it and can distinguish for himself whichare the essential ideas and which results are of minor importance, and onlythen will he be able to apply it intelligently. The chapters of this treatise arevi PREFACE TO THE ENLARGED AND CORRECTED PRINTINGtherefore samples rather than complete theories: indeed, I have systematically tried not to be exhaustive. The works quoted in the bibliography willalways enable the reader to go deeper into any particular theory.However, I have refused to distort the main ideas of analysis by presentingthem in too specialized a form, and thereby obscuring their power andgenerality. It gives a false impression, for example, if differential geometryis restricted to two or three dimensions, or if integration is restricted to Lebesgue measure, on the pretext of making these subjects more accessible orintuitive.On the other hand I do not believe that the essential content of the ideasinvolved is lost, in a first study, by restricting attention to separable metrizabletopological spaces. The mathematicians of my own generation were certainlyright to banish, hypotheses of countability wherever they were not needed: thiswas the only way to get a clear understanding.

Foundations of Mathematical Analysis

Foundations of Mathematical Analysis PDF Author: Richard Johnsonbaugh
Publisher: Courier Corporation
ISBN: 0486134776
Category : Mathematics
Languages : en
Pages : 450

Book Description
Definitive look at modern analysis, with views of applications to statistics, numerical analysis, Fourier series, differential equations, mathematical analysis, and functional analysis. More than 750 exercises; some hints and solutions. 1981 edition.

Foundations of Applied Mathematics, Volume I

Foundations of Applied Mathematics, Volume I PDF Author: Jeffrey Humpherys
Publisher: SIAM
ISBN: 1611974895
Category : Mathematics
Languages : en
Pages : 710

Book Description
This book provides the essential foundations of both linear and nonlinear analysis necessary for understanding and working in twenty-first century applied and computational mathematics. In addition to the standard topics, this text includes several key concepts of modern applied mathematical analysis that should be, but are not typically, included in advanced undergraduate and beginning graduate mathematics curricula. This material is the introductory foundation upon which algorithm analysis, optimization, probability, statistics, differential equations, machine learning, and control theory are built. When used in concert with the free supplemental lab materials, this text teaches students both the theory and the computational practice of modern mathematical analysis. Foundations of Applied Mathematics, Volume 1: Mathematical Analysis includes several key topics not usually treated in courses at this level, such as uniform contraction mappings, the continuous linear extension theorem, Daniell?Lebesgue integration, resolvents, spectral resolution theory, and pseudospectra. Ideas are developed in a mathematically rigorous way and students are provided with powerful tools and beautiful ideas that yield a number of nice proofs, all of which contribute to a deep understanding of advanced analysis and linear algebra. Carefully thought out exercises and examples are built on each other to reinforce and retain concepts and ideas and to achieve greater depth. Associated lab materials are available that expose students to applications and numerical computation and reinforce the theoretical ideas taught in the text. The text and labs combine to make students technically proficient and to answer the age-old question, "When am I going to use this?

The Foundations of Modern Time Series Analysis

The Foundations of Modern Time Series Analysis PDF Author: Terence C. Mills
Publisher: Springer
ISBN: 0230305024
Category : Business & Economics
Languages : en
Pages : 476

Book Description
This book develops the analysis of Time Series from its formal beginnings in the 1890s through to the publication of Box and Jenkins' watershed publication in 1970, showing how these methods laid the foundations for the modern techniques of Time Series analysis that are in use today.

Analysis I

Analysis I PDF Author: Herbert Amann
Publisher: Springer Science & Business Media
ISBN: 3764373237
Category : Mathematics
Languages : en
Pages : 436

Book Description
"This textbook provides an outstanding introduction to analysis. It is distinguished by its high level of presentation and its focus on the essential.'' (Zeitschrift für Analysis und ihre Anwendung 18, No. 4 - G. Berger, review of the first German edition) "One advantage of this presentation is that the power of the abstract concepts are convincingly demonstrated using concrete applications.'' (W. Grölz, review of the first German edition)

Foundations of Analysis

Foundations of Analysis PDF Author: Joseph L. Taylor
Publisher: American Mathematical Soc.
ISBN: 0821889842
Category : Mathematics
Languages : en
Pages : 411

Book Description
Foundations of Analysis has two main goals. The first is to develop in students the mathematical maturity and sophistication they will need as they move through the upper division curriculum. The second is to present a rigorous development of both single and several variable calculus, beginning with a study of the properties of the real number system. The presentation is both thorough and concise, with simple, straightforward explanations. The exercises differ widely in level of abstraction and level of difficulty. They vary from the simple to the quite difficult and from the computational to the theoretical. Each section contains a number of examples designed to illustrate the material in the section and to teach students how to approach the exercises for that section. --Book cover.

Foundations of Abstract Analysis

Foundations of Abstract Analysis PDF Author: Jewgeni H. Dshalalow
Publisher: Springer Science & Business Media
ISBN: 1461459621
Category : Mathematics
Languages : en
Pages : 756

Book Description
Foundations of Abstract Analysis is the first of a two book series offered as the second (expanded) edition to the previously published text Real Analysis. It is written for a graduate-level course on real analysis and presented in a self-contained way suitable both for classroom use and for self-study. While this book carries the rigor of advanced modern analysis texts, it elaborates the material in much greater details and therefore fills a gap between introductory level texts (with topics developed in Euclidean spaces) and advanced level texts (exclusively dealing with abstract spaces) making it accessible for a much wider interested audience. To relieve the reader of the potential overload of new words, definitions, and concepts, the book (in its unique feature) provides lists of new terms at the end of each section, in a chronological order. Difficult to understand abstract notions are preceded by informal discussions and blueprints followed by thorough details and supported by examples and figures. To further reinforce the text, hints and solutions to almost a half of more than 580 problems are provided at the end of the book, still leaving ample exercises for assignments. This volume covers topics in point-set topology and measure and integration. Prerequisites include advanced calculus, linear algebra, complex variables, and calculus based probability.

Foundations of Modern Probability

Foundations of Modern Probability PDF Author: Olav Kallenberg
Publisher: Springer Science & Business Media
ISBN: 9780387953137
Category : Mathematics
Languages : en
Pages : 670

Book Description
The first edition of this single volume on the theory of probability has become a highly-praised standard reference for many areas of probability theory. Chapters from the first edition have been revised and corrected, and this edition contains four new chapters. New material covered includes multivariate and ratio ergodic theorems, shift coupling, Palm distributions, Harris recurrence, invariant measures, and strong and weak ergodicity.

Modern Portfolio Theory

Modern Portfolio Theory PDF Author: Jack Clark Francis
Publisher: John Wiley & Sons
ISBN: 1118417208
Category : Business & Economics
Languages : en
Pages : 576

Book Description
A through guide covering Modern Portfolio Theory as well as the recent developments surrounding it Modern portfolio theory (MPT), which originated with Harry Markowitz's seminal paper "Portfolio Selection" in 1952, has stood the test of time and continues to be the intellectual foundation for real-world portfolio management. This book presents a comprehensive picture of MPT in a manner that can be effectively used by financial practitioners and understood by students. Modern Portfolio Theory provides a summary of the important findings from all of the financial research done since MPT was created and presents all the MPT formulas and models using one consistent set of mathematical symbols. Opening with an informative introduction to the concepts of probability and utility theory, it quickly moves on to discuss Markowitz's seminal work on the topic with a thorough explanation of the underlying mathematics. Analyzes portfolios of all sizes and types, shows how the advanced findings and formulas are derived, and offers a concise and comprehensive review of MPT literature Addresses logical extensions to Markowitz's work, including the Capital Asset Pricing Model, Arbitrage Pricing Theory, portfolio ranking models, and performance attribution Considers stock market developments like decimalization, high frequency trading, and algorithmic trading, and reveals how they align with MPT Companion Website contains Excel spreadsheets that allow you to compute and graph Markowitz efficient frontiers with riskless and risky assets If you want to gain a complete understanding of modern portfolio theory this is the book you need to read.