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21. Introduction to Complex Analysis
22. Genetic Analysis of Complex Traits
23. Complex Analysis and Algebraic
24. Complex Analysis (Universitext)
25. Complex Analysis with Applications
26. Complex Analysis (Volume 0)
27. Introduction to Complex Analysis
28. Protein, Protein Complexes: Analysis,
29. Complex Analysis: An Invitation
30. Complex Variables: Introduction
31. Practical Methods for Design and
32. Complex Analysis
33. Statistical Modeling for Biomedical
34. An Introduction to Complex Analysis
35. Complex Analysis
36. Functions of One Complex Variable
37. The Logic Of Failure: Recognizing
38. Complex Variables: Second Edition
39. Nine Introductions in Complex
40. Classical Complex Analysis (Pure

21. Introduction to Complex Analysis
by Zeev NEHARI
 Hardcover: Pages (1964)

Asin: B000GP25PM
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22. Genetic Analysis of Complex Traits Using SAS
by Arnold M. Sexton
Paperback: 312 Pages (2004-11-10)
list price: US$49.95 -- used & new: US$41.92
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Asin: 1590475070
Average Customer Review: 4.0 out of 5 stars
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Arnold Saxton, Ph.D., the editor of this volume, is a professor of animal science at the University of Tennessee, Knoxville. During years of research and teaching in statistics and genetics, Dr. Saxton recognized the need for a how-to introduction to SAS computer analysis for complex-trait genetics. He assembled 16 coauthors from around the world to create this unique compilation. Example-rich and experiment-driven, Genetic Analysis of Complex Traits Using SAS demonstrates how you can use SAS and SAS/Genetics to extract answers from your quantitative and molecular genetics data. The book guides you through the mix of genetic, statistical, and SAS skills that are needed, enabling you to apply what you've learned to your own experimental data. You'll find this an invaluable resource whether you are a researcher, scientist, graduate student, bioinformatician, or statistician--or any other SAS user interested in joining the highly active and exciting field of genetic analysis. ... Read more

Customer Reviews (1)

4-0 out of 5 stars Helpful
Regardless of how one feels about SAS as a programming language, it is readily apparent that it is very popular in areas such as financial and biological modeling. This book gives an introduction to how it is used in genetic analysis, and even though each chapter is written by a different author, the book can be useful to those (such as this reviewer) who are not experts in genetics but who may be called upon to apply their mathematical and statistical knowledge to problems in genetics (but using SAS instead of some other programming language to do so). Although the book assumes a thorough knowledge of genetics, it can still be read profitably by anyone who has a background in SAS and some knowledge of genetics. Being an interpreted language, SAS performance can be a problem with many applications, and its value in science is questionable for projects that require heavy computational power. For medium-sized projects though it can be helpful, even though its semantics can be hard to get used to for those who have programmed in more object-oriented environments.

SAS has been used widely to perform statistical studies in genetics using "classical" tools such as multivariate analysis and maximum likelihood, but there is one chapter in this book where Bayesian inference techniques are used for genetic analysis. In addition, and this makes the discussion in the chapter even more valuable, is that the estimation of the posterior distribution is done using Markov chain Monte Carlo (MCMC) techniques. The first genetics problem on which this is done regards two-point linkage analysis where Bayesian inference is used to estimate the recombination rate in a backcross between two completely homozygous lines for each of two loci. Even though this problem has an analytical solution, the authors use a simple Monte Carlo simulation to estimate the posterior mean and variance of the recombination rate to motivate how SAS can be used in this case.It should be pointed out here that the authors use SAS PROC Capability in their code and not all readers have this in their SAS implementation, but it can be replaced by PROC Univariate with no problems. This problem is generalized to the case of where there are three linked marker loci, with Bayesian inference and MCMC (via the Metropolis-Hastings algorithm) used to estimate the loci order and the recombination rates between the markers. The authors give the actual SAS code to implement this analysis, which is very readable (in spite of the ancient and annoying "goto" statements that are used within it). MCMC techniques are essential though in more general problems where analytical solutions are not possible. This is the case for a general genetic map construction that the authors discuss but do not give the explicit SAS code for (but it can be found on the Website that is associated with the book). They discuss briefly the pitfalls in doing MCMC for this case, and give a few alternatives. Bayesian inference is then applied to QTL analysis for the simple case of a single QTL model for backcrossing. ... Read more

23. Complex Analysis and Algebraic Geometry: A Collection of Papers Dedicated to K. Kodaira
Paperback: 416 Pages (2009-04-13)
list price: US$50.00 -- used & new: US$43.19
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Asin: 0521093341
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The articles in this volume cover some developments in complex analysis and algebraic geometry. The book is divided into three parts. Part I includes topics in the theory of algebraic surfaces and analytical surfaces. Part II covers topics in moduli and classification problems, as well as structure theory of certain complex manifolds. Part III is devoted to various topics in algebraic geometry analysis and arithmetic. A survey article by Ueno serves as an introduction to the general background of the subject matter of the volume. The volume was written for Kunihiko Kodaira, on the occasion of his sixtieth birthday, by his friends and students. Professor Kodaira was one of the world's leading mathematicians in algebraic geometry and complex manifold theory: and the contributions reflect those concerns. ... Read more

24. Complex Analysis (Universitext)
by Eberhard Freitag, Rolf Busam
Paperback: 532 Pages (2009-05-28)
list price: US$69.95 -- used & new: US$47.99
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Asin: 3540939822
Average Customer Review: 4.0 out of 5 stars
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The idea of this book is to give an extensive description of the classical complex analysis, here ''classical'' means roughly that sheaf theoretical and cohomological methods are omitted.

The first four chapters cover the essential core of complex analysis presenting their fundamental results. After this standard material, the authors step forward to elliptic functions and to elliptic modular functions including a taste of all most beautiful results of this field. The book is rounded by applications to analytic number theory including distinguished pearls of this fascinating subject as for instance the Prime Number Theorem. Great importance is attached to completeness, all needed notions are developed, only minimal prerequisites (elementary facts of calculus and algebra) are required.

More than 400 exercises including hints for solutions and many figures make this an attractive, indispensable book for students who would like to have a sound introduction to classical complex analysis.

For the second edition the authors have revised the text carefully.

... Read more

Customer Reviews (2)

3-0 out of 5 stars Excellent book/Terrible translation
This book was originally written in German, and the German version is just incredible: a real gem.Good reason to translate it!Unfortunately, this is one of the worst translations from German I have seen.Some of it is just awkward grammar, which the reader may be able to ignore.But, there are also some words and phrases which are translated incorrectly.
For example "Paragraphen" in German does not mean paragraph in English, it means section.But in this book it is translated as paragraph.Try looking for something at the end of a paragraph or in the previous paragraph, when you should actually be looking at the end of the section or in the previous section.An example of this can be found in the explanation of the addition theorem for complex exponents (p. 27).The English text claims there is a remark concerning this at the end of the "paragraph."The paragraph ends and there is no remark.Turn to the end of the section (p. 31) and you will find the remark just above the exercises.
My advice is, if you can read German, get the German version!If you can't read German, you can still get the English version, but you will have to be very patient with the mistakes incurred in the translation (not to be found in the German original). If you own this book, you should systematically go through it and replace "paragraph" everywhere with "section."Most of the other translation mistakes can be figured out by context.

5-0 out of 5 stars see review
I was truly delighted to find this text. It starts off with ordinary complex analysis at the level of sophomore undergraduate students and proceeds well into graduate-level complex analysis (analytic number theory, elliptic functions, abels theorem, etc). The 'advanced' results are shown using standard methods, so it was a great way for someone who learned the nuts and bolts of contour integration to move into theta functions, the prime number theorem, etc etc...fun stuff. ... Read more

25. Complex Analysis with Applications
by Richard A. Silverman
Paperback: 274 Pages (2010-10-18)
list price: US$12.95 -- used & new: US$11.01
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Asin: 0486647625
Average Customer Review: 3.5 out of 5 stars
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This volume contains the basics of what every scientist and engineer should know about complex analysis. A lively style combined with a simple, direct approach helps readers grasp the fundamentals, from complex numbers, limits in the complex plane, and complex functions to Cauchy's theory, power series, and applications of residues. 1974 edition.
... Read more

Customer Reviews (2)

5-0 out of 5 stars Excellent Reference
One of the best of Dover. Might be a litle
bit advanced though, if you are a real beginner.

2-0 out of 5 stars Caveat Emptor!!!
Buyer Beware!The book I have is missing the first chapter (it starts on chapter 2).Consult w/ seller to make sure book has first chapter. ... Read more

26. Complex Analysis (Volume 0)
by Serge Lang
Paperback: 476 Pages (2008-06-13)
list price: US$27.00 -- used & new: US$24.30
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Asin: 3540780599
Average Customer Review: 4.5 out of 5 stars
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This is a new, revised third edition of Serge Lang's Complex Analysis. The first part of the book covers the basic material of complex analysis, and the second covers many special topics, such as the Riemann Mapping Theorem, the gamma function, and analytic continuation. Power series methods are used more systematically than in other texts, and the proofs using these methods often shed more light on the results than the standard proofs do. The first part of Complex Analysis is suitable for an introductory course on the undergraduate level, and the additional topics covered in the second part give the instructor of a graduate course a great deal of flexibility in structuring a more advanced course. ... Read more

Customer Reviews (3)

5-0 out of 5 stars Nice complex book

This book is well written except the printing quality could be a little better!

5-0 out of 5 stars There's not much to say about Complex Anal.
Well, this book is a book about Complex Anal (short for analysis). It is required for graduate school, so I'm guessing it has to be good. This is a great price. I don't know why people buy the hardback copy, especially if they are going to be toting it around everywhere. THANK YOU, AMAZON, FOR HELPING MAKE GRADUATE SCHOOL JUST A LITTLE MORE AFFORDABLE!

3-0 out of 5 stars Not enough for getting a complete perspective.
My comment refers to the third edition of this book, but I don't think the fourth could be much better.

First of all, this title shouldn't be included in the "Graduate Texts in Mathematics" series becausethe material it covers is covered in introductory undergraduate courses.Second, eventhough the author made a great effort to include as much topicsas he could, the treatment of most of them is highly old-fashioned. I mean,he pays no attention to the most recent and elegant refinements of thebasic theory, so the student is not immediately able to understand the realimportant ideas behind the subject. For example, nowadays the proof of theCauchy integral formula is presented as a more ar less easy corollary ofthe general Stokes theorem. The Cauchy integral theorem is also obtainedeasily following the same fashion. Incredibly, the author explores thisline in one appendix, but not well done, and apparently he doesn't realizethat there is the key idea.

Also, keeping in mind that holomorphicfunctions are harmonic, most of the important results for holomorphicfunctions should follow at once from the corresponding ones for harmonicfunctions, but this old-fashioned texts don't take this remarkableimportant feature of complex analysis into account, making the treatmentinnecessarily complicated and leading the student to misunderstand bothcomplex and harmonic analysis. Eventhough the book includes a whole chapteron harmonic functions, the author doesn't use their power as heshould.

I'm afraid there are few famous introductory texts that I wouldsuggest for first-timers. The best of them is Markushevitch, unfortunatelyout of print.

There is also another serious drawback: The author pays noattention at all to boundary value problems and therefore to theCauchy-type integral, maybe the most important tool of complex analysis.The Hilbert transform is also not present.

If you have the opportunitytake a look at Muskhelishvili's "Singular Integral Equations" andGakhov's "Boundary Value Problems" and then you will understandmy point.

Lang's book could be used as a companion text and as areference for introductory courses. It's got some interestigexcercises.

Its contents are: Complex Nubers and Functions; Power Series;Cauchy's Theorem, First Part; Winding Numbers and Cauchy's Theorem;Applications of Cauchy's Integral Formula; Calculus of Residues; ConformalMappings; Harmonic Functions; Schwartz Reflection; The Riemann MappingTheorem; Analytic Continuation Along Curves; Applications of the MaximumPrinciple and jensen's Formula; Entire and Meromorphic Functions; EllipticFuctions; The Gamma and Zeta Functions; The Prime number Theorem;Appendices.

Please take a look to the rest of my reviews (just click onmy name above). ... Read more

27. Introduction to Complex Analysis
by H. A. Priestley
Hardcover: 344 Pages (2003-10-30)
list price: US$140.00 -- used & new: US$112.00
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Asin: 0198525613
Average Customer Review: 3.0 out of 5 stars
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Complex analysis is a classic and central area of mathematics, which is studies and exploited in a range of important fields, from number theory to engineering. Introduction to Complex Analysis was first published in 1985, and for this much-awaited second edition the text has been considerably expanded, while retaining the style of the original.More detailed presentation is given of elementary topics, to reflect the knowledge base of current students. Exercise sets have been substantially revised and enlarged, with carefully graded exercises at the end of each chapter. ... Read more

Customer Reviews (6)

5-0 out of 5 stars a great book
I learned complex analysis using the first edition of this book. I had never studied complex analysis before and I found the treatment rigorous but pleasurable. Complex analysis is one of the most beautiful areas of both pure and applied mathematics and learning it is essential for any serious student of mathematics. I can't think of a better place to start than Priestley. If you find this book hard then you probably need to spend more time learning basic analysis of the real line so you can follow the mathematical arguments.

1-0 out of 5 stars A terrible book.
I found this book incomprehensible even though I got A's in the prerequisite courses for the complex analysis course that used this book. I then got Churchill and Brown's book (ISBN:0070109052) and things were back to normal.

4-0 out of 5 stars Good for undergrads
The existing reviews refer to the 1st edition of this book, which I agree was a difficult read, though still accessible to undergraduates. The new book has been revised substantially to make it more readable, with a much more leisurely introduction and better partitioning of tougher material (which can be omitted by those such as physicists and engineers who require only a working knowledge of the subject). If anything I feel the result is too dumbed down; Priestley is loathe even to make use of such basic tools from real analysis as uniform convergence. Nevertheless, the second half of the book is more adventurous, making the totality a guide for an excellent undergrad class, such as the Oxford one on which the book was based. Beware: there is a large number of typos, which one must hope will be corrected in subsequent printings. Usually it will not be too challenging to circumnavigate these.

2-0 out of 5 stars Fails due to lack of examples and clear explanations
This book seems to be more of a reference to complex analysis theorems than a book that one can study from. There are very few examples, and even fewer are clearly worked through. There are no solutions or even answers to selected exercises. The text itself is rather formal and dry, notparticularly difficult to read through. Other books tend to follow a formaldefinition or theorem with a "plain English" description togetherwith an apt example - this is definitely lacking here.

So, if you knowcomplex analysis and are looking for a basic reference book, then this maysuit your needs. If on the other hand you want a book to study complexanalysis from, then unfortunately I cannot give my recommendation.

1-0 out of 5 stars Terrible for Undergraduate
This book is ridiculously skimpy in detail. It does not explain well, has few illustrative examples, and has no solutions at the back of the book for any of the exercises. I found it impossible to study from. Not reccomendedas a textbook for undergraduate level! ... Read more

28. Protein, Protein Complexes: Analysis, Modeling and Drug Design
by Martin Zacharias
Paperback: 400 Pages (2010-05-04)
list price: US$77.00 -- used & new: US$69.25
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Asin: 1848163398
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Given the immense progress achieved in elucidating protein protein complex structures and in the field of protein interaction modeling, there is great demand for a book that gives interested researchers/students a comprehensive overview of the field. This book does just that. It focuses on what can be learned about protein protein interactions from the analysis of protein protein complex structures and interfaces. What are the driving forces for protein protein association? How can we extract the mechanism of specific recognition from studying protein protein interfaces? How can this knowledge be used to predict and design protein protein interactions (interaction regions and complex structures)? What methods are currently employed to design protein protein interactions, and how can we influence protein protein interactions by mutagenesis and small-molecule drugs or peptide mimetics?

The book consists of about 15 review chapters, written by experts, on the characterization of protein protein interfaces, structure determination of protein complexes (by NMR and X-ray), theory of protein protein binding, dynamics of protein interfaces, bioinformatics methods to predict interaction regions, and prediction of protein protein complex structures (docking and homology modeling of complexes, etc.) and design of protein protein interactions. It serves as a bridge between studying/analyzing protein protein complex structures (interfaces), predicting interactions, and influencing/designing interactions. ... Read more

29. Complex Analysis: An Invitation
by Murali Rao, Henrik Stetkaer
Hardcover: 240 Pages (1991-02)
list price: US$46.00 -- used & new: US$46.00
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Asin: 9810203756
Average Customer Review: 4.0 out of 5 stars
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Customer Reviews (1)

4-0 out of 5 stars Not for the faint hearted
The book is well organized and covers an amazing lot of ground at a very fast pace. I find it suitable for a second course in complex analysis.

Proofs of the theorems are clearly outlined , but the reader is usually expected to fill in some of the details and that requires a good advanced calculus background, up to the elements of Lebesgue integration, series and point set topology. The exercises are comparatively easy (no solutions) and there is a lot of interesting gossip and good references to the literature. ... Read more

30. Complex Variables: Introduction and Applications (Cambridge Texts in Applied Mathematics)
by Mark J. Ablowitz, Athanassios S. Fokas
Paperback: 660 Pages (2003-04-28)
list price: US$77.00 -- used & new: US$47.62
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Asin: 0521534291
Average Customer Review: 5.0 out of 5 stars
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Complex variables offer very efficient methods for attacking many difficult problems, and it is the aim of this book to offer a thorough review of these methods and their applications. Part I is an introduction to the subject, including residue calculus and transform methods. Part II advances to conformal mappings, and the study of Riemann-Hilbert problems. An extensive array of examples and exercises are included. This new edition has been improved throughout and is ideal for use in introductory undergraduate and graduate level courses in complex variables. First Edition Hb (1997): 0-521-48058-2First Edition Pb (1997): 0-521-48523-1 ... Read more

Customer Reviews (6)

5-0 out of 5 stars Excellent book -- Unique selection of topics
This is the only textbook that I know that introduces and explains the Hilbert-Riemann problem in a pedagogical way. If anyone knows of any other such book, please tell us. It also deals in a very introductory way with all sort of really nice topics that one cannot find discussed (at a really introductory level) in any similar book: the Painleve property, the classification of singularities, asymptotic expansions, etc, etc. All very powerful applied mathematics.

5-0 out of 5 stars A very good text!
A very good text!

The best description of this book is that it provides a comprehensive, classical treatment of the subject with a modern touch and serves ideally the needs of anyone studying Complex Analysis.

Starting from the foundations of defining a complex number, through to applications in the evaluation of integrals, the WKB method, Fourier transforms and Riemann-Hilbert problems, the book covers a lot of ground in an easy to follow style. The chapters are long, but logically broken down into digestible sections and interspersed with well illustrated diagrams, numerous worked examples and exercises.The end of chapter exercises provide further opportunity for reinforcing the methods and there's a useful section at the end giving brief hints and answers to selected problems.

Complex Variable analysis is treated from the definition of an analytic function and its relation to the Cauchy-Riemann equations, and in turn their application to an ideal fluid flow. The ideas of multi-valued functions, complex integration, and Cauchy's theorem are excellently treated, as are the consequences: the generalised Cauchy integral formula, the Max-Mod principle, and Liouiville and Morera's theorems.

The rest of the first part of this book, which is essentially pure mathematics, deals with Laurent series, singularities, analytic continuation, the Mittag-Leffler theorem, the ALL IMPORTANT Cauchy Residue Theorem, dealing with branch points, Rouche's theorem, and their application to Fourier transforms.

The second half starts off with perhaps the best I have seen on Conformal Mappings and their application to physical problems in Fluid Mechanics and Electromagnetism.Asymptotic evaluation of integrals covers methods like Watson's lemma, the method of steepest descent, and the WKB method.

A good combination of pure and applied mathematics, though the book avoids either the rigour of classical works such as Whittaker and Watson or the marvellously visual presentation of Tristan Needham.

Highly recommended!

5-0 out of 5 stars The numerous pictures are enough to recommend this text
This text is distinguished by the numerous diagrams that appear on practically every other page. If you're graphically oriented, like I am, then this itself is enough to recommend this book. Concepts such as branch points and multivalued complex functions are much easier to understand when there is a picture to accompany the concept. The second half of the book is concerned with applications and includes several useful asymptotic methods such as Laplace's integral method. These asymptotic techniques are good for evaluating particularly nasty integrals in which the integrand is really concentrated somewhere in the interval. On the downside, this is not a very formally rigorous book. On the other hand, such formalism is easier to digest once you've seen numerous pictures and examples, in my own opinion.

5-0 out of 5 stars A complete reference book for complex variables
Whether you are a student, or just in need of a good reference text, Mark J. Ablowitz' and Athanassios Fokas' book belongs in your library.Complex Variables, Introduction and Applications is refreshingly well written.In clear and logical flow, the authors present the subject of complex variables in an easy-to-understand, yet complete format suitable for both students and practicing professionals.

This text offers a broad coverage of the subject, from fundamental properties of complex numbers, analytic functions, and singularities to more advanced topics such as conformal mapping and Riemann-Hilbert problems.Although individuals interested in pure mathematics may find some of the proofs insufficiently rigorous, those using the book as a reference for engineering or scientific problems may find the text too rigid.Overall, however, the authors have done an excellent job balancing the subject matter and successfully achieving their goal of, when necessary, "sacrificing a rigorous axiomatic development with a logical development based upon suitable assumptions."

Although the mathematical development of the text is clear, concise, and easy to follow, many of the applied examples, such as those for uniform flow in section 2.1, would benefit from further physical insight.Individuals already familiar with physics will have no difficulty following many of the examples, and extending them to other situations.Those less grounded in the physical sciences, however, may find the starting equations for some of the examples to be less than intuitive.Though additional explanations would increase the book's already substantial heft, the change would benefit many readers.

It is a joy to read a well-written technical book with almost no typographical or technical errors.Except for minor (and easily recognizable) typographical errors such as that in equation 2.2.12b, the book is nearly flawless.This leaves the student free to concentrate on learning the material unencumbered by worries about the text's accuracy.

The index is nicely composed, complete, and accurate.This makes the book particularly useful as a reference.Typically, the reader will have little trouble using the index to go directly to the pages of most interest and applicability regarding the subject of inquiry.It would be nice to see a more complete bibliography, as well as a summary of common symbols.Especially useful would be a summary of some of the more important equations (such as Green's theorem, Cauchy's theorem, the Fourier transform, the Helmholtz equation, etc.) derived or demonstrated inthe book.A list of important equations, particularly, would improve the book's utilization as a desk reference.

For the student, the text presents answers to odd-numbered questions in the back of the book.For the most part, the text presents only the answers, but occasionally the authors provide additional insight into the problem's solution, as in section 5.2.This will be useful for those engaged in independent study.

Overall, this is an excellent text, and one of the most complete and well-written books on complex variables I have seen.I highly recommend it to anyone interested in the subject, and have placed it prominently upon my reference bookshelf.

5-0 out of 5 stars Definitely a great book!
This is DEFINITELYgreat book! no question about it! it covers everything, it has enough examples, it is very clear, it suits for self learning for undergrate and graduate students, and I definitely recommendit with all my heart. ... Read more

31. Practical Methods for Design and Analysis of Complex Surveys (Statistics in Practice)
by Risto Lehtonen, Erkki Pahkinen
Hardcover: 360 Pages (2004-02-02)
list price: US$130.00 -- used & new: US$107.23
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Asin: 0470847697
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Large surveys are becoming increasingly available for public use, and researchers are often faced with the need to analyse complex survey data to address key scientific issues. For proper analysis it is also important to be aware of the different aspects of the design of complex surveys. Practical Methods for Design and Analysis of Complex Surveys features intermediate and advanced statistical techniques for use in designing and analysing complex surveys. This extensively updated edition features much new material, and detailed practical exercises with links to a Web site, helping instructors and enabling use for distance learning.

  • Provides a comprehensive introduction to sampling and estimation in descriptive surveys, including design effect statistic and use of auxiliary data.
  • Includes detailed coverage of complex survey analysis, including design-based ANOVA and logistic regression with GEE estimation.
  • Contains much new material, including handling of non-sampling errors, and model-assisted estimation for domains.
  • Features detailed real-li fe case studies, such as multilevel modeling in a multinational educational survey.
  • Supported by a Web site containing software codes, real data sets, computerized exercises with solutions, and online training materials.

Practical Methods for Design and Analysis of Complex Surveys provides a useful practical resource for researchers and practitioners working in the planning, implementation or analysis of complex surveys and opinion polls, including business, educational, health, social, and socio-economic surveys and official statistics. In addition, the book is well suited for use on intermediate and advanced courses in survey sampling. ... Read more

32. Complex Analysis
by Lars Ahlfors
Hardcover: 336 Pages (1979-01-01)
-- used & new: US$179.85
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Asin: 0070006571
Average Customer Review: 3.5 out of 5 stars
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A standard source of information of functions of one complex variable, this text has retained its wide popularity in this field by being consistently rigorous without becoming needlessly concerned with advanced or overspecialized material. Difficult points have been clarified, the book has been reviewed for accuracy, and notations and terminology have been modernized. Chapter 2, Complex Functions, features a brief section on the change of length and area under conformal mapping, and much of Chapter 8, Global-Analytic Functions, has been rewritten in order to introduce readers to the terminology of germs and sheaves while still emphasizing that classical concepts are the backbone of the theory. Chapter 4, Complex Integration, now includes a new and simpler proof of the general form of Cauchy's theorem. There is a short section on the Riemann zeta function, showing the use of residues in a more exciting situation than in the computation of definite integrals. ... Read more

Customer Reviews (23)

1-0 out of 5 stars Total Garbage
First, a little about my background.I have no problems with many "classic" books in mathematics, even some that I believe should have been retired years ago on the grounds that (pedagogically) better books in the field have since been developed.Rudin's "Principles of Mathematical Analysis" is excellent because it is so organized, rigorous and elegant, though I don't personally think it's best for an introductory analysis course.Royden's "Real Analysis", older than I am, is serviceable and likely still has a place in the world.As for complex analysis, I think Conway's "Functions of One Complex Variable" and Lang's "Complex Analysis" are books that deserve to be called classics in the field and ought to enjoy wider circulation than they actually do.A couple years ago I worked through the Conway text on my own up to Cauchy's Theorem and found it pleasant. Now, at last, I'm taking a graduate-level complex analysis course, and oh what a crying shame: we're using this ancient travesty by Ahlfors.

Look, I don't mind terse proofs, or what some code-name "elegant" proofs. Like I said, I really like Rudin, and no one is terse if Rudin isn't.I can fill in the gaps in a terse but organized proof just fine, and I can also fill in the gaps in intuitive "hand-waving" proofs like the kind you'll find in Hatcher's "Algebraic Topology". But Ahlfors often manages terseness without elegance and hand-waving without intuition.It's breath-taking -- how does he do it? He couldn't have typed the book in the dark because there are very few typos, so it must be some special skill one acquires through life-long study of the Obscure Arts.

It's true what others say: the exercises often seem to have little to do with whatever Ahlfors was rambling on about in the sub-subsection they're found in. (The book is broken down into itty-bitty morsels, and still you can't figure out what chapter you're in without flipping through a dozen pages.)Let me rephrase that: they do have something to do with his ramblings, but the ramblings leave you with almost no idea how to go about doing them. Pivotal concepts are treated awkwardly in a rushed, conversational jumble that is rather like talking to a jet-lagged researching professor during office hours on a Friday afternoon minutes before he needs to catch a train. There is a reason why symbols were invented to convey mathematics, and it seems to be lost on Ahlfors.Where a Conway or a Lang will show X implies Y by a sequence of clear mathematical steps, Ahlfors will crawl through a muddy thicket of words that kind of anecdotally "describe" why X should imply Y. "Just figure it out!" shouts the professor over his shoulder as he dashes out his office to catch his next flight.That's Ahlfors' "Complex Analysis" in a nutshell: all complex, no analysis.

Nonbelievers: go to a library, find the book, and turn to page 31 to find what is quite possibly the absolute worst "explanation" of partial fraction decomposition in the history of history. Of course, there is no example to be found there, just a general kind of description that you may not realize is supposed to be an algorithm until Ahlfors ironically ends the sub-subsection with the words "completely successful" and you look at the first exercise. Or just look at page 2: almost an entire page, complete with a system of equations, is devoted to explaining complex number division. Now draw your own conclusions about what one should expect from this author when the material really DOES get complicated. Rube Goldberg is a minimalist by comparison.

There is no coherent definition of a removable singularity, actually. On page 124 His Professorship says, basically, they're points where we "lack information", in which case I guess the whole book could be called a "removable singularity".A glance at Conway cleared things up there.

The book reads like an encyclopedia, but it wouldn't even make for a good reference. Everything's packed into dense paragraphs, obsolete terminology and notation abounds, and the same letter will be used for both a limit of integration and the variable of integration -- in the same integral! Big results like Liouville's Theorem and Morera's Theorem are buried in italics in the middle of paragraphs, while at other times theorems are referred to by a name instead of a number and I'm hard-pressed to figure out what theorem is meant (because theorems are numbered, not named). As for proof of the Fundamental Theorem of Algebra: don't blink, because it's dismissed almost contemptuously in a single paragraph.

Compare pages 30 and 129 to witness Ahlfors contradicting himself on the issue of whether a function can be defined at infinity.

Take a gander at Rouche's Theorem.Ahlfors utterly fails to mention in the conclusion of the theorem that f(z) and g(z) have the same number of zeros COUNTING MULTIPLICITIES.Absolutely every other complex analysis text I can get my hands on at home (Gamelin, Lang, Conway, and a couple of no-names) makes the multiplicity issue plain either by noting it in the statement of the theorem, or mentioning it in a real, honest-to-god example following the theorem.

Complex analysis depends a little more heavily on explicit computations than real analysis does, so it really begs to be elucidated with many, many examples.Well, when it comes to examples, Ahlfors is about as close to a hard vacuum as you're going to find in the entire complex analysis universe.Hard vacuums are not easy to come by in life, so I have to imagine that's the reason for the high price of this "textbook", along with, I guess, the fact that Ahlfors was some big name from "Hah-vahd". Make no mistake: for the purpose of digesting complex analysis, this book is virulently toxic.Why does it still garner an average of 3.5 stars on this site?Well, the Mathematical Elite is very loving toward its sacred cows, which is why it is actually very difficult to find ANY graduate-level math text averaging less than 4 stars out of a total sample size of at least, say, seven reviews. Don't take my word for it -- go take a look around for yourself. I'll wait. So taking this "grade inflation" into account, 3.5 stars out of 5 is really pretty terrible.I recommend Conway or Lang. Lang actually has an accompanying solution manual, if you're self-studying.

This is the first textbook for any math course I've ever taken (and I've taken dozens) that I refuse to buy. I do not want to be party to its perpetuation. This "classic" desperately needs to be euthanized.

5-0 out of 5 stars Excellent book
The book from the seller was in great shape and unlike some sellers, was shipped in time and the product particularly was in mint condition

4-0 out of 5 stars Complex analysis, Ahlfors
I bought Complex analysis by Lars Ahlfors, the delivery was quick, and the transaction was handled professionaly.

2-0 out of 5 stars Tough
As a reference for a Ph.D wanting a refresher, I could see this book being a gem.I do admire Ahlfors for the scope of material he covers (interesting material).However, as a textbook for a student who has not seen all of the advanced concepts, it is mediocre at best.Ahlfors takes very big leaps in his reasoning ("The concept of a joining polygon is so easy that I need not explain it here" and "The reader will have no trouble...").He is extremely hard to follow at many points (notably conformal mapping and Riemann surfaces).You will need another book(s) for reference(s) and an instructor if you do not already know the material 'upside down' and are using Ahlfors.To digest Ahlfors, you need (or at least I needed)

1. Introductory Real Analysis I and II(Rudin's PRA, Gaughan, Ross, Stromberg, etc.) and Topology (Munkres)
2. Two undergraduate complex variable courses (Saff/Snider is awesome!!!)
Other Alternatives (Brown/Churchill, Fisher, Schaum's, etc.)
3. Graduate complex analysis with Karunakaran (awesome as well). Silverman and Needham would be beneficial as supplements.Ash does a good job on integration.
4. A thorough understanding of undergraduate calculus and DE.
5. If you want to understand Chapter 1, section 3, you need some abstract algebra (Gallian) and a book on the construction of the reals (PRA, Spivak, etc).

We used Ahlfors for the first part of the semester and then switched to Karunakaran's book during the second half.Karunakaran's book was much easier.It did not dodge the hard topics.Instead, it covered them in much more detail.That is why I got an A- in the class instead of the expected C I would have had with Ahlfors' book.After learning the material from Karunakaran, I would go back to Ahlfors and see what he was talking about.

[This is a review from a mere mortal (aka student).While I cannot dictate who agrees with my review, feedback from students is preferred over that of professors.I did pretty well in the class (A-), so there are no sour grapes toward the subject itself].

5-0 out of 5 stars Classic book on complex analysis: one of the best, but overpriced
This book is a classic on complex analysis.Unlike some "classics" in mathematics, it is quite accessible, for students at the appropriate level.In order to understand this book, one would need a solid background in mathematical analysis/advanced calculus, and probably one prior course in complex analysis.

This book is concise but reads rather quickly, at least compared to other books that are similarly dense.I think Ahlfors is a very good writer.Although this book seems thin, it covers a lot of material.I find the order of the material to be quite natural.I also like the problem sets...they are not too difficult for a book at this level, and they are very well-designed to help reinforce the basic ideas as well as explore deeper questions.

I think this book would make an outstanding textbook for a graduate course in advanced calculus.However, there are also a number of more modern textbooks on the subject (Greene & Krantz) that would also make equally good textbooks, so the choice of a book is more a question of personal taste than anything else.As a more introductory book on the same topic, I would recommend a number of books, including the one by Churchhill, or at a more intermediate level, the one by Gamelin, or the book by Stein and Shakarchi.There are other good complex analysis books out there too.The book by Hahn is also worth looking at--it is far more thorough than this book, although both the style of writing and the typesetting are a little less clear.Price-wise, however, these other books might offer more value for your money than this classic text. ... Read more

33. Statistical Modeling for Biomedical Researchers: A Simple Introduction to the Analysis of Complex Data (Cambridge Medicine)
by William D. Dupont
Paperback: 542 Pages (2009-02-23)
list price: US$63.00 -- used & new: US$41.96
(price subject to change: see help)
Asin: 0521614805
Average Customer Review: 4.0 out of 5 stars
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For biomedical researchers, the new edition of this standard text guides readers in the selection and use of advanced statistical methods and the presentation of results to clinical colleagues. It assumes no knowledge of mathematics beyond high school level and is accessible to anyone with an introductory background in statistics. The Stata statistical software package is used to perform the analyses, in this edition employing the intuitive version 10.
Topics covered include linear, logistic and Poisson regression, survival analysis, fixed-effects analysis of variance, and repeated-measure analysis of variance. Restricted cubic splines are used to model non-linear relationships. Each method is introduced in its simplest form and then extended to cover more complex situations. An appendix will help the reader select the most appropriate statistical methods for their data. The text makes extensive use of real data sets available online through Vanderbilt University. ... Read more

Customer Reviews (9)

5-0 out of 5 stars An excellent book for new and seasoned researchers alike!
In general, there are 3 types of books on statistics: (1) Those that describe general statistical methods (2) those that describe specific (esoteric) models, and (3) those that teach "how to" implement statistical models in specific software packages.

In this book, William D. Dupont does an excellent job of providing sufficient descriptions of each of the major statistical modeling approaches along with the specific Stata software commands to make this a rather complete book. Topics include simple and multiple regression models of the various types (linear, logistic, Poisson) as well as survival and longitudinal modeling approaches.

While as an experienced researcher these concepts are not new to me, what I found the most helpful was Dr. Dupont's thoughtful approach to choosing, testing, and displaying the results of each method. On countless occasions I found myself thinking "huh, that was a clever idea."

This book can serve as an excellent text for an intermediate biostatistics course (preferably a class that uses Stata), as well as serve as a resource to experienced researchers who may want to find streamlined approaches to implementing these models in Stata.

5-0 out of 5 stars A statistical modeling text that is both clear and throrough.
This text is especially valuable because it is written in clear and concise language. It thus serves the needs of the biostatistical community while remaining accessible to the non-biostatistician. The latter is what is so often lacking in textbooks in this discipline. The new 2009 edition builds on and adds to the strengths of the first. As a clinical investigator, I turn to this first when I have a complex data issue that I need clarification about.

4-0 out of 5 stars Practical Introduction to Stata
This is a highly recommended book if you are trying to use Stata in biomedical research.This covers most of the standard procedures (t-tests, linear regression, multiple comparisons, logistic and other contingency table methods, Cox PH, Poisson (log-linear), GEE) and a reasonable amount of noncalculus statistical formula derivation to show what goes on inside the box.ANOVA is relegated to the back of the book, because in the author's opinion, the amount of control needed to pull off these studies is not normally feasible and GLM can cover the same ground.There isn't any other book that addresses GEE as comprehensively as this book.The Vittinghoff book is also recommended as a companion piece to give a more in-depth approach to regression topics.

4-0 out of 5 stars Good guide
If you are working with Stata this book will be a good help to understand the basic concepts of the multivarite analysis.

4-0 out of 5 stars Accessible Intermediate Text
Dupont's "Statistical Modeling for Biomedical Researchers" is an accessible, straightforward, easy-to-read text for students and/or researchers w/ some elementary background in biostatistics.As previous reviewers have indicated, this is largely a problem-based text, so for those of you who seek a detailed theoretical explanation of the tools presented therein, you may want to look elsewhere.A major advantage, however, is Dupont's presentation of how to run the respective analyses using the statistical software package, Stata, although it should be noted that the syntax presented is for version 7 of Stata -- not version 8.Parenthetically, all of the code -- w/ the exception of the graphing commands -- are essentially the same between versions.In short, this text is a good introduction to some of the techniques typically not discussed in an elementary biostatistics course, although the book is best characterized as an invaluable adjunct to more theoretical, comprehensive biostatistics textbooks. ... Read more

34. An Introduction to Complex Analysis in Several Variables, Third Edition (North-Holland Mathematical Library)
by L. Hormander
Hardcover: 268 Pages (1990-01-16)
list price: US$114.00 -- used & new: US$81.40
(price subject to change: see help)
Asin: 0444884467
Average Customer Review: 4.0 out of 5 stars
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A number of monographs of various aspects of complex analysis in several variables have appeared since the first version of this book was published, but none of them uses the analytic techniques based on the solution of the Neumann Problem as the main tool.

The additions made in this third, revised edition place additional stress on results where these methods are particularly important. Thus, a section has been added presenting Ehrenpreis' ``fundamental principle'' in full. The local arguments in this section are closely related to the proof of the coherence of the sheaf of germs of functions vanishing on an analytic set. Also added is adiscussion of the theorem of Siu on the Lelong numbers of plurisubharmonic functions. Since the L2 techniques are essential in the proof and plurisubharmonic functions play such an important role in this book, it seems natural to discuss their main singularities.

... Read more

Customer Reviews (3)

4-0 out of 5 stars excellent if you understand it
zooom.....Here's a clue;As I recall, he does all of one variable complex analysis in an introductory chapter less than 20 pages long, including a version of Cauchy's theorem more general than I wager most have ever seen.

3-0 out of 5 stars Book by a communication-challenged but expert mathematician
This book is pretty hard to read.
It's extremely terse, for one thing.In one place he said something followed from the Hahn-Banach theorem.It didn't _look_ related to the HB theorem.So I find a corollary to the HB theorem which does look related.But it requires the Riesz representation theorem to work.So I read the proof of the RR theorem for positive measures.That also doesn't quite do it.I puzzle a bit, then find there's a RR theorem for complex measures.And, Finally this one sly little sentence makes sense!
If you care about understanding the math, making sense of it, it is sure going to be slow reading!
But, a lot of it is also fairly straightforward.
It has a few typos, but for the most part it's carefully proofread.Typos are especially frustrating when his writing is so compressed, because there isn't much of a context to make sense of them.
He uses new symbols without defining them.You have to guess what they mean.For example, if V is an open set, C^k(V) means complex valued functions on V that are k times continuously differentiable.He does define that.Then he starts talking about C^k(K), where K is the closure of an open set, without saying what he means by being differentiable on the boundary.Maybe he only talks about C^k(K) if the boundary of K is nice enough that you can define a derivative on it?Then he mentions C^k_(0,1)(K).Leaving you to figure out from the context that he means differential forms of type (0,1) with coefficients in C^k(K).Later, he talks about a "schlicht domain" without defining schlicht.
He uses idiosyncratic notation, so it would be hard to use the book as a reference.You'd have to figure out what all the symbols mean, and he doesn't list them all in his symbol table at the start of the book.
But, I also felt I was hearing from a truly expert mathematician.I wasn't surprised when I found out he got a Fields medal.
It has been awfully frustrating reading about multivariable complex analysis, because a lot of the authors do make mistakes.Gunning and Rossi's book had a lot of mistakes.Robert Gunning's later book, "Introduction to holomorphic functions of several variables" also has many mistakes in proofs.The mistakes in Gunning and Rossi had been fixed up, but Bochner's tube theorem, which is new in the later book, had a wrong proof.An article by Sin Hitotumatu purported to prove the theorem, but there was a big gap in the proof!But Hormander, though it took me ages to puzzle through his writing, actually did prove the tube theorem.There were no mistakes in Hormander's book as far as I read it.Being right, not using up your time with long proofs that have mistakes in them, makes up for a great deal of obscurity.And reading his proofs can be a delight like watching the clever conjurations of a wizard.
I've only read the first 42 pages of Hormander's book.But I imagine these attributes I describe only get more intense once he's past the introductory things.
Later books on multivariable complex analysis have been written for people who have trouble with compressed mathematical gems like Hormander's book.
His book is referred to a lot by other books, although probably hardly anybody actually tries to follow his reasoning.

5-0 out of 5 stars High-level math, as expected from Hormander
I started to learn several complex variables a few weeks ago, and I noticed the absolute lack of textbooks on the subject. Probably the book that comes more naturally as an extension of undergraduate complex analysisis Gunning and Rossi, but this title is out-of-print (even finding a usedcopy is nearly impossible. Believe me, I've tried hard).

So, we haveHormander's book. Lars Hormander is known for writing high-level math texts(both in quality and difficulty), as seen in his famous 4-volume seriesabout PDE's, and this book is no exception. His point of view is morerelated to his area of research (PDE's, again), and his demands forprerequisites are higher than GR (basics from Lebesgue integration,differential forms, algebra and point-set topology are more than welcome),but this book is a masterpiece of mathematical craftsmanship. The methodshere developed are often unique, and the author presents the subject in afully rigorous way. Along with the fact that it is one of the very fewbooks on several complex variables still in print, this is a very valuabletext, set in a high standard of excellence. My only complaint is theobscenely high price for a book so important. Several complex variables arean indispensable background for complex manifolds and algebraic geometry,and several important topics in theoretical physics (string theory, twistortheory, conformal field theory), and it's a shame that books like GR goout-of-print without any others for substituting them. Hormander's bookdoesn't go much deep in these directions, but you won't find any other bookin print on the subject with such a high quality. ... Read more

35. Complex Analysis
by Ian Stewart, David Tall
Paperback: 304 Pages (1983-04-29)
list price: US$63.00 -- used & new: US$53.37
(price subject to change: see help)
Asin: 0521287634
Average Customer Review: 3.5 out of 5 stars
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This is a very successful textbook for undergraduate students of pure mathematics. Students often find the subject of complex analysis very difficult. Here the authors, who are experienced and well-known expositors, avoid many of such difficulties by using two principles: (1) generalising concepts familiar from real analysis; (2) adopting an approach which exhibits and makes use of the rich geometrical structure of the subject. An opening chapter provides a brief history of complex analysis which sets it in context and provides motivation. ... Read more

Customer Reviews (3)

2-0 out of 5 stars Horrible introduction to complex analysis
This despicable book provides a narrow-minded and unattractive introduction to complex analysis. The brief chapter 0 on the history of the subject is thoroughly distorted to conform with the way the authors want to approach the subject. So, for instance, since the authors don't want to provide any motivation at any stage they simply make up the fact that none is needed, claiming that complex analysis "seems to have been the direct result of the mathematician's urge to generalize. It was sought deliberately, by analogy with real analysis." The truth is of course that the mathematicians who developed complex analysis mostly did so with concrete problems in mind, and were convinced of the value of the theory by its many excellent applications as well as its inner beauty, neither of which is conveyed by this book. These mathematicians would rather have poked their eyes out than investigate stupid nonsense problems such as the arc length of t+it(sin(pi/t)) (example 6.3.2, very representative). It must surely be one of the most hypocritical moments in textbook history when the authors claim to be ardent geometers, speaking of "the dangers of blind 'formula-crunching' analysis. Complex analysis is a highly geometric subject, and the geometry should not be despised." They do indeed plot t+it(sin(pi/t)) in their boring example 6.3.2, but that's the height of their geometric imagination. Formula-crunching is the only way they ever do anything and the entire presentation is deeply antigeometric. Indeed, the authors have worked hard to make sure that no-one obtains any intuitive understanding of the subject at all by postponing the few geometrically insightful topics that actually are discussed (conformality, harmonic functions, Riemann surfaces) until the very end and then treating them extremely briefly without indicating their importance for a geometric understanding of what complex functions, derivatives and integrals really are---which is what all sensible readers were asking themselves 250 pages earlier.

5-0 out of 5 stars Uses geometry of complex plane well to make reading easy.
Great book.

It's written for 2nd year university mathematics students. It covers all the standard topics from complex differentiability through to Cauchy's integral theorem, Taylor and Laurent series and then through toevaluating real, definite integrals and finishes up on Reinmann surfaces.The concepts are developed thoroughly from a very simple starting point.The text places a large emphasis on the geometry of the complex planemeaning that diagrams and graphs are used frequently in examples and proofsmaking reading miles easier. It starts with a few simple theorems intopology (which assume no prior knowledge of the topic) and use these togive convincing proofs of concepts such as Cauchy's theorem and Merton'stheorem later in the book.

The index is quite comprehensive.

3-0 out of 5 stars Pretty good book
Most of the material is well thought out. Though I wish the author would give more concrete examples of the theory. For example in parametrising of paths :|z|<2 i,-i he would notshow how to do this. Though the theory would give you an idea. It would be nice if more concreteexamples were shownin the text. Other than , there is much interesting material and most of th e exercises are doable without too much real analysis being neeeded/ ... Read more

36. Functions of One Complex Variable (Graduate Texts in Mathematics - Vol 11) (v. 1)
by John B Conway
Hardcover: 330 Pages (1978)
list price: US$64.95 -- used & new: US$45.76
(price subject to change: see help)
Asin: 0387903283
Average Customer Review: 4.0 out of 5 stars
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"This book presents a basic introduction to complex analysis in both an interesting and a rigorous manner. It contains enough material for a full year's course, and the choice of material treated is reasonably standard and should be satisfactory for most first courses in complex analysis. The approach to each topic appears to be carefully thought out both as to mathematical treatment and pedagogical presentation, and the end result is a very satisfactory book for classroom use or self-study." --MathSciNet ... Read more

Customer Reviews (8)

5-0 out of 5 stars Excellent Book
I have used this book back in my college days. I am amazed to see such a low rating on this book. This is one of the best books on complex analysis.
Mind you this is a Graduate Text in Mathematics. So it is intended to cover lot of ground using clear logical path. I agree to some extent that this book does not have lot of examples but a GTM is supposed to be like that. The way I used/read this book is to supplement it with other books on the topic. The proofs of theorems in this book are complete without any errors.

If you are a graduate student and want to learn complex analysis, this is the best book available out there.

4-0 out of 5 stars Nicebook , good level
This book isa classic.Is goodfor an master degree course in mathematics.

1-0 out of 5 stars Should be avoided.
I concur with the reviewer Sidhant. I had tons of frustrations with this book this semester - it's so annoying. I just finished and reviewed Munkres' topology book, and Sterling Berberian's Fundamentals of Real Analysis, and the difference between these books and Conway's is (respectively) like the difference between say Bach and pure cacophony: cymbals, screeches, sirens, horns, etc.

Some of my complaints include, but are not limited to:

- No examples whatsoever; there may be one or two per chapter, jammed lamely into the body of the text
- The "expository prose" did nothing to elucidate the underlying mathematics; often Conway babbles for a while, then says something like "the proof is left to the reader". It came to a point last month where I simply just stopped reading the text and started to focus on just the theorems and proofs
- There were errors in some proofs, of omission and of commission. The two ugliest proofs I've ever seen in mathematics lie in this book: (1) a standard composition theorem for analytic functions done by cases (?) which ended with "the general case follows easily", and the argument was built upon sequences (?). In other books, the result is proved in three lines; (2) the Casorati-Weierstrass theorem: same sloppiness, but Wikipedia saved me with an elegant four-line proof. The open mapping theorem was almost incoherent; and a crucial part of it was left as an exercise. I managed to get this part from Adult Rudin with no problems, though.
- the exercises: some are actually fine, but many are obtuse, and obtusely stated. Ultimately - and this is a huge problem - one cannot trust whether or not exercises were written correctly, because of too much general and ubiquitous sloppiness.
- chapter 2 (mapping properties of analytic functions, mobius maps) is so poorly written i had to skip it entirely.

I have a whole list of complaints here on paper, that I collected while reading this book to expose when I reviewed it. It's simply not worth more time and effort to transcribe them.

Not the whole book is bad, the homotopy integral is treated fairly well (i guess), as are the earlier parts of complex integration, and isolated singularities. But all this stuff is elementary - the later chapters are what counts, and the two chapters following integration are a mess. I hate having to clean up SO MUCH of this book.

I recommend looking at Robert B. Ash's book, as it's only 15 dollars (and free online), compared to the 60 dollars which this book is, and more importantly he makes very wise comments regarding math pedagogy on his webpage. In contrast, Conway in his webpage is pictured drinking martinis; he was probably on his twelfth one when he began the writing of this book.

EDIT: i've been working through ash's online book from the start, and i notice the proofs are far more slick, yet far more intuitive. there are many more problems, and better, than in conway. plus there are hints and solutions - don't peek unless you really don't know where to start! ultimately i'm starting over somewhat. i can't pretend i know nothing after conway, but i've abandoned his book completely. i wasted a graduate semester on conway's garbage.

2-0 out of 5 stars Not recommended
This book was the recommended textbook for a course in Complex Analysis I took at college. I had already done a 1st course on analysis, but that didn't help me too much. This book, littered with loads of proofs and lemmas, is a little too terse, and the author expects students to understand a lot on their own. Concepts in Complex Analysis need to be demonstrated using examples, and diagrams, if possible. Like for eg. the concept of branches in complex functions. The book starts of defining the complex logrithmic function. The author never says what a branch exactly is. He writes down a hell lot of proofs and expects the student to figure out that the complex logarithm is infact a multi-valued function, and that a branch is essentially a "slice" of this multivalued function. Similiar problems crop up when the author discusses fractional linear transforms. Instead of showing whats happening with simple diagrams, the author makes things look extremely complicated with his equations and theorems. This book makes learning complex analysis a very mechanical exercise, devoid of all fun.

5-0 out of 5 stars A good read
We're using this book for my graduate level complex analysis course, and over all, I'm pleased with it.Aside from some goofy notation (i.e., an empty box to represent the empty set?), it's pretty well written.The pace of the text isn't too fast or too slow, and there are plenty of exercises of a varying degree of difficulty to help you learn the material.Another nice feature is the price; one can find it for less than $50, so it'll make a nice reference book even if it wasn't assigned for a class. ... Read more

37. The Logic Of Failure: Recognizing And Avoiding Error In Complex Situations
by Dietrich Dorner
Paperback: 240 Pages (1997-08-04)
list price: US$19.00 -- used & new: US$10.99
(price subject to change: see help)
Asin: 0201479486
Average Customer Review: 4.5 out of 5 stars
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our modern world, even though it was appropriate to older, simpler times. Working with imagination and often hilarious computer simulations, Dietrich Dorner provides a compass for intelligent planning and decision-making that can sharpen the skills of managers and policy-makers everywhere. ... Read more

Customer Reviews (52)

5-0 out of 5 stars a must-read for anyone interested in the world
for anyone interested in psychology, sociology, politics, economics, history, government...

Highly recommended! A good place to start building one's foundation in any of the above interests.

5-0 out of 5 stars I gave it to my 15 years old son to read it.
Great book written in 1989 by West German Professor Dorner. This is a good introduction into System dynamics and System thinking. The book gives several mental models of how people "attack" complex problems and why they often fail. Dorner describes several psychological experiments that help to differentiate "bad decision maker" form "good decision makers," as well as mental traps that lead to failures.Based on this analysis he presents his model of decomposition and planning. At the end of the book Dorner quotes Clausewitz that "...War is not an infinite mass of minor events... War consists rather of single, great, decisive actions, each of which needs to be handled individually." Such "strategic thinking" requires far greater expenditure of mental energy argues Dorner.

Dorner ends his book with the thought that "...If we cannot form a picture of a temporal configuration, we cannot adjust our thinking and actions to take that temporal pattern into account... We human being are creature of the present. But the world today must learn to think in temporal configuration."

The book is easy to read and comprehend. I gave it to my 15 years old son to read it. Hopefully he will use my advise to read it earlier in his life.

5-0 out of 5 stars Necessary reading for aspiring planners
Any person working as a so-called "change agent" should read this book. In the 1980s, Dörner and other German researchers conducted experimental simulations to investigate how people handle complex tasks. In the same vein as SimCity or Civilization, these experiments put people in a leadership role where they could affect many variables. The simulations range from rural African tribes to English factory towns to ecological balancing acts. What Dietrich does not do is assemble a step-by-step approach to tackling complex problems. Instead, this book analyzes the multiple ways that individuals failed to anticipate problems, understand complex systems, and manage time throughout the process.

One area where this book shines is the detailed analysis of how people analyze complex models. Participants in the simulations described above were recorded as they interacted with the researchers. The common tactics that led to failure were an inability to address multiple issues simultaneously, assumption that success depends on a single variable, and willful ignorance of the effects of past decisions. By contrast, the successful participants created dynamic models of the simulation, constantly gathered information, and did not rely on reductive hypotheses.

The chapter on goal setting was surprisingly interesting. The taxonomy he uses for goals includes five dimensions and the complications inherit to goals on these spectrum. For instance, a _clear, specific, and positive_ goal might be predicated on a _general and implicit_ goal (in the case of a firm seeking to reduce its carbon footprint by 20% in 2 years the general, implicit goal is that it intends to fight climate change). Dörner does an excellent job of identifying the ways that goals can conflict with one another along with the various options that exist for addressing these conflicts.

The book is a thorough anatomy of the failure of human intelligence to grasp complexity and dynamic interactions. One silver lining, and optimistic touch is that practitioners (people working in project management) did better at the simulations than laymen. The most plausible critique that I see is that informal buffers to systemic failures exist in most situations. For example, if Herman Haworth is promoted to the role of Senior Planner for a town, it seems likely that his colleagues will assist him in identifying the best strategies from their past experiences. As any non-hermit clearly knows, groups can make terrible mistakes. (Dörner cites the case of Chernobyl where a team of nuclear scientists failed to realize the mistakes that led to a meltdown.)If I were teaching a course on planning theory I would make this book mandatory reading.

3-0 out of 5 stars Computer simulations
At first I found the book interesting, but then I realized that i wasn't really offering up much in the way of solutions.The conclusions are sometimes contradictory and confusing.In one computer simulation experiment, the author concludes that, in general, the participants that made more decisions were more successful.In another similar experiment later, the participants that made fewer decisions were more successful.The author tries to explain why that finding might have been the case, but to me, the explanation wasn't all that satisfactory.

The book is based on the results of experiments with participants being asked to make decisions that determined the outcome of computer simulations.Participants who were best able to predict and control the simulations are branded as successes, and likewise, those who couldn't are failures.There are a couple of problems I saw with this approach:

First, the definition of success seemed ill-defined.In the Tanaland example in Chapter One, for example, anyone who create a rise in population followed by a decline in population is branded as a failure.In an attempt to improve living conditions, participants create overpopulation, which led to famines.The book claims that this should have been obvious, but participants couldn't predict the complex interaction of multiple, simulated variables, and thus failed.I wonder what would happen if the participants took no action at all?I think what may really be going on here is that the authors have set a trap for the participants, whereby an inherently unstable environment was created, and small changes to input variables created large, unstable swings in the output variables.The only person who succeeded in controlling the population made lots and lots of small corrections that would be impossible to implement in any real-world scenario.The simulation doesn't seem to have much bearing on real-life.

Second, as a computer scientist, I know from computer science theory that computer programs are inherently unpredictable.You can't, for example, write a computer program that will take as input another computer program, and produce as output a value of "true" or "false" as to whether the given computer program will ever finish running.This is famously known as the Halting Problem.If you want to know what happens in a simulated world after 10 simulated years, with a tsetse fly control program introduced in year 1, the only way to find the answer is to run the simulation for 10 years, with a tsetse fly control program introduced in year one.There are special cases where predictability is possible, but in the most general sense, the only way to know what a computer program will do is to run the computer program and see what it does.

The same thing is true of the real world.The future is inherently unpredictable.Want to know what will happen in 10 years?Wait 10 years, and you'll find out.

So in a sense, what the author is basically saying is "The reason why even really smart people can't predict the future is because the future can't be predicted."

5-0 out of 5 stars A book that will make you wiser
I read this book years ago and have been recommending it ever since. I always think it is better to learn from other's mistakes instead of your own and this book goes a long way in achieving this. This book has given me new insights to problems I have faced. I have relied too much on logic to solve problems in the past and now take the time to get all of the facts before I go ahead with a solution. The book also does a great job in explaining people's actions which at times make no sense. ... Read more

38. Complex Variables: Second Edition (Dover Books on Mathematics)
by Stephen D. Fisher
Paperback: 448 Pages (1999-02-16)
list price: US$18.95 -- used & new: US$12.03
(price subject to change: see help)
Asin: 0486406792
Average Customer Review: 4.5 out of 5 stars
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Editorial Review

Product Description
Hundreds of solved examples, exercises, and applications help students gain a firm understanding of the most important topics in the theory and applications of complex variables. Topics include the complex plane, basic properties of analytic functions, analytic functions as mappings, analytic and harmonic functions in applications, and transform methods. Perfect for undergrads/grad students in science, mathematics, engineering. A three-semester course in calculus is sole prerequisite. 1990 ed. Appendices.
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Customer Reviews (8)

5-0 out of 5 stars Simple, excellent
Ideal for undergraduate mathematics courses. Excellent introductory book to Complex Analysis.(with some more advanced chapters). Also, it is not expensive.

5-0 out of 5 stars I like this book.
My teacher used this book for the class. So we bought this books. The book is good.

5-0 out of 5 stars Cheap
I was worried for the cost of my books this quarter, but this book was affordable and it was great having it new.

4-0 out of 5 stars Inexpensive Intro to Complex Variables
Dover publications are inexpensive excellent-quality textbook-like items for self-study or review, and this item is no exception. I am using this book to learn complex variables for the first time. Examples are clear, with enough "missing" steps to challenge the student without confusion. The chapter on Analytic and Harmonic functions and their applications is particularly good. There are certainly more costly books, but this one packs in a lot of information for the money.

5-0 out of 5 stars an excellentbeginning
Fisher's book is ideal for a first course in complex variables: the complex plane, geometry of the plane, analytic functions (zeros, singularities, residue computations), Cauchy-and residue theorems, harmonic functions, conformal mappings, boundary value problems, applications, and a lovely last chapter on transform theory, Fourier, Laplace etc, and using contour integration.

Pedagogical features: The figures and illustrations are lovely! The exercises are many and well designed. Inclusion of solutions to odd-numbered exercises represents a good compromise. The book will work well for a mixed audience, students in math, in science, and in engineering alike. The presentation starts with a review of complex numbers functions and sequences, moves quickly to central aspects of complex function theory, elementary geometry, Mobius transformations, and conformal maps.

The book was published first in 1990, but reprinted since by Dover, starting in 1999. It is suitable as a text or as a supplement in a beginning course in complex function theory, at the undergraduate level. And it is suitable for self-study. While it contains the standard elements in such a course, we note that a systematic treatment of physical problems comes relatively late, in Section 4.2, beginning on page 254 (a little past halfway into the book.) Some readers might want to begin with that.

There are other Dover titles on the same subject, also elementary and suitable for a first course. They are slanted differently, and in particular, they point to different applications. Fisher's inclusion of transform theory gives this book an edge. See however also Churchill-Brown.

Other Dover books: We recommend the books by Fisher, Volkovyskii et al, Silverman, Schwerdtfeger, and Flanigan; all inexpensive! These books cover the fundamentals in functions of a single complex variable: analytic, harmonic, conformal mappings, and related applications. Further, there are non-Dover books such as: (a) R. V. Churchill - J. W. Brown, and (b) J. E. Marsden - M. J. Hoffman; both a lot more expensive. Review by Palle Jorgensen, August, 2006.
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39. Nine Introductions in Complex Analysis - Revised Edition, Volume 208 (North-Holland Mathematics Studies)
by Sanford L. Segal
Hardcover: 500 Pages (2007-10-24)
list price: US$218.00 -- used & new: US$170.04
(price subject to change: see help)
Asin: 0444518312
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Editorial Review

Product Description
The book addresses many topics not usually in "second course in complex analysis" texts. It also contains multiple proofs of several central results, and it has a minor historical perspective.

- Proof of Bieberbach conjecture (after DeBranges)
- Material on asymptotic values
- Material on Natural Boundaries
- First four chapters are comprehensive introduction to entire and metomorphic functions
- First chapter (Riemann Mapping Theorem) takes up where "first courses" usually leave off ... Read more

40. Classical Complex Analysis (Pure and Applied Mathematics)
by Mario Gonzalez
 Hardcover: 792 Pages (1991-09-24)
list price: US$99.95 -- used & new: US$235.07
(price subject to change: see help)
Asin: 0824784154
Canada | United Kingdom | Germany | France | Japan
Editorial Review

Product Description
Text on the theory of functions of one complex variable contains, with many elaborations, the subject of the courses and seminars offered by the author over a period of 40 years, and should be considered a source from which a variety of courses can be drawn. In addition to the basic topics in the cl ... Read more

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