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21. An Introduction to Mathematical
22. Real Analysis with Economic Applications
23. Mathematical and Statistical Methods
24. Mathematical Analysis II (Universitext)
25. Problems in Mathematical Analysis
26. Fundamentals of Mathematical Analysis
27. Intermediate Mathematical Analysis
28. Numerical Computing and Mathematical
29. Mathematical Analysis of Physical
30. An Introduction to Harmonic Analysis
31. Mathematical Analysis For Economists
32. Problems and Theorems in Analysis
33. A First Course in Mathematical
34. Advanced Mathematical Methods
35. Techniques of Mathematical Analysis
36. IV: Analysis of Operators, Volume
37. A problem book in mathematical
38. Mathematical Principles of Signal
39. A View from the Top (Student Mathematical
40. Counterexamples in Analysis (Dover

21. An Introduction to Mathematical Analysis for Economic Theory and Econometrics
by Dean Corbae, Maxwell B. Stinchcombe, Juraj Zeman
Hardcover: 688 Pages (2009-02-17)
list price: US$78.50 -- used & new: US$58.38
(price subject to change: see help)
Asin: 0691118671
Average Customer Review: 5.0 out of 5 stars
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Providing an introduction to mathematical analysis as it applies to economic theory and econometrics, this book bridges the gap that has separated the teaching of basic mathematics for economics and the increasingly advanced mathematics demanded in economics research today. Dean Corbae, Maxwell B. Stinchcombe, and Juraj Zeman equip students with the knowledge of real and functional analysis and measure theory they need to read and do research in economic and econometric theory.

Unlike other mathematics textbooks for economics, An Introduction to Mathematical Analysis for Economic Theory and Econometrics takes a unified approach to understanding basic and advanced spaces through the application of the Metric Completion Theorem. This is the concept by which, for example, the real numbers complete the rational numbers and measure spaces complete fields of measurable sets. Another of the book's unique features is its concentration on the mathematical foundations of econometrics. To illustrate difficult concepts, the authors use simple examples drawn from economic theory and econometrics.

Accessible and rigorous, the book is self-contained, providing proofs of theorems and assuming only an undergraduate background in calculus and linear algebra.

Begins with mathematical analysis and economic examples accessible to advanced undergraduates in order to build intuition for more complex analysis used by graduate students and researchers Takes a unified approach to understanding basic and advanced spaces of numbers through application of the Metric Completion Theorem Focuses on examples from econometrics to explain topics in measure theory ... Read more

Customer Reviews (4)

5-0 out of 5 stars Probably the best math-econ book for anyone who wishes to pursue a Ph.D. in economics
As a junior economics professor, I have been through a number of math-econ books (which means quite a lot of torture in the learning history). CSZ (Corbae, Stinchcombe, and Zeman) ranks the top place on my recommendation list of math-econ books for anyone who wishes to pursue a Ph.D. in economics.

I can not agree with the authors more that "this books bridges the gap that has separated the teaching of basic mathematics for economics and the increasingly advanced mathematics demanded in economics research today." They have done a fantastic job in building up this bridge. During the learning of math econ, a common problem (insofar as I know) is that after you finish the class with a good grade, you still do not know how to apply those math tools in the research practice. A first group of math-econ books are just all abstract math (sometimes, there are pure math books), including tough and intimidating real analysis, functional analysis, etc.... Yes, you can really learn a lot of math (after many many sleepless nights like I did before), but...but, those math are not coupled with econ questions. Such a course might help you understand the technical papers, but might not teach you well how to construct econ models by yourself. A second group of math-econ books do not set a high-level of technical requirements. They might teach a lot of comparative statics and linear algebra, followed by very limited of real analysis. If you merely take a math-econ book in the second group, I guess you will not make sense of SLP (Stokey, Lucas and Prescott).

Now CSZ fills the gap between the two groups among math-econ books. Starting from the very beginning, real analysis with its econ application is introduced in a step-by-step, self-contained, and sometimes entertaining approach. If you have a solid undergraduate background in calculus and linear algebra (do not tell me you got a C in those courses!), you should be able to completely understand the beginning chapters which provides proofs of theorems, (remarkably!) examples, and inspiring exercises. Once you work out those exercises in the beginning chapters, more profound math stuffs in the later chapters should be

In an accessible approach, it introduces rigorous math that is demanded by advanced econ research. Interestingly this textbook does not even have a chapter called "comparative statics", "constrained optimization", etc., but it beautifully embeds those stuffs into the discussions of logic, set theory, etc. In a similar approach does CSZ provide a math foundation for econometrics after Chapter 6. CSZ's introduction to metric spaces in the second and third sections of the textbooks makes me very conformable (i.e. better equipped) when I go back to those graduate econometrics textbooks (especially, if you want to study Paul Ruud's Introduction to Classical Econometrical Theory). So, it is perhaps a must-read material before you touch those popular graduate econometrics textbooks, such as Greene, Hayashi, and Ruud.

It is probably the best companion (besides Nolan Miller's Micro Notes) to MWG's Microeconomic Theory. I recognize that CSZ adopted MWG as an important reference for this textbook.You do not really have to study CSZ before you start learning MWG, but if you are ambitious to work out all the C-level questions in MWG, you are better to grab a copy of CSZ on your desk as well.
I would say, CSZ (as an intro to math econ) is very much like Wooldrige's Intro econometrics, in a sense that both books teach you the theories AND how to apply the theories in your OWN research. They are both textbooks and research guides.

Finally, I wish the next edition of CSZ could provide some discussions/examples on uncertainty and public econ. But of course, no single volume can cover every corner in the economic theory and econometrics.

5-0 out of 5 stars An excellent math econ book
I am not currently teaching Math Econ, but when I do again I intend to use this book.One problem with the typical first-year econ grad student is that they have little experience with theorem-proof mathematics; they are more familiar with applied mathematics, meaning that they set about to solve a given problem, than they are with the logical process of proving that problem has a solution.CSZ do a nice job of easing the student into this process, starting with the basics of mathematical logic.And they manage to cover the basics as well as some advanced topics.

My only quibble is that the book gives too little attention to dynamic programming and recursive competitive equilibria.These methods are now a standard part of any macroeconomist's toolkit, but students rarely get a mathematically careful presentation that is also appropriate as a textbook (SLP is more like a reference book, albeit one where the reader must provide their own proofs).CSZ of course cannot do everything in one book, even one that is 670 pages long, but I personally would have liked to see more on these topics.

As a whole, the book fills a clear need in the profession and recommend it to all incoming PhD econ students -- you should read the first couple of chapters before arriving at school in the fall.It will give you a leg up over your classmates (or catch you up) and make the transition to grad school a bit easier.

5-0 out of 5 stars An impressive collection of tools from Mathematical Analysis applied to different fields of economics
Every undergraduate who wishes to pursue a PhD in economics is told to take a sequence of certain math classes, the hardest of which is usually real analysis. I took a real analysis course based on Rudin's blue book and found it a painful transition from my previous courses. I had to quickly get used to reading and writing proofs. It was unclear if and how these tools can be used in economics. This book is a great solution because it helps the reader to gently transition to writing proofs and is chock-full of applications at every step.

This book has three parts: The first 3 chapters introduce the reader to abstract math and proof writing techniques. The second part, chapters 4-8, teach standard material that is often covered in a 2-semester sequence on real analysis. This includes metric spaces, measure theory and probability, and Lp spaces. This also includes a chapter on convex analysis which is rarely covered in books on real analysis designed for math students. The last 3 chapters cover advanced material which is useful for readers interested in economic and econometric theory.

The thing that I liked most about this book is its impressive collection of applications to economics, here are some:

The first chapter on Logic discusses general equilibrium and proves the first fundamental theorem of welfare economics. In the second chapter on set theory they discuss lattices and apply these tools to introduce Monotone Comparative Statics (MCS) (which was a hot topic in the 90's and hasn't even been introduced into most microeconomics textbooks yet, not even in MasColell). They explain how MCS is a generalization of regular Comparative Statics based on the implicit function theorem, which requires strong assumptions about differentiability. The discussion of real numbers in chapter 3 is very thorough, so an econ student doesn't need to follow every detail but in case he gets curious about some property of the real numbers he can always refer back to it.

In chapter 4 they talk about the finite dimensional vector space of real numbers. This is a more gentle approach than I experienced when I learned analysis, because we jumped straight into general metric spaces. They apply these tools to Linear Dynamical Systems, Markov Chains, and most notably to Dynamic Programming. Chapter 5 covers finite-dimensional convex analysis, which includes all kinds of convex separation theorems and applies these tools to prove the second fundamental theorem of welfare economics. They also cover everything you ever wanted to know about constrained optimization, the implicit function theorem and Kuhn Tucker conditions in horrendous detail.The authors proceed to discuss general metric spaces and include more applications to dynamic programming generalizing many of the topics discussed in previous chapters.

Chapter 7, which is a bit more technical than the previous chapters, discusses measure theory and measure-theoretic probability. This includes applications to all kinds of useful limit theorems and 0-1 laws, and a cool application to quantile estimation on page 405 and state dependent preferences on page 445. Chapter 8 introduces Lp spaces with applications to Statistics and Econometrics including a theoretical discussion of parametric and non-parametric regression. This chapter also includes an application to Artificial Neural Networks.

I haven't spent much time on the final 3 chapters, though I look forward to studying Chapter 11 on expanded spaces (Nonstandard Analysis) whichBerkeley's Robert M. Anderson claims can be very useful in the future. In his manuscript on Nonstandard Analysis, Anderson writes "a very large number of papers could be significantly simplified using nonstandard arguments."

The applications make this the only book of its kind that I have seen. Efe Ok's text on Real Analysis assumes a stronger background than this text, and doesn't include such an eclectic collection of applications. Ok's text is more suitable for someone who wants to work in pure theory.

I would have liked to have seen additional material on general topological spaces covered earlier in the text so for example their discussion of open sets in Euclidean space can be seen as a special type of topological space.

I would strongly recommend this book to anyone who wants to see how mathematical analysis can be applied to economics.

5-0 out of 5 stars easy to read; good exercise questions
I'm currently a economics graduate student. I was in Max's class when he used the manuscript of this textbook as the course material. This book definitely covers what an economics student will need during the infancy of research. I especially like the questions in the book. They help a lot in understanding. I highly recommend this book to any economics graduate student. ... Read more

22. Real Analysis with Economic Applications
by Efe A. Ok
Hardcover: 664 Pages (2007-01-02)
list price: US$99.00 -- used & new: US$72.91
(price subject to change: see help)
Asin: 0691117683
Average Customer Review: 5.0 out of 5 stars
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There are many mathematics textbooks on real analysis, but they focus on topics not readily helpful for studying economic theory or they are inaccessible to most graduate students of economics. Real Analysis with Economic Applications aims to fill this gap by providing an ideal textbook and reference on real analysis tailored specifically to the concerns of such students.

The emphasis throughout is on topics directly relevant to economic theory. In addition to addressing the usual topics of real analysis, this book discusses the elements of order theory, convex analysis, optimization, correspondences, linear and nonlinear functional analysis, fixed-point theory, dynamic programming, and calculus of variations. Efe Ok complements the mathematical development with applications that provide concise introductions to various topics from economic theory, including individual decision theory and games, welfare economics, information theory, general equilibrium and finance, and intertemporal economics. Moreover, apart from direct applications to economic theory, his book includes numerous fixed point theorems and applications to functional equations and optimization theory.

The book is rigorous, but accessible to those who are relatively new to the ways of real analysis. The formal exposition is accompanied by discussions that describe the basic ideas in relatively heuristic terms, and by more than 1,000 exercises of varying difficulty.

This book will be an indispensable resource in courses on mathematics for economists and as a reference for graduate students working on economic theory.

... Read more

Customer Reviews (5)

5-0 out of 5 stars Gift for an economist -- he loves it and is reading and re-reading it
Bought this as a gift -- the economist/recipient loves it and is reading and re-reading it.

5-0 out of 5 stars One of a kind
This book has a wealth of material on analysis. A quick perusal of the contents list should be enough to convince anyone, even working mathematicians, that this is a book worth having (see author's website for the content list.) Don't let "with economic applications" fool you, this is a highly rigorous, compendious, well-exposited tome on real analysis.

The economic focus means that some of the topics that are covered exhaustively in this book are rarely seen in books of this level (e.g., emphasis on fixed point theorems and correspondences). There is also a very good chapter on differential calculus on normed spaces -- a topic that is (inexplicably) left out of many other functional analysis books. Another excellent book which covers differential calculus is Zeidler's book on applied functional analysis, Zeidler's exposition is actually better than Ok's for those who are interested in this topic specifically.

Any economist who is already fairly comfortable with analysis will enjoy this book. Mathematicians will also find things they've probably not seen before in standard analysis courses or texts. As an added bonus, the economic applications provide some direct motivation for the material. Normally, it is rare to find a textbook on analysis which includes accessible and non-mathematical applications, but this book is filled with them. You rarely have to learn any economics to be able to appreciate the applications in this book.

However, that said, this book is not suitable as an introduction to analysis. Although it is self-contained, a level of mathematical maturity is necessary. Ideally, you should have a couple of undergraduate analysis courses behind you before you attempt this book. That is, you should be fairly comfortable with limits, continuity, convergence, metric spaces, etc.

The only serious complaint I have about the book is that occasionally, rigor gets in the way of clarity. Sometimes, proofs can get cumbersome. Certain parts of the book seemed to be unnecessarily complicated by excessive formalism.

5-0 out of 5 stars Excellent Book
This is an excellent real analysis book with a lot of material that fits perfectly any one's interests in economic theory. Other real analysis books out there do not cover things that are very important in economics, e.g, fix point theorems, correspondences, and convexity. This books covers all that and much more in a rigorous way so it also fits perfectly the needs of any math grad student, particularly if he/she has some interest in economics. I strongly recommend this book to any econ grad student who wants to learn the tools needed in economic theory.

5-0 out of 5 stars A fantastic book which fills a gaping hole.
A fantastic book which fills a gaping hole. I have yet to find a comparable book. Incredibly well-written with an embarrassingly large wealth of material. The ideal book for graduate students in mathematics, economics or mathematical economics. Any mathematician with a strong interest in Analysis and curiosity about economics (or any economist with a strong interest in mathematics) would do well to read and re-read this book!

5-0 out of 5 stars Great book for mathematical economics
This is a very interesting book that explains real analysis focusing on economics issues and, I must say, it does its job beautifully and with no lack of rigour. When it comes to the mathematical aspects of microeconomics, the book turns out to be even better. A great book that will help very much Mas-Colell's Microeconomic Theory readers. ... Read more

23. Mathematical and Statistical Methods for Genetic Analysis
by Kenneth Lange
Hardcover: 384 Pages (2002-03-28)
list price: US$124.00 -- used & new: US$75.99
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Asin: 0387953892
Average Customer Review: 4.0 out of 5 stars
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During the past decade, geneticists have cloned scores of Mendelian disease genes and constructed a rough draft of the entire human genome. The unprecedented insights into human disease and evolution offered by mapping, cloning, and sequencing will transform medicine and agriculture. This revolution depends vitally on the contributions of applied mathematicians, statisticians, and computer scientists.

Mathematical and Statistical Methods for Genetic Analysis is written to equip students in the mathematical sciences to understand and model the epidemiological and experimental data encountered in genetics research. Mathematical, statistical, and computational principles relevant to this task are developed hand in hand with applications to population genetics, gene mapping, risk prediction, testing of epidemiological hypotheses, molecular evolution, and DNA sequence analysis. Many specialized topics are covered that are currently accessible only in journal articles.

This second edition expands the original edition by over 100 pages and includes new material on DNA sequence analysis, diffusion processes, binding domain identification, Bayesian estimation of haplotype frequencies, case-control association studies, the gamete competition model, QTL mapping and factor analysis, the Lander-Green-Kruglyak algorithm of pedigree analysis, and codon and rate variation models in molecular phylogeny. Sprinkled throughout the chapters are many new problems.

Kenneth Lange is Professor of Biomathematics and Human Genetics at the UCLA School of Medicine. At various times during his career, he has held appointments at the University of New Hampshire, MIT, Harvard, and the University of Michigan. While at the University of Michigan, he was the Pharmacia & Upjohn Foundation Professor of Biostatistics. His research interests include human genetics, population modeling, biomedical imaging, computational statistics, and applied stochastic processes. Springer-Verlag published his book Numerical Analysis for Statisticians in 1999. ... Read more

Customer Reviews (5)

5-0 out of 5 stars great book where few texts of a statistical nature exist
This second edition updates the first with the many advances in the rapidly growing field of genetics. It provides a nice treatment of the mathematical and stochastic models that are useful in genetic studies.
It is a little disappointing that it does not go into the microarray technology that has become so important for experimentation in the last few years. Other recent books that cover statistical aspects of genetic research are Weir (1996) "Genetic Data Analysis II" Sinauer Associates (publisher) and Yang (2000) "Introduction to Statistical Methods in Modern Genetics" Gordon and Breach Science Publishers.

5-0 out of 5 stars Read this book and you might learn something
This book is not for the novice dabbling in statistical genetics.This is a highly sophisticated, thought provoking book targeted to individuals with considerable mathematical ability and training. As such, this book is an invaluable tool for individuals hoping to make a real impact in the field of statistical genetics.I particularly enjoyed the chapter on Markov Chain Monte Carlo methods for pedigree data.

4-0 out of 5 stars OK, but not for me
I'm interested in molecular genetics, this seems to be more about population genetics. There is some material, towards the back, about phylogeny. I can bash that a bit to make it match my needs, but it's still a bit of a stretch.

It seems to be a pretty good presentation of population genetics, the kind of genetics taught in high schools in the 70s. I can't comment on this book's merits, but I can warn the biochem types to spend their money elsewhere.

4-0 out of 5 stars Mathematical Details of Genetics
This book has an excellent coverage on the mathematical subtlies of genetics. The complicated theories are complimented by numerous examples. The exercise at the end of each chapter has a collection of probing questions that tests the understanding of the topics covered in the respective chapter. However, there is no discussion on association studies and quantitative traits which are two of the most active areas of genetic epidemiology.Moreover, the coverage on linkage is not adequate.

3-0 out of 5 stars Mathematical details about genetics
The book has an excellent coverage of the mathematical subtlities of genetics. Theories are illustrated through numerous examples and the exercises at the end of each chapter containprobing questions which would test the understanding of the topics covered in the respective chapters. However, there are no chapters devoted to quantitative traits and association analysis, which are currently active areas of research. The coverage of linkage is also not adequate. ... Read more

24. Mathematical Analysis II (Universitext) (v. 2)
by V. A. Zorich
Paperback: 688 Pages (2008-11-21)
list price: US$59.95 -- used & new: US$41.86
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Asin: 3540874534
Average Customer Review: 5.0 out of 5 stars
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This softcover edition of a very popular two-volume work presents a thorough first course in analysis, leading from real numbers to such advanced topics as differential forms on manifolds, asymptotic methods, integral transforms, and distributions. Especially notable in this course is the clearly expressed orientation toward the natural sciences and its informal exploration of the essence and the roots of the basic concepts and theorems of calculus. Clarity of exposition is matched by a wealth of instructive exercises, problems and fresh applications to areas seldom touched on in real analysis books.

The second volume expounds classical analysis as it is today, as a part of unified mathematics, and its interactions with modern mathematical courses such as algebra, differential geometry, differential equations, complex and functional analysis. The book provides a firm foundation for advanced work in any of these directions.

... Read more

Customer Reviews (4)

5-0 out of 5 stars amazing and outsanding
This is a two-volume treatise on Mathematical Analysis at undergraduate level. These two volumes are the most complete that I have seen so far. There is plenty of material here; one could easily spend two academic years (4 semesters of 6 quarters) to cover both volumes completely. Everything needed in undergraduate analysis is here: convergence (pointwise and uniform), differentiation, integration, integrals depending on parameters, interchanging limits, metric spaces, partial derivatives, multiple integrals, Stokes' Theorem, and much, much more. The author is a very good writer, and his proofs are slick, but readable. Exercises range from routine to quite challanging. Anyone studying real analysis (or mathematical analysis) should have these two volumes handy. Highly recommended.

5-0 out of 5 stars Outstanding
These two books written by V.A. Zorich represent a great course in analysis, both for people who just started dealing with the subject and for more experienced students. The treatment is thorough andspreads from an entire chapter about real numbers to very advanced problems. It also points out many applications in natural sciences.
A good and rather necessary addition would be the solutions to the problems given in these books. Thus students would have a way to check their work. Nevertheless it's worth more than five stars.

5-0 out of 5 stars Glowing review, but a correction....
Since I am listed by Amazon (but not by Springer) as one of the authors, you should quite properly be skeptical of my 5-star review.But I really mean it: I think the book is outstanding.

Now the correction.I am IN NO SENSE a co-author of this book, merely its translator.The translation was very enjoyable work, and I enjoyed the interaction with the author that it made possible.That, however, does not make me a co-author.(But if you'd like to see some books that I HAVE authored, please search.)

Roger Cooke

5-0 out of 5 stars Analysis made palatable, even for physicists.
The book besides covering a broad material on classical analysis(with a modern touch), exposes the basic core of analysis expected from a mathematics or physics student without making use of pedantic and unnecessary formalism. The author emphasizes the connection of important ideas via concrete and substancial examples more than insisting in pathological and or trivial examples. It has plenty of examples coming from physics and other sciences(following thetradition of the russian school : of teaching mathematics emphasizing links with other areas). We can't forget to mention the many geometrical insights provided. Moreover the book is "filled" w/ good exercises that really colaborates for a solid mathematical education and has also a detailed appendix where an instructor can find some very interesting and challenging problems for a seminar discussion or final exams. Undoubtly an worthwhile reading! ... Read more

25. Problems in Mathematical Analysis (Pure and Applied Mathematics)
by Piotr Biler, Alfred Witkowski
Hardcover: 244 Pages (1990-02-09)
list price: US$90.95 -- used & new: US$32.55
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Asin: 0824783123
Average Customer Review: 5.0 out of 5 stars
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Chapter 1 poses 134 problems concerning real and complex numbers, chapter 2 poses 123 problems concerning sequences, and so it goes, until in chapter 9 one encounters 201 problems concerning functional analysis. The remainder of the book is given over to the presentation of hints, answers or referen ... Read more

Customer Reviews (1)

If you are a math major, you should definitely own this book. If you are interested in analysis, you should by all means have a copy on your bookshelf! It contains all types of typical problems in mathematical analysis (real and complex) ranging from non-routine problem to very difficulty ones. A great source for the quals and the Putnam's real analysis part.

IF YOU ARE a NON-Math major, then it can be helpful if you are studying on your own to learn analysis or taking such a course. Probably most of the hardes problems in your homework assignment can be found here! ... Read more

26. Fundamentals of Mathematical Analysis
by Rod Haggarty
 Paperback: 340 Pages (1993-01-18)
-- used & new: US$104.21
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Asin: 0201631970
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Providing students with a clear and understandable introduction to the fundamentals of analysis, this book continues to present the fundamental concepts of analysis in as painless a manner as possible. To achieve this aim, the second edition has made many improvements in exposition. ... Read more

27. Intermediate Mathematical Analysis
by Anthony E. Labarre Jr.
Paperback: 272 Pages (2008-02-29)
list price: US$15.95 -- used & new: US$8.95
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Asin: 0486462978
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Geared toward those who have studied elementary calculus, this book stresses concepts rather than techniques. It prepares students for a first demanding course in analysis, dealing primarily with real-valued functions of a real variable. Complex numbers appear only in supplements and the last two chapters. 1968 edition.
... Read more

28. Numerical Computing and Mathematical Analysis (Computer science series)
by Stephen M. Pizer
Hardcover: 529 Pages (1975-06)
list price: US$30.35
Isbn: 0574191550
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29. Mathematical Analysis of Physical Problems
by Philip R. Wallace
Paperback: 616 Pages (1984-10-01)
list price: US$17.95 -- used & new: US$155.25
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Asin: 0486646769
Average Customer Review: 4.5 out of 5 stars
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Clear, even-paced presentation links classical and modern physics through common techniques and concepts. Contents: The Vibrating String, Linear Vector Spaces, The Potential Equation, Problems of Diffusion and Attenuation, Probability and Stochastic Processes, more. Ideal primary, supplementary text. 1972 edition. 34 figures. Problems.
... Read more

Customer Reviews (5)

5-0 out of 5 stars Great Book!
OK, the cover is tacky and the print looks like it has been done on a 1960s Remington, but I am yet to see a book which explains mathematical methods so well, and also shows you how you can use them to solve physics problems.I have loved every Dover book I've read, and this one too is a masterpiece just like the others. Beautiful stuff!

5-0 out of 5 stars Unique book - just what I was looking for
I have a graduate physics degree (as well as an undergrad math,physics dual major deal..) What I was looking for (and having a hard time finding) - was a book that explained HOW certain equations came about. For e.g. - we all know the equation of a vibrating string or of an electron in a potential well - but if you were the FIRST person to try and discover the equation - how would you go about formulating it? In other words - what would be your 'mathematical analysis' of the 'physical problem' of the vibrating string etc?
While this book does not go the whole 9 yards in this regard - it is one of the few books (in my limited experience) that actually DOES attempt to 'derive' these equations from scratch! For that reason - I give it 5 stars.

3-0 out of 5 stars It is not Mathematical Analysis of Physical Problems
Well this is a good Mathematical Reference Books for Theoretical Physisicst but has nothing to do with Mathematical Analysis of Physical Problems. It has all the tools you need that is fine, there are many similiar books as a reference book but if you think you will find ideas and methods "how to structure the Physical Problems in Mathematical terms", this is not the book.

4-0 out of 5 stars a book to get the mathematics for physics
This is a very good feeling, when you handle a book which provides all the mathematics (separation of variables, Fourier Laplace analysis, complex plane integration, Green's functions...) necessary to solve almost all the physical problems; especially dealing with partial derivative equations (from vibrating string to Schroedinger equation). The price is also a good point. Thank you Dover.

5-0 out of 5 stars Great book
This book is much different than the other books dealing with math and physics. A brief description for this book is represent the link between the math used to describe the physical phenomena and the physical phenomenaitself, in other words is the answer for this question why this mathematicsexactly used in this particular phenomena? which a lot of physicsmathematics books don't viewing this point. It is unique and great book. ... Read more

30. An Introduction to Harmonic Analysis (Cambridge Mathematical Library)
by Yitzhak Katznelson
Hardcover: 336 Pages (2004-01-12)
list price: US$108.00 -- used & new: US$79.99
(price subject to change: see help)
Asin: 0521838290
Average Customer Review: 5.0 out of 5 stars
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Awarded the American Mathematical Society Steele Prize for Mathematical Exposition, this Introduction, first published in 1968, has firmly established itself as a classic text. Yitzhak Katznelson demonstrates the central ideas of harmonic analysis and provides a stock of examples to foster a clear understanding of the theory. This new edition has been revised to include several new sections and a new appendix. ... Read more

Customer Reviews (3)

5-0 out of 5 stars Still one of the best.
When the first edition of Katznelson's book appeared back in 1968 (when I was a student), it soon became the talked about, and universally used, reference volume for the standard tools of harmonic analysis: Fourier series, Fourier transforms, Fourier analysis/synthesis, the math of time-frequency filtering, causality ideas, H^p-spaces, and the various incarnations of Norbert Wiener's ideas on the Fourier transform in the complex domain, Paley-Wiener, spectral theory, and more. It is easy to pick up the essentials in this lovely book. Now, many years later, I occasionaly ask beginning students what their favorite reference is on things like that, and more often than not, it is Katznelson. Thanks to Dover, it is on the shelf of most university bookstores, and priced under US$ 10.

5-0 out of 5 stars Great Introduction to Classical Harmonic Analysis
This is a great book for looking at classical harmonic analysis: the study of Fourier Series on the "typical" groups, includes a quick look at the general situation and ends with an introduction to commutative Banach Algebras. Both topics are continued in [Loomis].

5-0 out of 5 stars An essential book for anyone studying Harmonic Analysis
Katznelson's book considers harmonic analysis primarily on the circle group. He does this from a thorougly modern point of view. An understanding of the basic ideas of Banach spaces is required. This book should be on the shelf of any aspiring Harmonic Analyst, especially one with an abstract viewpoint. ... Read more

31. Mathematical Analysis For Economists
by R.G.D. Allen
Hardcover: 572 Pages (2008-11-04)
list price: US$46.95 -- used & new: US$42.25
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Asin: 1443725226
Average Customer Review: 5.0 out of 5 stars
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MATHEMATICAL ANALYSIS FOR ECONOMISTS by R. G. D. ALLEN. Originally published in 1937. FOREWORD; THIS book, which is based on a series of lectures given at the London School of Economics annually since 1931, aims at providing a course of pure mathematics developed in the directions most useful to students of economics. At each stage the mathematical methods described are used in the elucidation of problems of economic theory. Illustrative examples are added to all chapters and it is hoped that the reader, in solving them, will become familiar with the mathematical tools and with their applications to concrete economic problems. The method of treatment rules out any attempt at a systematic development of mathematical economic theory but the essentials of such a theory are to be found either in the text or in the examples. I hope that the book will be useful to readers of different types. The earlier chapters are intended primarily for the student with no mathematical equipment other than that obtained, possibly many years ago, from a matriculation course. Such a student may need to accustom himself to the application of the elementary methods before proceeding to the more powerful processes described in the later chapters. The more advanced reader may use the early sections for purposes of revision and pass on quickly to the later work. The experienced mathematical economist may find the book as a whole of service for reference and discover new points in some of the chapters. I have received helpful advice and criticism from many mathe maticians and economists. I am particularly indebted to Professor A. L. Bowley and to Dr. J. Marschak and the book includes numerous modifications made as a result of their suggestions on reading the original manuscript. I am also indebted to Mr. G. J. Nash who has read the proofs and has detected a number of slips in my construction of the examples. R. G. D. ALLEN THE LONDON SCHOOL OF ECONOMICS October, 1937.Contents include: FOREWORD ----------v A SHORT BIBLIOGRAPHY - ..... xiv THE USE OF GREEK LETTERS IN MATHEMATICAL ANALYSIS - - ...... xvi I. NUMBERS AND VARIABLES -------1 1.1 Introduction ---------1 1.2 Numbers of various types ------3 1.3 The real number system -------6 1.4 Continuous and discontinuous variables ... - 7 1.5 Quantities and their measurement ..... 9 1.0 Units of measurement - - - - - - - 13 1.7 Derived quantities - - - - - - - - 14 1.8 The location of points in space - - - - - 1G 1.9 Va viable points and their co-ordinates 20 EXAMPLES 1 The measurement of quantities graphical methods ---------23 . JpOJ ACTIONS AND THEIR DIAGRAMMATIC REPRESENTATION 28 2.1 Definition and examples of functions 28 2.2 The graphs of functions - - - - - - - 32 2.3 Functions and curves - - - - - - - 3 5 2.4 Classification of functions - - - - - - 38 2.5 Function types - - - - - - - - 41 2.6 The symbolic representation of functions of any form - 45 2.7 The diagrammatic method - - - - - - 48 2.8 The solution of equations in one variable 50 2.9 Simultaneous equations in two variables 54 EXAMPLES II Functions and graphs the solutionjof equa- tions ......... 57 III. ELEMENTARY ANALYTICAL GEOMETRY 61 3.1 Introduction ......... 61 3.2 The gradient of a straight line ..... 03 3.3 The equation of a straight line - - - 66 viii CONTENTS CHAP. 3.4 The parabola 09 3.5 The rectangular hyperbola - - - - - - 72 3.6 The circle 75 3.7 Curve classes and curve systems . - ... 76 3.8 An economic problem in analytical geometry 80 EXAMPLES III--The straight line curves and curve systems 82 IV... ... Read more

Customer Reviews (1)

5-0 out of 5 stars A useful text for math and economics
I have an old copy of this text and was happy to find that was still in print.I used it during my graduate work back in the early 70's and found its review of mathematical principles and its application of those principles to economics most understandable and useful.It remains relevant. ... Read more

32. Problems and Theorems in Analysis I: Series, Integral Calculus, Theory of Functions (Classics in Mathematics)
by George Polya, Gabor Szegö
Paperback: 392 Pages (2004-03-17)
list price: US$49.95 -- used & new: US$38.80
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Asin: 3540636404
Average Customer Review: 5.0 out of 5 stars
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A classic of this century that has had a lot of influence on teaching, & research in several branches of hard analysis, particularly complex function theory. An essential source book for mathematicians. Paper. DLC: Series, integral calculus, theory of functions. ... Read more

Customer Reviews (3)


Problems in Mathematical Analysis (Hardcover)
by g. yankovsky (Translator), B. Demidovich (Author
Publisher: mir publisher; 4th Printing edition (1976)

5-0 out of 5 stars A Beautiful Classic
This book by Polya and Szego contains many wonderful gems of mathematics.The exercises are very interesting, and sometimes I pick the book up just for fun.I wish I had been able to purchase a hardcover copy. Unfortunately, it's only available in paperback.

This book is suitable for mathematics graduate students.

5-0 out of 5 stars Excellent. A good way to start researches
The selected problems aren't the typical ones. The great beauty of manyresults are marvellous and, disposed in dificulty ascendent, are teh bestway to start researches. I teach in the University of Málaga and I'minterested in the second vol. ... Read more

33. A First Course in Mathematical Analysis
by David Alexander Brannan
Paperback: 472 Pages (2006-09-04)
list price: US$59.00 -- used & new: US$40.61
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Asin: 0521684242
Average Customer Review: 5.0 out of 5 stars
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Mathematical Analysis (often called Advanced Calculus) is generally found by students to be one of their hardest courses in Mathematics. This text uses the so-called sequential approach to continuity, differentiability and integration to make it easier to understand the subject.Topics that are generally glossed over in the standard Calculus courses are given careful study here. For example, what exactly is a 'continuous' function? And how exactly can one give a careful definition of 'integral'? The latter question is often one of the mysterious points in a Calculus course - and it is quite difficult to give a rigorous treatment of integration! The text has a large number of diagrams and helpful margin notes; and uses many graded examples and exercises, often with complete solutions, to guide students through the tricky points. It is suitable for self-study or use in parallel with a standard university course on the subject. ... Read more

Customer Reviews (2)

5-0 out of 5 stars The best introductory text on analysis that I've seen.
This book is a gem.

As the author states in the introduction, this is a student friendly book - the notes in the margins are really useful, the worked examples are clear and well thought out while the book has a good flow to it. A lot of thought has been put into this text and it shows. The bottom line is that I learnt a lot from this book and now feel ready to tackle more advanced texts.

5-0 out of 5 stars Excellent first intro to Analysis
This book pretty much copies the Real Analysis part of the Open University's excellent course 'Into to Pure Mathematics' which also covered Group Theory and Linear Algebra . If you're new to Analysis I cannot more highly recommend another book, though I would also recommend Spivak's Calculus which is at the same level, and pretty much covers the same material. I did the course (and have the book) and found it a breeze, all due to the excellently presented material, and the many examples, where like the SUMS books (of which I recommend most), all answers are givern in detail; which is important when you start more advanced maths (sic) and especially when you're teaching yourself!However it is only an introduction, but will prepare you for more advanced Analysis books like Rudin, Royden and my new favourite Knapp and his 2 Real Analysis books. Personally I wish they would produce more of the OU Maths courses in book format, as the material that I have read and studied has rarely been bettered in the standard books. Maybe this is a start of a new trend with the OU, I hope! ... Read more

34. Advanced Mathematical Methods for Scientists and Engineers: Asymptotic Methods and Perturbation Theory (v. 1)
by Carl M. Bender, Steven A. Orszag
Hardcover: 593 Pages (1999-10-29)
list price: US$99.00 -- used & new: US$55.00
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Asin: 0387989315
Average Customer Review: 4.5 out of 5 stars
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This book gives a clear, practical and self-contained presentation of the methods of asymptotics and perturbation theory for obtaining approximate analytical solutions to differential and difference equations. These methods allow one to analyze physics and engineering problems that may not be solvable in closed form and for which brute-force numerical methods may not converge to useful solutions. The presentation is aimed at teaching the insights that are most useful in approaching new problems; it avoids special methods and tricks that work only for particular problems, such as the traditional transcendental functions.

Intended for graduate students and advanced undergraduates, the book assumes only a limited familiarity with differential equations and complex variables.

The presentation begins with a review of differential and difference equations; develops local asymptotic methods for differential and difference equations; explains perturbation and summation theory; and concludes with a an exposition of global asymptotic methods, including boundary-layer theory, WKB theory, and multiple-scale analysis. Emphasizing applications, the discussion stresses care rather than rigor and relies on many well-chosen examples to teach the reader how an applied mathematician tackles problems. There are 190 computer-generated plots and tables comparing approximate and exact solutions; over 600 problems, of varying levels of difficulty; and an appendix summarizing the properties of special functions. ... Read more

Customer Reviews (16)

5-0 out of 5 stars Every home should have one
I have learned a lot of asymptotic methods from this book, having spent several previous years wondering what that stationary phase method that the physicsts were on about was (by the way B&O poo-poo stationary phase). The problems are great, the style is clear, the selection of material is wonderful. The authors are giants of applied mathematics (and Orszag is the father of Peter Orszag, which, on second thought is probably not a plus). The book has traditionally been insanely expensive (over $100), but has now gotten to a reasonable price.

1-0 out of 5 stars Very disappointed.
I had seen this book in a bookstore over 15 years ago and regretted that I did not buy it at that time. Now that I have it, I am very disappointed. First of all, the print for the examples is very very small. The book is more of a summary of methods than any details of the methods themselves. There is no systematic development of the mathematical theory for these methods. This reinforces the worst aspects of books on aymptotic methods and perturbation theory: it's all just a bunch of random trial and error jibbrish!

The authors tried to pile in a lot of methods into the book without detailed explanations. I find it hard to believe that a scientist or engineer would get a lot out of this book. As a mathematician, I found it lacking in any significant mathematical meaning and purpose. I would recommend Nayfeh's book on peturbation methods instead.

5-0 out of 5 stars outstanding!
I was looking for a long time for a textbook to use for a graduate course in advanced mathematics for engineers and this book is exactly what I need! The book has plenty of examples and not too many proofs so it is perfect for engineers. Highly recommend it!

5-0 out of 5 stars Still the Best
I used this book in grad school about 15 years ago and got it out again yesterday to learn more about sophisticated path deformations in the complex plane. This style of going through interesting examples, pointing out possible trouble and explaining the main ideas is perfect for physicists who need advanced math tools but hate typical math papers of the proof-lemma-proof-type.
It's not outdated, symbolic math software can do a lot, but often can't handle the full problem and you have to simplify by hand before starting the computer.

5-0 out of 5 stars Excellent !!!!!!!!
This is one of the finest books ever written on classical asymptotic analysis, one of the most useful areas in mathematics for engineering applications. The material is quite outdated now since the present research is almost completely computational.

Nevertheless, one of the finest applied mathematics texts. ... Read more

35. Techniques of Mathematical Analysis (Unibooks)
by Clement John Tranter
 Paperback: 396 Pages (1974-01-01)

Isbn: 0340116412
Average Customer Review: 5.0 out of 5 stars
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Customer Reviews (1)

5-0 out of 5 stars Great collection of Cambridge/Oxford scholarship math questions
This is an out-of-print 1960s British classic at a level slightly tougher than the Advanced Placement Calculus BC test. It is basically a great collection of challenging but traditional Pure-Mathematics questions, many from the venerable Cambridge/Oxford math entrance exams for "Mathematical Scholarships & Exhibitions"; many of these are derived from first-year Math Tripos-like colleges-exam questions. These entrance exams were later replaced by easier STEP papers (sixth-form examination papers I/II/III) in the 1980s administered by OCR. Somewhat of a chronicle of a bygone era in rigorous high-school mathematics. Useful for U.S. freshman honors calculus classes. ... Read more

36. IV: Analysis of Operators, Volume 4 (Methods of Modern Mathematical Physics)
by Michael Reed, Barry Simon
Hardcover: 325 Pages (1978-05-12)
list price: US$166.00 -- used & new: US$132.79
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Asin: 0125850042
Average Customer Review: 5.0 out of 5 stars
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BESTSELLER of the XXth Century in Mathematical Physics voted on by participants of the XIIIth International Congress on Mathematical Physics

This revision will make this book mroe attractive as a textbook in functional analysis. Further refinement of coverage of physical topics will also reinforce its well-established use as a course book in mathemtical physics. ... Read more

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5-0 out of 5 stars eigenvalues for schrodinger
The book covers the theory about eigenvalues of Schrodinger operators. It is complete success in explaining clearly the basic concepts involved: perturbation theory (summability questions, fermi golden rule), min-maxprinciple for discrete spectrum, Weyl theorem, HVZ theorem, the absence ofsingular continuous spectrum, ground state questions, periodic operators,semiclassic distribution of eigenvalues, compactness criteria.

It isstill a usable book and little has change in the subject (except inSingular Continuous Spectra). ... Read more

37. A problem book in mathematical analysis
by G. N Berman
 Hardcover: 462 Pages (1977)
-- used & new: US$91.35
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Asin: B0007AL4WG
Average Customer Review: 5.0 out of 5 stars
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Customer Reviews (2)

5-0 out of 5 stars Truely useful
I agreed with the previous reviewer. This book contains tons of problems with little overlapping. It's comprehensive and collective! Should be called a comprehensive collection of problems in mathematical analysis (at undergraduate level). It's theeee most comprehensive one out there. While Kazac and Nowak's books Problems in Mathematical Analysis have more hard problems (Putnam type), this one helps you build up the knowledge you need to understand advanced graduate level Real Analysis. Highly recommended for econ/math/physics majors.

5-0 out of 5 stars Great problem book
While this may not be classed among the legendary problem books such as Polya Szegö, it still serves as an interesting and stimulating problem book covering most of an Analyis I and II course at the undergrad level. Starting with the truly elementary and progressing to multidimensional and vector analysis, this book gives a good overview. Furthermore, aside from the chapters concerned with pure mathematics, there are also a number of examples in a chapter on applications to physics. The book consists of some 4000 problems, with numerical or otherwise noncomprehensive answers to all of them in the appendix. ... Read more

38. Mathematical Principles of Signal Processing: Fourier and Wavelet Analysis
by Pierre Bremaud
Paperback: 288 Pages (2010-11-02)
list price: US$115.00 -- used & new: US$91.73
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Asin: 1441929568
Average Customer Review: 5.0 out of 5 stars
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From the reviews: "[…] the interested reader will find in Bremaud’s book an invaluable reference because of its coverage, scope and style, as well as of the unified treatment it offers of (signal processing oriented) Fourier and wavelet basics." Mathematical Reviews

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5-0 out of 5 stars mathematically rigorous approach to signal processing
If you don't like the sloppy arguments often provided by engineering books, then this is the book for you!The prerequisite is some familiarity with the Lebesgue Integral.The author provides a clean development of the L1 and L2 theory for both Fourier Series and the Fourier Transform.In addition, he covers the basics of signal processing and wavelets in a concise, but rigorous, style. ... Read more

39. A View from the Top (Student Mathematical Library)
by Alex Iosevich
Paperback: 136 Pages (2007-11-01)
list price: US$29.00 -- used & new: US$25.80
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Asin: 0821843974
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This book is based on a capstone course that the author taught to upper division undergraduate students with the goal to explain and visualize the connections between different areas of mathematics and the way different subject matters flow from one another. In teaching his readers a variety of problem solving techniques as well, the author succeeds in enhancing the readers' hands-on knowledge of mathematics and provides glimpses into the world of research and discovery. The connections between different techniques and areas of mathematics are emphasized throughout and constitute one of the most important lessons this book attempts to impart. This book is interesting and accessible to anyone with a basic knowledge of high school mathematics and a curiosity about research mathematics. The author is a professor at the University of Missouri and has maintained a keen interest in teaching at different levels since his undergraduate days at the University of Chicago. He has run numerous summer programs in mathematics for local high school students and undergraduate students at his university. The author gets much of his research inspiration from his teaching activities and looks forward to exploring this wonderful and rewarding symbiosis for years to come. ... Read more

40. Counterexamples in Analysis (Dover Books on Mathematics)
by Bernard R. Gelbaum, John M. H. Olmsted
Paperback: 218 Pages (2003-06-04)
list price: US$14.95 -- used & new: US$8.98
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Asin: 0486428753
Average Customer Review: 4.5 out of 5 stars
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These counterexamples, arranged according to difficulty or sophistication, deal mostly with the part of analysis known as "real variables," starting at the level of calculus. The first half of the book concerns functions of a real variable; topics include the real number system, functions and limits, differentiation, Riemann integration, sequences, infinite series, uniform convergence, and sets and measure on the real axis. The second half, encompassing higher dimensions, examines functions of two variables, plane sets, area, metric and topological spaces, and function spaces. This volume contains much that will prove suitable for students who have not yet completed a first course in calculus, and ample material of interest to more advanced students of analysis as well as graduate students. 1962 edition. 12 figures. Bibliography. Index. Errata.
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Customer Reviews (14)

5-0 out of 5 stars You can't understand something without counterexamples.
Like the authors warned, I would've liked it if there were some counterexamples I thought of put in the book, but I realize this is technically infeasible.

Really, this book acts as a handy reference."Oh, is this true? (look for counterexample) Maybe it is/No it's not."It helps quicken the learning experience quite a bit.The fact that it's only around $10 also makes it handier.

5-0 out of 5 stars The most important math book an undergrad can buy
I wish I had this book when I took my first undergraduate analysis course.

Up until analysis, math is easy and intuitive to just about everyone who pays attention at each step because everything studied is built upon concepts learned in grade school.You know what a triangle is, so trigonometry makes sense.You know what a rectangle is, so low level calculus makes some sense (though as it is normally taught, there appears to be some mathematical voodoo going on when dealing with limits and such).

Then analysis hits, and every student has to deal with concepts that, at the time, appear arcane and bizarre.Open and closed sets?Compactness?Sequences and series?Where did all this stuff come from, and where is the familiar math as used by engineers?

That's where this book shines.Best used as a supplement to standard analysis text, its primary virtue is that it makes all of these strange new concepts easy to grasp.Each chapter gives a brief review of concepts you might vaguely remember from prior reading or a professor's lecture, and after that it launches into useful examples that render the concepts clear and provide motivation for having a good working knowledge of the material.

This results in, as others have pointed out, a good development of intuition for analysis, and that intuition becomes the bedrock for future success.Many students limp away from intro analysis with a shaky grasp of the material that only solidifies when the same concepts show up again in future courses.This book eases that burden and erases some of the feeling of playing catch-up when the really strange stuff comes along later.

5-0 out of 5 stars Classic book, now IN PRINT from Dover
All the positive reviews here are true.This is an awesome book that every serious math student should own, especially graduate students preparing for qualification exams.And unlike so many graduate level works this one is a bargain in a well made Dover edition.As one reviewer notes "Just get it".

4-0 out of 5 stars Recommended by Analysis Professor
Counterexamples in Analysis was recommended by our professor as a resource for a course, Introduction to Analysis.It is a support for writing proofs that makes an excellent addition to the home library for mathematics majors.For non-mathematics majors, it makes some important points more clear, but is sometimes not the quickest route to solving problems.

5-0 out of 5 stars Fascinating and Useful; Maybe a Tad Too Focused
I have owned this book for years and have quite enjoyed reading in it. I must admit that I have not read it through; it is tough going. Although it is surely a great book, to my taste it is too thoroughly focused on details of pure analysis and not sufficiently attentive to pedagogy and logic. In fact, it is so focused on the internals of pure analysis that it does not even bother to tell the reader what this field is. It does not note that analytic geometry is the application of pure analysis to geometry or that analytic number theory is the application of pure analysis to the theory of numbers. For more on the nature of pure analysis see page 540 of the 1999 CAMBRIDGE DICTIONARY OF PHILOSOPHY, which included an article "Mathematical Analysis" because of the importance of the subject to philosophy of mathematics. John Corcoran might have had this book in mind when he wrote the following in his abstract "Counterexamples and Proexamples", page 460 in the 2005 BULLETIN OF SYMBOLIC LOGIC. I quote the whole abstract because I think that readers will enjoy the book even more if they have Corcoran's ideas in mind--not to imply that I agree with everything Corcoran says there.
"Abstract: Every perfect number that is not even is a counterexample for the universal proposition that every perfect number is even.Conversely, every counterexample for the proposition "every perfect number is even" is a perfect number that is not even.Every perfect number that is odd is a proexample for the existential proposition that some perfect number is odd.Conversely, every proexample for the proposition "some perfect number is odd" is a perfect number that is odd.As trivial these remarks may seem, they can not be taken for granted, even in mathematical and logical texts designed to introduce their respective subjects.One well-reviewed book on counterexamples in analysis says that in order to demonstrate that a universal proposition is false it is necessary and sufficient to construct a counterexample.It is easy to see that it is not necessary to construct a counterexample to demonstrate that the proposition "every true proposition is known to be true" is false - necessity fails.Moreover the mere construction of an object that happens to be a counterexample does not by itself demonstrate that it is a counterexample - sufficiency fails.In order to demonstrate that a universal proposition is false it is neither necessary nor sufficient to construct a counterexample.Likewise, of course, in order to demonstrate that an existential proposition is true it is neither necessary nor sufficient to construct a proexample.This article defines the above relational concepts of counterexample and of proexample, it discusses their surprising history and philosophy, it gives many examples of uses of these and related concepts in the literature and it discusses some of the many errors that have been made as a result of overlooking the challenging subtlety of the proper use of these two basic and indispensable concepts." ... Read more

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