Introduction to Analysis

Introduction to Analysis

Rigorous and carefully presented, the text assumes a year of calculus and features problems at the end of each chapter. 1968 edition.

Author: Maxwell Rosenlicht

Publisher: Courier Corporation

ISBN: 9780486650388

Category: Mathematics

Page: 254

View: 652

Written for junior and senior undergraduates, this remarkably clear and accessible treatment covers set theory, the real number system, metric spaces, continuous functions, Riemann integration, multiple integrals, and more. Rigorous and carefully presented, the text assumes a year of calculus and features problems at the end of each chapter. 1968 edition.
Categories: Mathematics

An Introduction to Analysis

An Introduction to Analysis

This book presents a concise and sharpley focused introduction to the basic concepts of analysis - from the development of real numbers through uniform convergences of a sequence of functions - and includes coverage both of the analysis of ...

Author: Gerald Bilodeau

Publisher: Jones & Bartlett Learning

ISBN: 0763774928

Category: Computers

Page: 333

View: 466

This book presents a concise and sharpley focused introduction to the basic concepts of analysis - from the development of real numbers through uniform convergences of a sequence of functions - and includes coverage both of the analysis of functions of more than one variable and of differential equations. Examples and figures are used extensively to assist the reader in understanding the concepts and then applying them.
Categories: Computers

An Introduction to Analysis

An Introduction to Analysis

Originally published in 2010, reissued as part of Pearson's modern classic series.

Author: William Wade

Publisher: Math Classics

ISBN: 0134707621

Category: Mathematics

Page: 696

View: 320

Originally published in 2010, reissued as part of Pearson's modern classic series.
Categories: Mathematics

A Concise Introduction to Analysis

A Concise Introduction to Analysis

This book provides an introduction to the basic ideas and tools used in mathematical analysis.

Author: Daniel W. Stroock

Publisher: Springer

ISBN: 3319244671

Category: Mathematics

Page: 218

View: 907

This book provides an introduction to the basic ideas and tools used in mathematical analysis. It is a hybrid cross between an advanced calculus and a more advanced analysis text and covers topics in both real and complex variables. Considerable space is given to developing Riemann integration theory in higher dimensions, including a rigorous treatment of Fubini's theorem, polar coordinates and the divergence theorem. These are used in the final chapter to derive Cauchy's formula, which is then applied to prove some of the basic properties of analytic functions. Among the unusual features of this book is the treatment of analytic function theory as an application of ideas and results in real analysis. For instance, Cauchy's integral formula for analytic functions is derived as an application of the divergence theorem. The last section of each chapter is devoted to exercises that should be viewed as an integral part of the text. A Concise Introduction to Analysis should appeal to upper level undergraduate mathematics students, graduate students in fields where mathematics is used, as well as to those wishing to supplement their mathematical education on their own. Wherever possible, an attempt has been made to give interesting examples that demonstrate how the ideas are used and why it is important to have a rigorous grasp of them.
Categories: Mathematics

An Introduction to Analysis

An Introduction to Analysis

The book discusses basic material on point set topology, such as normed and metric spaces, topological spaces, compact sets, and the Baire category theorem.

Author: Robert C. Gunning

Publisher: Princeton University Press

ISBN: 9781400889419

Category: Mathematics

Page: 384

View: 244

An essential undergraduate textbook on algebra, topology, and calculus An Introduction to Analysis is an essential primer on basic results in algebra, topology, and calculus for undergraduate students considering advanced degrees in mathematics. Ideal for use in a one-year course, this unique textbook also introduces students to rigorous proofs and formal mathematical writing--skills they need to excel. With a range of problems throughout, An Introduction to Analysis treats n-dimensional calculus from the beginning—differentiation, the Riemann integral, series, and differential forms and Stokes's theorem—enabling students who are serious about mathematics to progress quickly to more challenging topics. The book discusses basic material on point set topology, such as normed and metric spaces, topological spaces, compact sets, and the Baire category theorem. It covers linear algebra as well, including vector spaces, linear mappings, Jordan normal form, bilinear mappings, and normal mappings. Proven in the classroom, An Introduction to Analysis is the first textbook to bring these topics together in one easy-to-use and comprehensive volume. Provides a rigorous introduction to calculus in one and several variables Introduces students to basic topology Covers topics in linear algebra, including matrices, determinants, Jordan normal form, and bilinear and normal mappings Discusses differential forms and Stokes's theorem in n dimensions Also covers the Riemann integral, integrability, improper integrals, and series expansions
Categories: Mathematics

An Introduction to Analysis

An Introduction to Analysis

The third edition of this widely popular textbook is authored by a master teacher. This book provides a mathematically rigorous introduction to analysis of real­valued functions of one variable.

Author: James R. Kirkwood

Publisher: CRC Press

ISBN: 9781000403558

Category: Mathematics

Page: 336

View: 679

The third edition of this widely popular textbook is authored by a master teacher. This book provides a mathematically rigorous introduction to analysis of real­valued functions of one variable. This intuitive, student-friendly text is written in a manner that will help to ease the transition from primarily computational to primarily theoretical mathematics. The material is presented clearly and as intuitive as possible while maintaining mathematical integrity. The author supplies the ideas of the proof and leaves the write-up as an exercise. The text also states why a step in a proof is the reasonable thing to do and which techniques are recurrent. Examples, while no substitute for a proof, are a valuable tool in helping to develop intuition and are an important feature of this text. Examples can also provide a vivid reminder that what one hopes might be true is not always true. Features of the Third Edition: Begins with a discussion of the axioms of the real number system. The limit is introduced via sequences. Examples motivate what is to come, highlight the need for hypothesis in a theorem, and make abstract ideas more concrete. A new section on the Cantor set and the Cantor function. Additional material on connectedness. Exercises range in difficulty from the routine "getting your feet wet" types of problems to the moderately challenging problems. Topology of the real number system is developed to obtain the familiar properties of continuous functions. Some exercises are devoted to the construction of counterexamples. The author presents the material to make the subject understandable and perhaps exciting to those who are beginning their study of abstract mathematics. Table of Contents Preface Introduction The Real Number System Sequences of Real Numbers Topology of the Real Numbers Continuous Functions Differentiation Integration Series of Real Numbers Sequences and Series of Functions Fourier Series Bibliography Hints and Answers to Selected Exercises Index Biography James R. Kirkwood holds a Ph.D. from University of Virginia. He has authored fifteen, published mathematics textbooks on various topics including calculus, real analysis, mathematical biology and mathematical physics. His original research was in mathematical physics, and he co-authored the seminal paper in a topic now called Kirkwood-Thomas Theory in mathematical physics. During the summer, he teaches real analysis to entering graduate students at the University of Virginia. He has been awarded several National Science Foundation grants. His texts, Elementary Linear Algebra, Linear Algebra, and Markov Processes, are also published by CRC Press.
Categories: Mathematics

Introduction to Real Analysis

Introduction to Real Analysis

Therefore, this book provides the fundamental concepts and techniques of real analysis for readers in all of these areas.

Author: Robert G. Bartle

Publisher: John Wiley & Sons Incorporated

ISBN: UOM:39015048768512

Category: Mathematics

Page: 388

View: 317

In recent years, mathematics has become valuable in many areas, including economics and management science as well as the physical sciences, engineering and computer science. Therefore, this book provides the fundamental concepts and techniques of real analysis for readers in all of these areas. It helps one develop the ability to think deductively, analyze mathematical situations and extend ideas to a new context. Like the first two editions, this edition maintains the same spirit and user-friendly approach with some streamlined arguments, a few new examples, rearranged topics, and a new chapter on the Generalized Riemann Integral.
Categories: Mathematics

The Analysis of Time Series

The Analysis of Time Series

Highlights of the Sixth Edition: A new section on handling real data New discussion on prediction intervals A completely revised and restructured chapter on more advanced topics, with new material on the aggregation of time series, ...

Author: Chris Chatfield

Publisher: Chapman and Hall/CRC

ISBN: 1584883170

Category: Mathematics

Page: 352

View: 167

Since 1975, The Analysis of Time Series: An Introduction has introduced legions of statistics students and researchers to the theory and practice of time series analysis. With each successive edition, bestselling author Chris Chatfield has honed and refined his presentation, updated the material to reflect advances in the field, and presented interesting new data sets. The sixth edition is no exception. It provides an accessible, comprehensive introduction to the theory and practice of time series analysis. The treatment covers a wide range of topics, including ARIMA probability models, forecasting methods, spectral analysis, linear systems, state-space models, and the Kalman filter. It also addresses nonlinear, multivariate, and long-memory models. The author has carefully updated each chapter, added new discussions, incorporated new datasets, and made those datasets available for download from www.crcpress.com. A free online appendix on time series analysis using R can be accessed at http://people.bath.ac.uk/mascc/TSA.usingR.doc. Highlights of the Sixth Edition: A new section on handling real data New discussion on prediction intervals A completely revised and restructured chapter on more advanced topics, with new material on the aggregation of time series, analyzing time series in finance, and discrete-valued time series A new chapter of examples and practical advice Thorough updates and revisions throughout the text that reflect recent developments and dramatic changes in computing practices over the last few years The analysis of time series can be a difficult topic, but as this book has demonstrated for two-and-a-half decades, it does not have to be daunting. The accessibility, polished presentation, and broad coverage of The Analysis of Time Series make it simply the best introduction to the subject available.
Categories: Mathematics

An Introduction to Combinatorial Analysis

An Introduction to Combinatorial Analysis

This book introduces combinatorial analysis to the beginning student.

Author: John Riordan

Publisher: Princeton University Press

ISBN: 9781400854332

Category: Mathematics

Page: 258

View: 729

This book introduces combinatorial analysis to the beginning student. The author begins with the theory of permutation and combinations and their applications to generating functions. In subsequent chapters, he presents Bell polynomials; the principle of inclusion and exclusion; the enumeration of permutations in cyclic representation; the theory of distributions; partitions, compositions, trees and linear graphs; and the enumeration of restricted permutations. Originally published in 1980. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Categories: Mathematics

Statistics and Data Analysis

Statistics and Data Analysis

At the end of each chapter is a brief summary which reviews the material and explains key terms. Following this are questions which help readers review main new concepts and ideas, and practice problems (many with real data sets).

Author: Andrew F. Siegel

Publisher: John Wiley & Sons Incorporated

ISBN: STANFORD:36105003822017

Category: Mathematics

Page: 518

View: 159

An introductory text for nontechnical students that integrates traditional statistical inference with the more modern idea of data analysis. Material begins with simple data sets and proceeds to those with more structure. Examples are plentiful and have been chosen from diverse fields, making the subject accessible to students of any academic field. Contains many pictures, as well as detailed calculations with step-by-step instructions and formulas that indicate in mathematical notation exactly what is being done. At the end of each chapter is a brief summary which reviews the material and explains key terms. Following this are questions which help readers review main new concepts and ideas, and practice problems (many with real data sets). Requires limited background in mathematics.
Categories: Mathematics

Unitary Representations and Harmonic Analysis

Unitary Representations and Harmonic Analysis

The principal aim of this book is to give an introduction to harmonic analysis and the theory of unitary representations of Lie groups.

Author: M. Sugiura

Publisher: Elsevier

ISBN: 0080887597

Category: Mathematics

Page: 451

View: 776

The principal aim of this book is to give an introduction to harmonic analysis and the theory of unitary representations of Lie groups. The second edition has been brought up to date with a number of textual changes in each of the five chapters, a new appendix on Fatou's theorem has been added in connection with the limits of discrete series, and the bibliography has been tripled in length.
Categories: Mathematics

An Introduction to Pollen Analysis

An Introduction to Pollen Analysis

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.

Author: G Erdtman

Publisher: Andesite Press

ISBN: 1298504481

Category:

Page: 266

View: 905

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Categories:

Explorations in Analysis Topology and Dynamics An Introduction to Abstract Mathematics

Explorations in Analysis  Topology  and Dynamics  An Introduction to Abstract Mathematics

This book is an introduction to the theory of calculus in the style of inquiry-based learning. The text guides students through the process of making mathematical ideas rigorous, from investigations and problems to definitions and proofs.

Author: Alejandro Uribe A.

Publisher: American Mathematical Soc.

ISBN: 9781470452704

Category: Education

Page: 178

View: 985

This book is an introduction to the theory of calculus in the style of inquiry-based learning. The text guides students through the process of making mathematical ideas rigorous, from investigations and problems to definitions and proofs. The format allows for various levels of rigor as negotiated between instructor and students, and the text can be of use in a theoretically oriented calculus course or an analysis course that develops rigor gradually. Material on topology (e.g., of higher dimensional Euclidean spaces) and discrete dynamical systems can be used as excursions within a study of analysis or as a more central component of a course. The themes of bisection, iteration, and nested intervals form a common thread throughout the text. The book is intended for students who have studied some calculus and want to gain a deeper understanding of the subject through an inquiry-based approach.
Categories: Education

Data Analysis and Data Mining

Data Analysis and Data Mining

This book presents key statistical concepts by way of case studies, giving readers the benefit of learning from real problems and real data.

Author: Adelchi Azzalini

Publisher: Oxford University Press

ISBN: 9780199942718

Category: Business & Economics

Page: 288

View: 555

An introduction to statistical data mining, Data Analysis and Data Mining is both textbook and professional resource. Assuming only a basic knowledge of statistical reasoning, it presents core concepts in data mining and exploratory statistical models to students and professional statisticians-both those working in communications and those working in a technological or scientific capacity-who have a limited knowledge of data mining. This book presents key statistical concepts by way of case studies, giving readers the benefit of learning from real problems and real data. Aided by a diverse range of statistical methods and techniques, readers will move from simple problems to complex problems. Through these case studies, authors Adelchi Azzalini and Bruno Scarpa explain exactly how statistical methods work; rather than relying on the "push the button" philosophy, they demonstrate how to use statistical tools to find the best solution to any given problem. Case studies feature current topics highly relevant to data mining, such web page traffic; the segmentation of customers; selection of customers for direct mail commercial campaigns; fraud detection; and measurements of customer satisfaction. Appropriate for both advanced undergraduate and graduate students, this much-needed book will fill a gap between higher level books, which emphasize technical explanations, and lower level books, which assume no prior knowledge and do not explain the methodology behind the statistical operations.
Categories: Business & Economics

An Introduction to Statistics with Python

An Introduction to Statistics with Python

As it also provides some statistics background, the book can be used by anyone who wants to perform a statistical data analysis.

Author: Thomas Haslwanter

Publisher: Springer

ISBN: 9783319283166

Category: Computers

Page: 278

View: 418

This textbook provides an introduction to the free software Python and its use for statistical data analysis. It covers common statistical tests for continuous, discrete and categorical data, as well as linear regression analysis and topics from survival analysis and Bayesian statistics. Working code and data for Python solutions for each test, together with easy-to-follow Python examples, can be reproduced by the reader and reinforce their immediate understanding of the topic. With recent advances in the Python ecosystem, Python has become a popular language for scientific computing, offering a powerful environment for statistical data analysis and an interesting alternative to R. The book is intended for master and PhD students, mainly from the life and medical sciences, with a basic knowledge of statistics. As it also provides some statistics background, the book can be used by anyone who wants to perform a statistical data analysis.
Categories: Computers

An Introduction to Syntactic Analysis and Theory

An Introduction to Syntactic Analysis and Theory

To facilitate comprehension of basic principles and theories, useful ‘Practice’ boxes are included throughout the text, with more advanced concepts in syntactic theory also highlighted throughout.

Author: Dominique Sportiche

Publisher: John Wiley & Sons

ISBN: 9781118470473

Category: Language Arts & Disciplines

Page: 472

View: 706

An Introduction to Syntactic Analysis and Theory offersbeginning students a comprehensive overview of and introduction toour current understanding of the rules and principles that governthe syntax of natural languages. Includes numerous pedagogical features such as‘practice’ boxes and sidebars, designed to facilitateunderstanding of both the ‘hows’ and the‘whys’ of sentence structure Guides readers through syntactic and morphological structuresin a progressive manner Takes the mystery out of one of the most crucial aspects of theworkings of language – the principles and processes behindthe structure of sentences Ideal for students with minimal knowledge of current syntacticresearch, it progresses in theoretical difficulty from basic ideasand theories to more complex and advanced, up to date concepts insyntactic theory
Categories: Language Arts & Disciplines

An Introduction to Multivariate Statistical Analysis

An Introduction to Multivariate Statistical Analysis

The Third Edition features new or more extensive coverageof: Patterns of Dependence and Graphical Models–a newchapter Measures of correlation and tests of independence Reduced rank regression, including the limited-informationmaximum ...

Author: Theodore W. Anderson

Publisher: Wiley-Interscience

ISBN: 0471360910

Category: Mathematics

Page: 752

View: 167

Perfected over three editions and more than forty years, thisfield- and classroom-tested reference: * Uses the method of maximum likelihood to a large extent to ensurereasonable, and in some cases optimal procedures. * Treats all the basic and important topics in multivariatestatistics. * Adds two new chapters, along with a number of new sections. * Provides the most methodical, up-to-date information on MVstatistics available.
Categories: Mathematics

Ultrametric Calculus

Ultrametric Calculus

This is an introduction to p-adic analysis which is elementary yet complete and which displays the variety of applications of the subject. Dr Schikhof is able to point out and explain how p-adic and 'real' analysis differ.

Author: W. H. Schikhof

Publisher: Cambridge University Press

ISBN: 0521242347

Category: Mathematics

Page: 320

View: 300

This is an introduction to p-adic analysis which is elementary yet complete and which displays the variety of applications of the subject. Dr Schikhof is able to point out and explain how p-adic and 'real' analysis differ. This approach guarantees the reader quickly becomes acquainted with this equally 'real' analysis and appreciates its relevance. The reader's understanding is enhanced and deepened by the large number of exercises included throughout; these both test the reader's grasp and extend the text in interesting directions. As a consequence, this book will become a standard reference for professionals (especially in p-adic analysis, number theory and algebraic geometry) and will be welcomed as a textbook for advanced students of mathematics familiar with algebra and analysis.
Categories: Mathematics