Product Description
This textbook provides an introduction to the methods and language of functional analysis, including Hilbert spaces, Fredholm theory for compact operators, and spectral theory of self-adjoint operators. It also presents the basic theorems and methods of abstract functional analysis and a few applications of these methods to Banach algebras and the theory of unbounded self-adjoint operators.

The text corresponds to material for two semester courses (Part I and Part II, respectively) and is essentially self-contained. Prerequisites for the first part are minimal amounts of linear algebra and calculus. For the second part, some knowledge of topology and measure theory is recommended. Each of the 11 chapters is followed by numerous exercises, with solutions given at the end of the book.

The text is ideal for a one-year course. It will also provide a sound basis for further study. It is suitable for graduate students and researchers interested in operator theory and functional analysis. ... Read more

Customer Reviews (1)

Great Condition Poor Choice of Text
Delivered fine. Great condition and delivered well on time. Wish my professor wasn't using this text, however. Not the best handling of the material that I've seen so far. ... Read more

Product Description
This book outlines an elementary, one-semester course which exposes students to both the process of rigor, and the rewards inherent in taking an axiomatic approach to the study of functions of a real variable. The aim of a course in real analysis should be to challenge and improve mathematical intuition rather than to verify it. The philosophy of this book is to focus attention on questions which give analysis its inherent fascination. ... Read more

Customer Reviews (19)

Good.
The product was shipped as soon as possible and I got this package before I even expected it. The book was in good condition as stated. There was a lot of writing and highlighting in the book but it's to be expected because the book is not new. It was at a very reasonable price. So overall I am very happy with this purchase.

I love it
This is a real product for students who want to get "A" grade in Analysis.

Adequate, but missing solutions is frustrating.
It's a good introductory book, but it leaves a prodigious amount of the Theorems as exercises.This makes studying out of the book very difficult in a time crunch.Still, easy to understand the explanations that are given.

A book which is too unfocused for beginners
I attempted to teach out of this book and my students found it difficult since many of its exercises aren't properly prefaced in the sections for which they were intended. The ordering of the ideas is also haphazard and the general presentation assumes far more mathematical knowledge and familiarity with basic concepts than can be gleaned from its pages alone. An extension to the introductory section on set theory and mappings would be helpful to the presentation. Many sections are unnecessarily chatty in the wrong places and unfocused. It is an inexpensive book, but Bartle and Sherbert's masterful introduction is well worth 5 times its price.

Super user-friendly well written analysis book delightful to read!
I currently own Baby Rudin, Kolmogorov and Fomin, Marsden,John Royden, Probability and Analysis and this book
I think if this book provides a solutions manual, it will be the best self-study book. Sure Rudin is elegant and very general in a sense that it covers huge amount of materials through pithy and concise yet rigorous proofs but this is exactly why i don't think it is a good book to start.

When i started with Rudin because of its fame, I was very frustrated because of the density of the book. It is veryheavy reading that you need to explicate in your head to understand. This is all good and well if you already grasp the idea but for first time learners rudin should be used as a reference. ( i am sure lots of people disagree, this is just my view).

This book on the other hand is super friendly and when you read it, it does the explicating of the ideas for you. it is as if you are listening to a professor who does the thinking for you. OF COURSE this is not GOOD for learning how to proof stuff. That, one must learn by himself. However, When one wants to learn the ideas and grasp the general overview and the beauty of analysis, it serves one well.

I recommend this book to anyone who wants to leisurely yet rigorously learn analysis.usually, those two words are oxymorons but this book combines them - leisure and rigor come together. ... Read more

Product Description
The book gives an introduction to $p$-adic numbers from the point of view of number theory, topology, and analysis. Compared to other books on the subject, its novelty is both a particularly balanced approach to these three points of view and an emphasis on topics accessible to undergraduates. In addition, several topics from real analysis and elementary topology which are not usually covered in undergraduate courses (totally disconnected spaces and Cantor sets, points of discontinuity of maps and the Baire Category Theorem, surjectivity of isometries of compact metric spaces) are also included in the book. They will enhance the reader's understanding of real analysis and intertwine the real and $p$-adic contexts of the book. The book is based on an advanced undergraduate course given by the author. The choice of the topic was motivated by the internal beauty of the subject of $p$-adic analysis, an unusual one in the undergraduate curriculum, and abundant opportunities to compare it with its much more familiar real counterpart. The book includes a large number of exercises. Answers, hints, and solutions for most of them appear at the end of the book. Well written, with obvious care for the reader, the book can be successfully used in a topic course or for self-study. ... Read more

Customer Reviews (1)

Nice little library
It can be difficult as a new student in non-Archimedean analysis to reconcile the real analysis world with such a strange new world. All too often young mathematicians are assumed to understand what is referred to as elementary, only to stumble over the 'simple' and understand the theory. However, they remain unable to bridge the gap between the two and truly understand what is going on.This little text gives the reader a self contained comparison that allows the reader to use their knowledge of standard analysis to strengthen their pursuit of the non-Archimedean. ... Read more

Product Description
This introduction to mathematical analysis contains graphs to help with the visualization of important ideas, and includes historial and philosophical discussions. Topics covered include Euclidean squares and functions of bounded variation. ... Read more

Customer Reviews (2)

Get Lost
I used this book for a first course in real analysis.I was unable to complete the problems at the end of the first section of the first chapter and it only got worse.I can't recall a single example that was helpful in completing end of section questions.The entire class was clueless for the entirety of the semester.This book succeeds in making simple ideas incredibly complex. Quite possibly the worst text I have ever used.This book should not be considered a viable choice for use in an introductory real analysis course.

A masterful treatment of Analysis
Analysis is considered by many students to be the most challenging area of Mathematics.

This book however, does a superb job of guiding the student through the study of Mathematical Analysis in a very accessible,yet rigorous way.This wonderful text covers everything from the basicproperties of the Real number system, to basic Topological concepts, toFunction Analysis, to Differentiation and Integration in R^n, to BasicFourier Analysis.All this and more, in an upfront, logical fashion whichanyone could follow.The excercises given in each section are superb andgeniunely serve to extend the student's understanding.

After readingthis book I was able to test out of all the undergraduate Analysis coursesat my University and jump straight into Graduate level courses, which I didvery well in.I could not be more appreciative of Dr. Douglass'help.

Douglass should be commended for this extremely insightful, helpfulwork.Whether you have never studied Analysis before, or are seeking tofurther your understanding of this most interesting and honored subject, Iheartily recommend this outstanding text.You will not be dissapointed. ... Read more

Product Description
This volume will serve several purposes: to provide an introduction for graduate students not previously acquainted with the material, to serve as a reference for mathematical physicists already working in the field, and to provide an introduction to various advanced topics which are difficult to understand in the literature. Not all the techniques and application are treated in the same depth. In general, we give a very thorough discussion of the mathematical techniquesand applications in quatum mechanics, but provide only an introduction to the problems arising in quantum field theory, classical mechanics, and partial differential equations. Finally, some of the material developed in this volume will not find applications until Volume III. For all these reasons, this volume contains a great variety of subject matter. To help the reader select which material is important for him, we have provided a "Reader's Guide" at the end of each chapter. ... Read more

Product Description
This guide presents an introduction to the many basic problems of scientific computing and the wide variety of methods used for their solutions. It is suitable for students on first year maths or computation degree courses. It provides the reader with the basic principles of numerical analysis and tries to avoid using complicated techniques in analysis and algebraic manipulation except where they are essential to a rigorous approach. By presenting BASIC programs to solve selected examples the book also provides a useful grounding for more practical work using computers. ... Read more

Product Description
Designed for use in a two-semester course on abstract analysis, REAL ANALYSIS: An Introduction to the Theory of Real Functions and Integration illuminates the principle topics that constitute real analysis.Self-contained, with coverage of topology, measure theory, and integration, it offers a thorough elaboration of major theorems, notions, and constructions needed not only by mathematics students but also by students of statistics and probability, operations research, physics, and engineering.Structured logically and flexibly through the author's many years of teaching experience, the material is presented in three main sections:Part 1, chapters 1through 3, covers the preliminaries of set theory and the fundamentals of metric spaces and topology. This section can also serves as a text for first courses in topology.Part II, chapter 4 through 7, details the basics of measure and integration and stands independently for use in a separate measure theory course.Part III addresses more advanced topics, including elaborated and abstract versions of measure and integration along with their applications to functional analysis, probability theory, and conventional analysis on the real line. Analysis lies at the core of all mathematical disciplines, and as such, students need and deserve a careful, rigorous presentation of the material. REAL ANALYSIS: An Introduction to the Theory of Real Functions and Integration offers the perfect vehicle for building the foundation students need for more advanced studies. ... Read more

Product Description

The purpose of the volume is to provide a support for a first course in Mathematical Analysis, along the lines of the recent Programme Specifications for mathematical teaching in European universities. The contents are organised to appeal especially to Engineering, Physics and Computer Science students, all areas in which mathematical tools play a crucial role. Basic notions and methods of differential and integral calculus for functions of one real variable are presented in a manner that elicits critical reading and prompts a hands-on approach to concrete applications. The layout has a specifically-designed modular nature, allowing the instructor to make flexible didactical choices when planning an introductory lecture course. The book may in fact be employed at three levels of depth. At the elementary level the student is supposed to grasp the very essential ideas and familiarise with the corresponding key techniques. Proofs to the main results befit the intermediate level, together with several remarks and complementary notes enhancing the treatise. The last, and farthest-reaching, level consists of links to online material, which enable the strongly motivated reader to explore further into the subject. Definitions and properties are furnished with substantial examples to stimulate the learning process. Over 350 solved exercises complete the text, at least half of which guide the reader to the solution.

Product Description
This book is a report of a cognitive journey towards the reliable simulation of scattering problems using finite element methods. The pre-asymptotic analysis of Galerkin FEM for the Helmholtz equation with moderate and large wave number forms the core of the book. The topics include a priori and a posteriori error estimation as well as the stabilized methods. The mathematical investigation of model problems is given in close connection with the physical problem of acoustic scattering and fluid-solid interaction. Starting from the basic physical assumptions, the author methodically develops both the strong and weak forms of the governing equations. The main chapter on finite element analysis is preceded by a systematic treatment of Galerkin methods for indefinite sesquilinear forms. The book also contains broad reference material on numerical methods for the Helmholtz equation in unbounded domains, including Dirichlet-to-Neumann methods, absorbing boundary conditio!ns, infinite elements and the perfectly matched layer. In the final chapter, three dimensional computational simulations are presented and compared with experimental data. Students and researchers in mathematics, physics and engineering, as well as scientists and computational engineers working on scattering problems will find this book of interest. The author has produced a self-contained and easily readable work containing numerous illustrations of the theory with numerical examples and computational results. ... Read more

Product Description

The objective of this textbook is to provide a very basic and accessible introduction to option pricing, invoking only a minimum of stochastic analysis. Although short, it covers the theory essential to the statistical modeling of stocks, pricing of derivatives (general contingent claims) with martingale theory, and computational finance including both finite-difference and Monte Carlo methods. The reader is led to an understanding of the assumptions inherent in the Black & Scholes theory, of the main idea behind deriving prices and hedges, and of the use of numerical methods to compute prices for exotic contracts.

The author's style is compact and to-the-point, requiring of the reader only basic mathematical skills. In contrast to many books addressed to an audience with greater mathematical experience, it can appeal to many practitioners, e.g. in industry, looking for an introduction to this theory without too much detail.

It dispenses with introductory chapters summarising the theory of stochastic analysis and processes, leading the reader instead through the stochastic calculus needed to perform the basic derivations and understand the basic tools

It focuses on ideas and methods rather than full rigour, while remaining mathematically correct.

The book aims at describing the basic assumptions (empirical finance) behind option theory, something that is very useful for those wanting actually to apply this. Further, it includes a big section on pricing using both the pde-approach and the martingale approach (stochastic finance).

Finally, the reader is presented the two main approaches for numerical computation of option prices (computational finance). In this chapter and also in the companion CD-ROM, Visual Basic code is supplied for all methods, in the form of an add-in for Excel. The book could be used at introductory level in Universities, with exercises (with solutions) after each chapter. Finally, I also discuss questions about incomplete markets, and have references to different practical/theoretical approaches to solve pricing problems in such markets. ... Read more

Customer Reviews (1)

Option Mathematics
This is a highly mathematical introduction to the Option Theory at university level and can be read and understood only with the necessary background in higher mathematics particularly in the field of stochastic analysis. Bearing this in mind, this is a great book for it covers the theoretical background for statistical methods applied to the financial science. ... Read more

Product Description
This classic text has entered and held the field as the standard book on the applications of analysis to the transcendental functions. The authors explain the methods of modern analysis in the first part of the book and then proceed to a detailed discussion of the transcendental function, unhampered by the necessity of continually proving new theorems for special applications. In this way the authors have succeeded in being rigorous without imposing on the reader the mass of detail that so often tends to make a rigorous demonstration tedious. Researchers and students will find this book as valuable as ever. ... Read more

Customer Reviews (18)

A Coures of modern Analysis
Haven't read the hole book and solved every example but it has a lot of fascinating treatments, methods of analysis and techniques.

unexpected
1- The book is not printed. They have taken pictures of the original book (1920s?) and printed the pictures.
The result is tiny fonts and a quite old pagination style.
2- Some people may like the no-frills and matter-of-fact text but I personally find an endless list of dry-to-the-bone mathematical facts a little bit stifling. And, yes, I know that this is a mathematical book, but it doesn't have to be this airless.
3- As far as I can tell there is an error in the first line at page 12. I haven't read much more and so I cannot vouch for the rest of the book.

All in all, I wouldn't recommend it and I wouldn't have bought it had I had a chance of looking at it first

Book in bad conditions.
The product I recieved is in terrible conditions, very used and dirty, the book must have been a new edition (in blue color) but this one is grey. I send you some photos in another message in order to show you the bad conditions of this book.

Whittaker & Watson
Classic text. Good encyclopedic source of mathematics - pure & applied.Definitely not a picture book and takes a bit of digging to find what one needs. Typical abbreviated index found in British texts of that era.

This book is worth it's weight in gold!!
If I could, I would give this book ten stars.When I first sat down to read it, I couldn't believe what I was seeing.This is the only book I have ever seen on complex analysis (or any scientific field for that matter) in which the authors cover so much material (everything from residues to integral equations to elliptic functions and MUCH more) and yet manage to make the whole text fit into a framework which is relatively easy to follow, even for someone completely new to complex analysis.Moreover, the majority of the many hundreds of excercizes in this book range from moderately to nail-bitingly hard, and encourage a true understanding of the material being covered.I would reccommend this book for ANYONE who has mastered basic calculus and analysis and wishes to begin learning complex analysis and the theory of special functions.The book's coverage of the following topics is especially noteworthy:The gamma function (the book uses the INFINITE PRODUCT as the basic definition), the hypergeometric function (and the confluent hypergeometric function), bessel functions (a field in which G.N. Watson was a leading expert), and the Weirstrassian and Jacobean elliptic functions and theta functions (I LOVED the intuitive development of the theory of the elliptic functions, which is made to parrallel that of the trigonometric functions, which are of course familiar to the reader).I would ESPECIALLY recommend this book for those pursuing SELF-STUDY (although it is NOT for the mathematically weak-of-heart, but no book on the topic is), as it is quite self-contained and readable for a book on complex analysisis.Once you buy it, you won't even think to complain about the high pricetag, because you will be way too absorbed in the math to think about anything else. ... Read more

Product Description
This is a widely accessible introductory treatment of infinite series of real numbers, bringing the reader from basic definitions and tests to advanced results.An up-to-date presentation is given, making infinite series accessible, interesting, and useful to a wide audience, including students, teachers, and researchers.

"Real Infinite Series"presents the theory of real infinite series, including elementary and advanced tests for convergence or divergence, the harmonic series, the alternating harmonic series, and closely related results.One chapter offers 107 concise, crisp, surprising results about infinite series.Recognizing the interest in problem solving that abounds with students of mathematics, the authors devote a chapter to problems on infinite series, and solutions, which have appeared on the annual William Lowell Putnam Mathematical Competition.

The lighter side of infinite series is treated in the concluding chapter where three puzzles, eighteen visuals (what Martin Gardner calls "look-see" diagrams), and several fallacious proofs are made available.

Three appendices provide a listing of true or false statements, answers to why the harmonic series is so named, and an extensive list of published works devoted entirely or partially to infinite series. ... Read more

Customer Reviews (2)

Real Infinite Series For Beginners.
This is an excellent book.The prose is very readable and there are numerous illustrative examples to clarify the main points. Chapter 1 defines infinite series, discusses intuition and infinity, and covers the basic convergence tests.Chapter 2 covers the work of Cauchy and discusses more involved tests of convergence such as Kummer's results, the tests of Raabe and Gauss, and the tests of Abel. Chapter 3 examines the harmonic series. Chapter 4 covers a number of interesting results involving infinite series. Chapter 5 presents 101 problems involving infinite series from the Putnam Mathematical Competition. Answers to all problems are provided. Chapter 6 presents a plethora of puzzles, proofs without words, fallacious proofs, and fallacies, flaws, and flimflam. Answers to the puzzles are given. Two appendices present 101 True or False questions on infinite series with answers and a brief article on harmonic series. References, both books and journals, are also given. A brief but thorough index concludes the book. This book would serve very well as a resource for high school and college calculus teachers. Undergraduate mathematics majors with an interest in infinite series would find it appealing.Finally, readers like myself who majored in mathematics but pursued other careers would enjoy using it to refresh their knowledge of infinite series.(they may need to review a little calculus). The authors have produced a gem of a book and anyone who hasa passion for mathematics will enjoy reading this volume. Chapters 1 and 6 are especially readable,informative, and enjoyable. Chapter 6 is just plain fun! Get your hands on a copy of this book as it will provide hours of fascinating reading and problem solving.

Like Father, Like Son
I am pleased to say that I was one of the first to have this wonderful book. In all honesty - I don't understand anything in this book. I tried to just read chapter 1 - the definitions, and I fell asleep. I tried to read chapter 2 and I got a headache.

However, I'm the father of one of the author's and I'm awfully proud of him!

Please buy many copies.

Mike Sr. ... Read more

Product Description
This book is intended to serve as a text in mathematical analysis for undergraduate and postgraduate students. It opens with a brief outline of the essential properties of rational numbers using Dedekind's cut, and the properties of real numbers are established. This foundation supports the subsequent chapters. The material of some of topics-real sequences and series, continuity, functions of several variables, elementary and implicit functions, Riemann and Riemann-Stieltjes integrals, Lebesgue integrals, line and surface Integrals, double and triple integrals are discussed in details. Uniform convergence, Power series, Fourier series, and Improper integrals have been presented in a simple and lucid manner. A large number of solved examples taken mostly from lecture notes make the book useful for the students.

A chapter on Metric Spaces discussing completeness, compactness and connectedness of the spaces and two appendices discussing Beta-Gamma functions and Cantor's theory of real numbers add glory to the contents of the book.

KEY FEATURES:

-New version of outstanding textbook catering to international segments
-Well developed, rigorous and not too pedantic subject matter
-Application of modern methods to smooth out and shorten classical techniques
-Special effort has been made to include most of the lecture notes based on author's decadal teaching experience

CONTENTS:

Real Numbers
Open Sets, Closed Sets and Countable Sets
Real Sequences
Infinite Series
Functions of a Single Variable (I)
Functions of a Single Variable (II)
Applications of Taylor's Theorem
Functions
The Riemann Integral
The Riemann-Stieltjes Integral
Improper Integrals
Uniform Convergence
Power Series
Fourier Series
Functions of Several Variables
Implicit Functions
Integration on R2
Integration on R3
Metric Spaces
The Lebesgue Integral

Also available:

Mathematical Physics for Engineers - ISBN 1906574022
Optimization Techniques - ISBN 1906574219 ... Read more

Customer Reviews (1)

Awesome Book to Start Analysis
If you have never studied Analysis before and a little scared about the subject , then this is the book for you.
It is well written and concepts are explained really well.I never liked analysis before reading this book ... Read more

Product Description
The classic analysis textbook from Burkill and Burkill is now available in the Cambridge Mathematical Library. This straightforward course, based on the idea of a limit, is for students of mathematics and physics who have acquired a working knowledge of calculus and are ready for a more systematic approach. The treatment given here also brings in other limiting processes, such as the summation of infinite series and the expansion of trigonometric functions as power series. Particular attention is given to clarity of exposition and the logical development of the subject matter. ... Read more

Customer Reviews (2)

A jewel of analysis
This book is a truly jewel of analysis, the best book I have found so far in analysis, not for nothing it is the one used for the real analysis course dictated at my University and is the one more asked by mathematics students from the Astronomy, Physics & Mathematics library here also (Pontificia Catholic University of Chile). It has 14 chapters, of which I have only studied the first 9 with exception of chapter 8. In general, I haven't done the exercises but just a few, my approach with books is like peeling an onion on a first reading just read and understand what's being said, on a second reading try the exercises (in this way you can go as quick as you can on covering the material) etc. Also about the exercises I MUST point out that the majority come with answers at the back of the book! I found this awesome and specially suited for self study (which is my case, by the way).
The writing is very clear, beautiful and complete. I specially like chapters 1 to 3 where the main concepts addressed are sets, metric spaces, functions and point set topology, chapter 7 where everything related to the concept of the linear derivative for functions of arbitrary domain and range (e.g. f:Rm x Rn-->Rp) are deal with paving the way for the all importants Implicit and Inverse theorem. Chapter 9 (the one I'm currently working on) is about Fourier Series and I must say that I have not found in anywhere else such a complete treatment about Fourier Series and I'm very pleased about this situation.
Finally I must tell you that I also have on mathematical analysis the books of T.Apostol, W.Rudin, Courant-John and this is by far the better so if you are thinking about this title my advice is buy it because you will be getting one of those book whose weight is worth on gold, that is, a terrific jewel of analysis.

A Second Course in Mathematical Analysis
This is the second volume ot the authors little book "A first course in mathematical analysis". This volume is a well written and rigorous exposition of the study of functions in several variables. Differentiation , integration and all. Very good reference book. ... Read more

Product Description
Provides systematic coverage of the mathematical theory of modelling epidemics in populations, with a clear and coherent discussion of the issues, concepts and phenomena. Mathematical modelling of epidemics is a vast and important area of study and this book helps the reader to translate, model, analyse and interpret, with numerous applications, examples and exercises to aid understanding. ... Read more

Customer Reviews (2)

Very Advanced
Great book but unless you are a computational biologist with very advanced mathematical skills-don't bother.This was over my head as a basic epidemiology student.I was searching for a book to elucidate R-zero...this was not it.

Great, but not as an intro to Infectious Disease Modeling
I purchased this book partially because one review proposed that this text would serve as a good, teach-yourself introduction to mathematical modeling of infectious disease (I.D.).I'm currently in a master's-level class on I.D. modeling which has no specific text requirement, and having only a so-so math background and little knowledge of model construction, I thought a self-teach book would be nice.

Simply said, this book is not for those who stumbled through calculus 1.In fact, unless you're quite well-to-do in the math department, you'll find much of this text either very challenging or impenetrable.The worked-out problems are a very nice touch--one that many authors would do well to note--but the high-level math is too much for this budding epidemiologist. ... Read more

Product Description
This book provides a concrete introduction to a number of topics in harmonic analysis, accessible at the early graduate level or, in some cases, at an upper undergraduate level. Necessary prerequisites to using the text are rudiments of the Lebesgue measure and integration on the real line. It begins with a thorough treatment of Fourier series on the circle and their applications to approximation theory, probability, and plane geometry (the isoperimetric theorem). Frequently, more than one proof is offered for a given theorem to illustrate the multiplicity of approaches. The second chapter treats the Fourier transform on Euclidean spaces, especially the author's results in the three-dimensional piecewise smooth case, which is distinct from the classical Gibbs-Wilbraham phenomenon of one-dimensional Fourier analysis. The Poisson summation formula treated in Chapter 3 provides an elegant connection between Fourier series on the circle and Fourier transforms on the real line, culminating in Landau's asymptotic formulas for lattice points on a large sphere. Much of modern harmonic analysis is concerned with the behavior of various linear operators on the Lebesgue spaces $L^p(\mathbb{R}^n)$. Chapter 4 gives a gentle introduction to these results, using the Riesz-Thorin theorem and the Marcinkiewicz interpolation formula. One of the long-time users of Fourier analysis is probability theory. In Chapter 5 the central limit theorem, iterated log theorem, and Berry-Esseen theorems are developed using the suitable Fourier-analytic tools. The final chapter furnishes a gentle introduction to wavelet theory, depending only on the $L_2$ theory of the Fourier transform (the Plancherel theorem). The basic notions of scale and location parameters demonstrate the flexibility of the wavelet approach to harmonic analysis. The text contains numerous examples and more than 200 exercises, each located in close proximity to the related theoretical material. Originally published by Brooks Cole/Cengage Learning as ISBN: 978-0-534-37660-4. ... Read more

Customer Reviews (3)

Excellent textbook and reference, which is readable!
I needed to learn Fourier Analysis and Wavelets, and this book is excellent as a textbook and as a reference.It is also quite readable.We need more mathematics books like this one.

Fourier Analysis and Wavelets for Everyone
As a probabilist and statistician, with a Ph.D., having worked at universities, as a consultant, and in industry for approximately forty years, I had previously employed Fourier Analysis only as a tool, not having studied the subject as a discipline unto itself. Dr. Pinsky's book has allowed me to learn the subject more deeply, and from a different, exciting viewpoint. In addition, I needed a resource that would permit me to learn about wavelets. How wonderful to find a book that includes both topics! Moreover, this book is a pleasure to read, with pencil and paper, to work through the ideas. It is extraordinarily well-written, which is not surprising, given the clarity and excellence of Dr. Mark A. Pinsky's other works. Pinsky's grammar is excellent, which is extremely refreshing. Many modern authors cause me to believe that I should have a red pen to correct grammatical errors while reading their works. This book is much more than just a textbook; it is beautiful mathematically and beautifully written.

For the Students!
Courses in harmonic analysis have a central place in the course offerings of every math department, be it pure or applied;-- and the subject is as important as ever! Yet it has not always been easy for an instructor to find a book that is right for the students. Some books might be too skimpy on proofs, or not deep enough.-- Or the applications may somehow be artificial, or contrived. Afterall, we teach the material to engineers!-- It is a relief to find, in Pinsky's lovely new book, a balanced approach to the subject. The motivation and the history receive a beautiful presentation, as do the technical points and proofs. And the historical comments- sprinkled throughout the book- bring the subject to life. At the same time, the book is forward looking, and it has been tested in courses. Great exercises! The structure of the exposition is friendly, and gently leads the reader toward the exciting new wavelet material in the last hundred or so pages of the book. The student thereby gets a sense of how the central questions in wavelet theory have their root in the more classical ideas of harmonic analysis. ... Read more

Product Description
This is an advanced text for the one- or two-semester course in analysis taught primarily to math, science, computer science, and electrical engineering majors at the junior, senior or graduate level. ... Read more

Customer Reviews (23)

Great Learning Experience
This is truly a well-crafted book. The organization is tight and the book is largely self-sufficient, really only calling upon material covered in his previous book, Principles of Mathematical Analysis. Rudin only proves such lemmas as he needs to get to the major results; peripheral facts and theorems are left to the exercises, which are far from routine and require a lot of thought and patience to get through. The book is rather terse, but there's a powerful elegance behind it. The proofs are rigorous and avoid hand-waving, albeit Rudin intentionally leaves gaps for the reader to fill. Working carefully through this book and doing as many exercises as possible, one can get a good grasp of the material.

However, this is not a book I would recommend for people who have not had prior experience with measure theory or complex analysis. Rudin provides little motivation. His arguments are elegant, but his methods are designed to give the quickest route to the results, which is seldom the most intuitive one. For example, where other authors explicitly construct Lebesgue measure, Rudin opts for a difficult proof of the Riesz Representation Theorem from which he pulls Lebesgue measure as a magician might pull a rabbit out of a hat. A lot of the material has a lot of geometric intuition behind it, but Rudin seldom goes out of his way to point it out. The beginner would be much better served getting an introduction to the material elsewhere before tackling Rudin. It will enable one to get much more out of the book than slogging through it blindly. It's one thing to know the definitions and be able to follow the proofs, and another thing to understand what it all means; Rudin doesn't hold the reader's hand where the latter is concerned.

For those with adequate preparation and sufficient daring, this book makes for a great learning experience and I daresay is even fun in places.

One of a Kind
I normally don't review books that already have this many reviews, especially when I agree so much with the reviews that already exist.But I'm teaching out of green Rudin for the first time this semester, 20 years after getting to know the book well as a student, and I find myself so enthusiastic about it again, that I just had to chime in with an "Amen" to the other positive reviews.When it comes to mathematical writing, it doesn't get any more exquisitely elegant than this.

Probably all our reviews are irrelevant, however, because there are probably very few discretionary purchases of this book:There will be nearly a one-to-one correspondence between buyers of the book and students in classes for which it is required.For them, I can only recommend skipping the outrageously expensive hardback (which even at its high price is pretty cheaply constructed nowadays) and opting for the more reasonable international paperback edition.

Rewarding, but has limitations
This is a very nice book, but in my opinion it is the worst of Rudin's three well-known books on analysis.The third, Functional Analysis, is a better representation of the subject, and (as opposed to this book) contains applications of analysis to other areas of mathematics, such as number theory and PDE.

The chapters here are very good for reference, but they are not well-written (at all) for self-study.So my two cents is: it's good, but frustrating at times. Rudin has a talent for making difficult things clear, but he has a more sinister talent for making simple things appear difficult.

I love this book!
I love this book, even though I have not absorbed more than a small portion of it yet.I find this to be a much better book than the "baby Rudin", which struck me as dry, overly concise, and without motivation.This book provides ample motivation, and although it proceeds in great generality, proceeds at a reasonable pace.

The best thing about this book, however, is the spirit of it--the integrated approach to analysis that Rudin takes is unique and greatly appreciated--Rudin is, like Lang, a testimony to the fact that the best mathematicians do not draw artificial lines between different areas within mathematics.Rudin presents the material in ways that connect to other areas of mathematics and will help the reader become a better mathematician, even if she never directly uses any of the material contained in this volume.

I would not recommend this book as a first exposure to measure theory or complex analysis--it is advanced and requires a great deal of background to fully understand and appreciate.But I think this is a book that any serious mathematician should add to their collection and eventually work through.People wanting to learn measure theory might look to the book by Inder K. Rana, or to the classic book by Royden.For more elementary treatments of complex analysis I would recommend the classic by Ahlfors, Theodore Gamelin's book, or the book by Greene and Krantz.

My 2 cents
There are some excellent reviews here for this outstanding book, so I will try to avoid repetition. In preparation for my qualifying exams in graduate school, two of my colleagues and I did all of the exercises in Rudin (give or take a couple, no more). What I found striking at the time was how Rudin took three subjects -- measure theory, functional analysis, and complex analysis -- and weaved them together seamlessly. It is not that I believed them to be separate subjects, but until then I hadn't realized just how they all fit together. Really, this book is superb.

A word of warning, though. Rudin's prose is concise, and his proofs leave you wondering if you'd ever be able to reproduce them on your own. It is what we in the business are used to call 'elegant'. It pays to work in groups, persevere, and go over everything twice or more. Good luck. ... Read more

Product Description
This book is written by award-winning author, Frank Morgan. It offers a simple and sophisticated point of view, reflecting Morgan's insightful teaching, lecturing, and writing style. Intended for undergraduates studying real analysis, this book builds the theory behind calculus directly from the basic concepts of real numbers, limits, and open and closed sets in $\mathbb{R}^n$. It gives the three characterizations of continuity: via epsilon-delta, sequences, and open sets. It gives the three characterizations of compactness: as "closed and bounded," via sequences, and via open covers. Topics include Fourier series, the Gamma function, metric spaces, and Ascoli's Theorem. This concise text not only provides efficient proofs, but also shows students how to derive them. The excellent exercises are accompanied by select solutions. Ideally suited as an undergraduate textbook, this complete book on real analysis will fit comfortably into one semester. Frank Morgan received the first Haimo Award for distinguished college teaching from the Mathematical Association of America. He has also garnered top teaching awards from Rice University (Houston, TX) and MIT (Cambridge, MA). ... Read more

Customer Reviews (4)

For beginners and a quick review for not so beginners
This is no conventional Analysis book. It is written to drive the reader's focus to a single topic each time. The chapters are 1-2 pages long and it is useful for what is is thought for. Continuity? You read 1 page, straight to the point. Facts about number sets and infinity? 1 page. Obviously it leaves out many consequences, but the uniqueness of this book is that you will always find the basic facts you need right in the first page you happen to open. It is written so concisely that you will understand everything in the first read. In fact, I like to refer to it as "my first real analysis book". OK, it is true that maybe it is too much to ask $40 for it, but is definitely nice to have it around.

perfect for what it's written for
This book is simply beautiful. It is written as a textbook for just one semester of undergraduate study, and it does the job. It is concise, jet it contains all the main theorems with the proofs rigorous enough. It begins with elementary concepts of numbers and logic, and even topology (so it treats continuity via open sets as well!), compactness is treated in three different ways, Fourier series is explained, and it even touches metric spaces... The book doesn't go very deep, but it talks well about basic issues in analysis and it's rigorous enough for an undergraduate text. The book can even serve well as a manual for those who need to refresh their knowledge about main theorems of analysis while considering other fields of mathematics invoking some analysis issues, because it's concise, rigorous enough and well organized. Very useful.

Perfect start beyond linear algebra.
This book is designed to be a one semester book in undergrad analysis.

It covers almost all the material in either Rudin's or Krantz's, which are usually covered in two semesters. however, Prof. Morgan does sacrafice some of the depth that other texts go into(example: theorem a sequence is convegent <=> cauchyis only proved the forward way).

Why I like it:
-This approach is perfect. You get a solid underpinning in the basics and get a taste of many diffrent subjects, (fourier, stirling's formula, Volumes of N-balls etc...). It is perfect for a first class in upper math (beyond linear algebra).

-the problems sets are actual problem sets that should be done on a per lecture basis. other books are filled with extensive problems that usually overwhelm a student with only a linear algebra background.

-all the proofs relating to compactness are written with the three equivilent def. of compactness (closed & bounded in R^N, open covers, sequential compactness). This allows a student to fully appreciate the modern defenition of open covers for compactness.
the same goes for proofs involving continuity (sequential, epsilon-selta, inverse images of opens sets are open).
Both of these techniques makes the transition to general metric spaces, where the open covers and inverse images are primaraly used, smooth.

Real Analysis for preschoolers
This is a truly awful textbook. It is written in a patronizing and demeaning tone, suggesting the author does not consider his audience actually capable of learning real analysis. The chapters are brief, often only a single page, and seem to barely scratch the surface of the topic. Many proofs are left out altogether, with occasional suggestions that the reader "find the proof on the internet." Important concepts are also excluded or mentioned only in problems, such as the definition of a Cauchy sequence. The section on Fourier Series includes misprints in two essential definitions. The book is almost entirely void of examples, and often seems to do little more than merely list theorems. Although the price is much less than many other introductory texts, it would be worth your money to look elsewhere. ... Read more

Product Description
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. ... Read more

Customer Reviews (29)

Real Analysis
This book came in great condition. It looks brand new, no marks, and half the price as anywhere else I could find.

If i wanted a book with bent corners, i could have bought used
I had many options at the time that i purchased this book. I could have ordered a used book in excellent condition for far less than a new one..one in good condition with only bent corners for even less.. But on the other hand,if i bought a new one i could sell it when my class was over and recover most of my money. I chose to go new. When i recieved the book the corners were all bent because there was nothing in the box to protect it. I guess just beware..if your buying a very expensive text book and plan to resale it when your done..look for the best deal on used because the high price of new will not get you a much better book!!

A relatively difficult but extremely rewarding book
I used this book all through my freshman and sophomore years. I struggled with it and really tried hard to solve the problems. I mulled over every word and every proof of the first few chapters for days. However at the end of this rather trying exercise, I had a real sense of satisfaction and thought I had a firm grasp of the basics of real analysis. This is not one of those volumes that will instantly get you hooked but it's a volume that rewards patience like few other math books do. If you master the first few chapters of the book including those on series and sequences, you should have as good as grasp of elementary real analysis as anyone else. The book is for the serious student of mathematics and it provides a rigorous and comprehensive introduction to real analysis. To master it you will have to read and understand the proofs as carefully as possible; don't be discouraged and become impatient if you cannot do this easily, since the time spent on doing it is worth it. However, having a good instructor to help out will be enormously useful.

Way better than Pugh
What a breath of fresh air after dealing with Pugh's book!The language is clear.The proofs are concise and easy to follow.The illustrations are good without being overwhelming.I cannot say enough good things about this book.Poor math teachers are obsessed with the most general case and introduce it first.A good teacher starts with a specific case, relates it to what the student already knows, and then begins to generalize it slowly, layer by layer until the most general case is achieved.This is how the mind works, this is how mathematics really developed over time, and this is how math should always be taught!Bartle and Sherbert do a outstanding job of this!

One word of caution.Don't let real analysis be your first proofing class.Take a proofing class first and if your university doesn't have one, demand one!.Real analysis is not the place to learn propositional logic, quantifiers, truth tables and the like!.Learn that stuff first and do your first proofs in elementary number theory or geometry, then when you have a repertoire of proofing tools and some skill in proofing, then take real analysis.You cannot learn proofing and real analysis at the same time.First learn to proof, then take real analysis! If not you will be miserable and you will take it out on your teacher and text!

Really hard, but Really good
Like some others, I really disliked Real Analysis at first b/c the proofs were so much more complex than anything else I had seen. I struggled, ordered other analysis books to help me, only to find that this one really is good! You do need a great instructor to go with this book or you may be lost. That said, the appendices are fantastic and the authors give "hints" (and some answers) to selected problems. The proofs themselves are terse, so without an instructor who understands the gaps, you may not connect the steps solo. Good text which is now part of my math library. ... Read more

Product Description

The volume contains the proceedings of the OTAMP 2006 (Operator Theory, Analysis and Mathematical Physics) conference held at Lund University in June 2006. The conference was devoted to the methods of analysis and operator theory in modern mathematical physics. The following special sessions were organized during the conference: Spectral analysis of Schrödinger operators; Jacobi and CMV matrices and orthogonal polynomials; Quasi-periodic and random Schrödinger operators; Quantum graphs.