Book Description
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 (19)

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.

pedgogically worthless
I'm not sure why the other reviews are so positive.The book is very thorough and rigorous I'm sure, but the explanations are terrible.Everyone I've talked to in my class agrees that it's extremely difficult to learn from if you don't already know complex analysis, bbecause the definitions and order of treatment are very unintuitive.Example: residue at a is defined as the number R that makes f-R/(z-a) the derivative of a single-valued analytic function in 0<|z-a| A classic at an obscene price
This book has for decades been THE classic graduate level text in Complex Analysis.It is important to point out that it is not for beginners.To learn complex analysis from the ground up, my own recommendations are the book by Saff & Snider or the somewhat dated, but delightfully conversational book by Stewart and Tall.

Not only does this book require some previous understanding of Complex Analysis, but it also requires that mysterious ability called "mathematical maturity" - the ability to fill in omitted steps and details when following an argument.But, for a person posessing the prerequisites, this is a fine book.

However, any review of this book would be incomplete if it didn't address the issue of price.Advanced math books are all expensive, it is true.But this book is a particularly egregious case of price-gouging.For one thing, the book was written many years ago, so the publisher is not trying to recover any recent high cost of paying the author for his work.Secondly, the book is only something like 336 pages long (much shorter, for example, than a mystery novel by Elizabeth George).It comes out to about 40 cents per page!

Math students, as a rule, are not wealthy people.The price of this book is simply offensive.You can save more than 25% off the price of this book and get BOTH volumes of the Conway book, "Functions of One Complex Variable".I'm not thoroughly familiar with that Conway book, but I've browsed it online.It seems to be well written and has more material (in the two volumes together) than this (Ahlfors) book has.Furthermore, just in principle, I don't think a publisher should be rewarded for this kind of unwarranted greed and price-gouging.Refuse to buy this until the price becomes more reasonable.

why 4 stars and not five?
I was a (French)graduate student in France some 25 years ago and I would have been delighted to use this book if translated in French; I had to rely on Cartan's book which is a very good book too but which takes for granted that one already knows quite a lot on complex numbers, series, convergence and topology...As a substitute to Cartan, there was a translation of Rudin's real and complex analysis which begins with measure theory...Anyway, it is very difficult to learn this subject in any book without advice from instructors and attending lectures.
There could be more worked examples in this book but it is nota self teaching book (neither is Cartan's...which is very similar in essence to Ahlforsbut more narrow minded). For a more "basic" book in the subject, see Marsden's Basic complex analysis but proofs are often mixed up with exercises...which does not suit everybody. My final point is the following: this book contains much more stuff to work at or to think about than its French counterpart; moreover,in this book, efforts are made to avoid formalism (Bourbaki?). US maths students are very lucky indeed. But the book is certainly too expensive.

A Classic
Another classic text from graduate school (text for class taught by P.L. Duren) providing a background in introductory complex analysis.This book is nicely written with some elegant exploration of the motivations and backgound for a number of the central concepts.This may be surprising given the physical slimness of the text (I noticed elegance of the exposition and attention to motivation on a recent reread of some of the book after nearly twenty years -- I had not remembered this exposition, perhaps because the reading in graduate school was not quite as "liesurely" (unless "fear driven" and "pressured" are synonyms for "liesurely").The theory topics are nicely covered -- if, however, you are an engineer looking for methods of calculating complex intgral there are other texts. ... Read more

Book Description
This reader-friendly book presents traditional material using a modern approach that invites the use of technology. Abundant exercises, examples, and graphics make it a comprehensive and visually appealing resource.Chapter topics include complex numbers and functions, analytic functions, complex integration, complex series, residues: applications and theory, conformal mapping, partial differential equations: methods and applications, transform methods, and partial differential equations in polar and spherical coordinates.For engineers and physicists in need of a quick reference tool. ... Read more

Customer Reviews (1)

A Very well written text
This book is by far one of the best out there in the area of complex analysis.The author combined application with detailed proofs, giving the reader everything that he/she needs.A course with emphasis on applications can be easily planned out using this as the text.Similarly, if an instructor decides to focus more on proofs, the structure of this book allows this too.Simply put, this is the best out there.

You might also be wondering what I think of Churchill's text, as compared to this one.Yes I agree that it is also a good book.However Churchill's proofs are sometimes too hand-waving.Occassionally, I find Churchill using terms like "see exercise for details of this proof".Now, I really dislike this when author does this.This book by Asmar, rarely makes such comment and this therefore is also one of the reasons that I like about this book.

So trust me, if you want to learn about complex analysis, GET THIS BOOK!!Besides, the 2nd half the book talks about pdf, if you are an engineer and needs to deal with partial differential equations at work, this is a 2-IN-ONE text!!!!!

The book is worth every penny that I paid for!!Asmar ROCKS!!
... Read more

Book Description
In this second edition of a Carus Monograph Classic, Steven G. Krantz, a leading worker in complex analysis and a winner of the Chauvenet Prize for outstanding mathematical exposition, develops material on classical non-Euclidean geometry. He shows how it can be developed in a natural way from the invariant geometry of the complex disk. He also introduces the Bergmann kernel and metric and provides profound applications, some of which have never appeared in print before. In general, the new edition represents a considerable polishing and re-thinking of the original successful volume. A minimum of geometric formalism is used to gain a maximum of geometric and analytic insight. The climax of the book is an introduction to several complex variables from the geometric viewpoint. Poincaré's theorem, that the ball and bidisc are biholomorphically inequivalent, is discussed and proved. ... Read more

Book Description

With this second volume, we enter the intriguing world of complex analysis. From the first theorems on, the elegance and sweep of the results is evident. The starting point is the simple idea of extending a function initially given for real values of the argument to one that is defined when the argument is complex. From there, one proceeds to the main properties of holomorphic functions, whose proofs are generally short and quite illuminating: the Cauchy theorems, residues, analytic continuation, the argument principle.

With this background, the reader is ready to learn a wealth of additional material connecting the subject with other areas of mathematics: the Fourier transform treated by contour integration, the zeta function and the prime number theorem, and an introduction to elliptic functions culminating in their application to combinatorics and number theory.

Thoroughly developing a subject with many ramifications, while striking a careful balance between conceptual insights and the technical underpinnings of rigorous analysis, Complex Analysis will be welcomed by students of mathematics, physics, engineering and other sciences.

The Princeton Lectures in Analysis represents a sustained effort to introduce the core areas of mathematical analysis while also illustrating the organic unity between them. Numerous examples and applications throughout its four planned volumes, of which Complex Analysis is the second, highlight the far-reaching consequences of certain ideas in analysis to other fields of mathematics and a variety of sciences. Stein and Shakarchi move from an introduction addressing Fourier series and integrals to in-depth considerations of complex analysis; measure and integration theory, and Hilbert spaces; and, finally, further topics such as functional analysis, distributions and elements of probability theory.

Customer Reviews (5)

The exercises are not very good
I used this book in a first year graduate course.I found the exposition not very clear, and the exercises particularly uninteresting.If you have the choice, I definitely recommend Gamelin's Complex Analysis instead.

bad book
This book is not helpful.There are no answers to problems.Symbols used in the problems are not explained.It is difficult to learn unless you have someone explaining the concepts for you.I would not buy this book now.

Beautifully written !
This is a very beautifully written book on complex analysis. It is not very easy to read though, especially if you've never been exposed to the subject before. Most proofs are clearly presented, and can be easily understood by the mature reader. Other proofs require filling in the gaps to get the whole picture. As far as problems go, there's a list of relatively easy exercises at the end of each chapter. Following the exercises is a list of problems which require some head scratching. Overall, I had a fun time reading and learning from this book.

A Gem
In reviewing a textbook, one should consider the background of the book's audience.I believe that this text by Stein and Shakarchi on complex analysis is outstanding, and is appropriate for a student who has the background of a course in real analysis at the level of Rudin's "Principles of Mathematical Analysis".

The text has a number of strengths.Some of these are the following:

1. The choice of material and the order of presentation are superb.Just to give you a sample, within the first 100 pages, the authors cover Runge's Theorem, the Schwarz Reflection Principle, Riemann's Theorem on Removable Singularities, the Casorati-Weierstrass Theorem, Rouche's Theorem, and the homotopy version of Cauchy's Integral Theorem.The novice is thus treated to some beautiful mathematics very quickly.

2. The statements of theorems and definitions are simple and clear.The authors carefully avoid unnecessary technicalities that would only tend to confuse the beginner and obfuscate the essential concepts.

3. The proofs are very clear and elegant.The main ideas are emphasized, and just enough details are given so that a diligent student with the background stated above will be able to grasp the arguments.

4. The examples are nontrivial, and worked out in detail.Some may prefer a greater number and variety of examples, but I found that there were enough to illustrate the theory.

5. The authors pay considerable attention to motivating the development of ideas.It seems to me that the authors were keen to enhance the reader's intuition for the subject and to impart an appreciation for the inherent beauty of complex function theory.

6. The book is very well edited.There are very few typos, none of which should cause difficulty for a beginner.

For these reasons and others, I highly recommend this book to anyone who desires to learn complex analysis, or who simply desires to learn some beautiful mathematics, and who has the suggested background.Stein and Shakarchi have written a book which is a joy to read!

very good indeed
The two authors are indeed very good writers. This book presents the elements of complex analysis at the graduate level (so the assumption is that the reader has gone through undergraduate real and complex analysis). All the topics covered are covered well (I especially like their treatment of the Prime Number Theorem and Elliptic Functions). Note: theorems of Picard and Mittag-Leffler are not proved in the textbook - they are actually assigned as exercises for the reader to prove). If you need the proofs of these theorems, look them up elsewhere. Overall, a very solid book. ... Read more

Book Description
This textbook is an introduction to the classical theory of functions of a complex variable. The author's aim is to explain the basic theory in an easy to understand and careful way. He emphasizes geometrical considerations, and, to avoid topological difficulties associated with complex analysis, begins by deriving Cauchy's integral formula in a topologically simple case and then deduces the basic properties of continuous and differentiable functions. The remainder of the book deals with conformal mappings, analytic continuation, Riemann's mapping theorem, Riemann surfaces and analytic functions on a Riemann surface. The book is profusely illustrated and includes many examples. Problems are collected together at the end of the book. It should be an ideal text for either a first course in complex analysis or more advanced study. ... Read more

Product Description
This classic book gives an excellent presentation of topics usually treated in a complex analysis course, starting with basic notions (rational functions, linear transformations, analytic function), and culminating in the discussion of conformal mappings, including the Riemann mapping theorem and the Picard theorem. The two quotes above confirm that the book can be successfully used as a text for a class or for self-study. ... Read more

Customer Reviews (2)

Just what I expected
The book was just as expected.Took a little long to be delivered, but overall I was satisfied.

Helpful but short
The Student Guild is helpful, but keep in mind that only the bulleted problems from Basic Complex Analysis are explained (only a few from each section).And the cost was a little high, expecially considering it's 135 pages. ... Read more

Book Description
This book discusses a variety of problems which are usually treated in a second course on the theory of functions of one complex variable. It treats several topics in geometric function theory as well as potential theory in the plane. In particular it covers: conformal equivalence for simply connected regions, conformal equivalence for finitely connected regions, analytic covering maps, de Branges' proof of the Bieberbach conjecture, harmonic functions, Hardy spaces on the disk, potential theory in the plane. The level of the material is gauged for graduate students. Chapters XIII through XVII have the same prerequisites as the first volume of this text, GTM 11. For the remainder of the text it is assumed that the reader has a knowledge of integration theory and functional analysis. Definitions and theorems are stated clearly and precisely. Also contained in this book is an abundance of exercises of various degrees of difficulty. ... Read more

Book Description

This book gives a comprehensive introduction to complex analysis in several variables. It clearly focusses on special topics in complex analysis rather than trying to encompass as much material as possible. Many cross-references to other parts of mathematics, such as functional analysis or algebras, are pointed out in order to broaden the view and the understanding of the chosen topics. A major focus is extension phenomena alien to the one-dimensional theory, which are expressed in the famous Hartog's Kugelsatz, the theorem of Cartan-Thullen, and Bochner's theorem.

Customer Reviews (1)

a unique collection
This nice little book by Volkovyskii et al (translated from Russian) is a collection of exercises, and it covers the central aspects of and themes in complex function theory, elementary geometry, harmonic and analytic functions. It contains graphics and illustrations, and the last third of the book consists of answers and solutions.

The central topics are (in this order) complex numbers, calculus and geometry of the plane, conformal mappings, harmonic functions, power series and analytic functions, and the standard Cauchy-and residue theorems, symmetry, Laurent series, infinite products, ending with a brief chapter on Riemann surfaces, and applications to hydrodynamics and electrostatics. All the material is presented in the form of exercises.

The book was published first in 1965, but reprinted since by Dover. It is suitable and recommended as a supplement in a standard course in complex function theory, late undergraduate level, or beginning graduate.

Of other Dover titles on the same subject we recommend the books by Flanigan, Schwerdtfeger, and Silverman. Review by Palle Jorgensen, August 5, 2006.



... Read more

Book Description
This book is intended to serve as a text for first and second year courses in single variable complex analysis. The material that is appropriate for more advanced study is developed from elementary material. The concepts are illustrated with large numbers of examples, many of which involve problems students encounter in other courses. For example, students who have taken an introductory physics course will have encountered analysis of simple AC circuits. This text revisits such analysis using complex numbers. Cauchy's residue theorem is used to evaluate many types of definite integrals that students are introduced to in the beginning calculus sequence. Methods of conformal mapping are used to solve problems in electrostatics. The book contains material that is not considered in other popular complex analysis texts. For example, one chapter is devoted to an analysis of multivalued functions, with applications to the evaluation of certain types of integrals. Another chapter deals with the singularity structure of functions that are defined by integrals which cannot be evaluated in terms of elementary functions. A third chapter develops dispersion relations, which are mathematical tools for determining a complete function from a knowledge of just the real part, or just the imaginary part of the function. ... Read more

Customer Reviews (1)

elegant and useful theorems
The text takes you from simple complex number manipulation all the way to contour integration. Cohen draws in examples from various sciences and engineering, to illustrate the myriad usages of complex analysis.

If you are a student majoring in the physical sciences, engineering or, of course, maths, this text can be valuable in teaching the key ideas. Like residues, Laurant series, index numbers and the Residue Theorem. While some of you might at first wonder at the relevance of this to anything useful, the book's examples should disabuse you. Culminating in being able to evaluate a contour integral by finding the enclosed singularities. Elegant and beautiful. Hopefully, you will agree by the time you've gone through the book. ... Read more

Book Description
This volume contains all the exercises, and their solutions, for Serge Lang's fourth edition of "Complex Analysis," ISBN 0-387-98592-1. The problems in the first 8 chapters are suitable for an introductory course at the undergraduate level and cover the following topics: power series, Cauchy's theorem, Laurent series, singularities and meromorphic functions, the calculus of residues, conformal mappings, and harmonic functions. The material in Chapters 9-16 is more advanced. The reader will find problems on Schwartz reflection, analytic continuation, Jensen's formula, the Phragmen-Lindeloef theorem, entire functions, Weierstrass products and meromorphic functions, the Gamma function and Zeta function. This volume also serves as an independent source of problems with detailed answers beneficial for anyone interested in learning complex analysis. ... Read more

Customer Reviews (2)

INCOMPLETE EXPLANATIONS
This book cannot be used without purchasing the actual book which it represents. This book has some solutions for another complex analysis book. What I thought was, that this book is similar to something like Schaum's solved problems (which is independent and not dependent on another book). In many cases, there is no work shown at all, and simply the answers. So its really of no use and has a deceptive title. I already had 4 other books in complex analysis, so there was no need for me to purchase another book which it represents.

The Right Stuff !!!!!!!!!!!!!!
I bought this book with the goal to enhance my problem solving skills on complex analysis. I am a theoritical physics student and needed to gain a very comprehensive and operational understanding of the topic. This book had it all: it's very well written, very rigourous and gives an extra dimension to just reading a pure text explaining the theory of the subject. I wish we had this type of books in physics ! Lang's book and Shakarchi's solutions are the winning combination to learn complex analysis!!!!! 2 thumbs up ... Read more

Book Description
Complex analysis is a classic and central area of mathematics, which is studied 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.This is the latest addition to the growing list of Oxford undergraduate textbooks in mathematics, which includes: Biggs: Discrete Mathematics 2nd Edition, Cameron: Introduction to Algebra, Needham: Visual Complex Analysis, Kaye and Wilson: Linear Algebra, Acheson: Elementary Fluid Dynamics, Jordan and Smith: Nonlinear Ordinary Differential Equations, Smith: Numerical Solution of Partial Differential Equations, Wilson: Graphs, Colourings and the Four-Colour Theorem, Bishop: Neural Networks for Pattern Recognition, Gelman and Nolan: Teaching Statistics. ... Read more

Customer Reviews (5)

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.

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.

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.

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!

Very clear exposition
I never formally got taught complex analysis, and used this to cram the subject into my head.Very readable and logical arguments, although it tends more toward functionality (being aimed at undergraduates).Doesn'tquite give a working knowledge - look elsewhere for problems andapplications. ... Read more

Product Description
Since the 1960s, there has been a flowering in higher-dimensional complex analysis. Both classical and new results in this area have found numerous applications in analysis, differential and algebraic geometry, and, in particular, contemporary mathematical physics. In many areas of modern mathematics, the mastery of the foundations of higher-dimensional complex analysis has become necessary for any specialist. Intended as a first study of higher-dimensional complex analysis, this book covers the theory of holomorphic functions of several complex variables, holomorphic mappings, and submanifolds of complex Euclidean space. ... Read more

Book Description
This text is part of the International Series in Pure and Applied Mathematics. It is designed for junior, senior, and first-year graduate students in mathematics and engineering. This edition preserves the basic content and style of earlier editions and includes many new and relevant applications which are introduced early in the text. ... Read more

Customer Reviews (29)

Very poor book
Brown and Churchill's book is neither rigorous nor intuitive; it is a true pedagogical nightmare. The authors are extremely sloppy with their exposition, structure and rigor.
Some trivial results are "proved" with pedantic detail, but even there the proof is not exhaustive. As an example, to prove sufficient conditions for differentiability (p. 63-5), two pages are devoted to setting up some elaborate structure, but the real meat (basically Taylor's theorem) is not even mentioned, rather the authors cite another text. Similarly, equality of mixed partial derivatives is waved off as "a theorem in advanced calculus." What is complex analysis but advanced calculus, and why do the authors here devote space to prove thoroughly trivial results (e.g. limit of sums converges to sum of limits), while leaving out other important foundations?
A similar sloppiness is shown even in those results that are more fully proved in the book. For example, the theorem presented in Section 26 depends on a theorem in Section 68! Pedagogically this is inexcusable, as the authors introduce these results willy-nilly, not as a coherent whole; the book must be read at least twice to check its consistency!
The layout of the book is awfully confusing. There is practically no white space, and a single font and font size are used throughout the book, for explanations, theorems, examples and exercises. Examples sometimes are placed within the section they illustrate, and sometimes bizarrely they are given their own section. This means that the table of contents cannot indicate the relative importance of book content. Likewise proofs are sometimes given their own sections, sometimes buried in an overly large section.
The exercises are mostly computational, and usually they are spoiled by "hints" that are so exhaustive that the only thing left for the student to do is to move some symbols around as directed by the book.
In general, the book causes both my mathematically rigorous colleagues and my application oriented colleagues to cringe in pain. Compared to some other works on analysis, this volume is a true abomination. Walter Rudin's Principles of Mathematical Analysis is an exquisite, mathematically thorough and rigorous treatise on the subject, in which practically every exercise is meaningful. That the publisher of the present book dares to charge as much money for this seventy-year old volume as Rudin's book costs is farcical.

It is what it is
God knows this book is used by everybody and their brother to teach Complex Variables.Why, I do not know.Dry as dust and even more boring."Proofs" are minimal and the exercises are plug and chug.Still, it has the acceptance of academia.Enjoy.

Better for Engineering, Physics, and others in the Applied areas, than for pure mathematics students
This is a nice book for understanding the basic concepts of early Complex Analysis.The integral formulas, residue theorems, Fourier Analysis, infinite series/sequences, etc. are all covered.There are plenty of exercises and examples.Everything is so clearly presented, that it is easy for people with very little background in analysis to read (ie, you don't really need real analysis before reading this book).

My problems with the book are thus:There are very, very few proofs to any of the theorems.I'd rather have more proofs than examples.The problems are almost all computational.Almost none of the exercises require much thought, although some of them will take a while to do.There is no discussion on the importance of certain topics to the wider context of math.No discussion of certain standard complex-valued functions like elliptic functions, zeta functions, or gamma functions.

If anything, I see this as mostly a how-to book for engineers and physicists who come across complex variables in their work.For math students, I'd recommend the books by Shakarchi/Stein, Lang, Conway, Ahlfors.

needs complete student manual
could be better if included the solution manual for all the sections, not only for chapters 1-7

Very clear, great for learning and understanding quickly, a bit slow at times
This book is simply clearer than any other complex analysis book I've read, although it's not particularly advanced or concise.

This book is a great text for undergraduates studying complex analysis for the first time.It does not assume a strong background in rigorous analysis, making the material accessible to a wider audience.

At times I find that this book moves a bit slow for my personal taste, but what it loses in speed it makes up for in clarity.The explanations are always clear.I find that I never get stuck in a proof in this book.If there is a certain topic that I absolutely must understand, and I want to understand in a straightforward, useful way, as quick as possible, I turn to this book.

I would recommend this book for self-study as well as a textbook at the introductory level.It is not a particularly advanced book, and is not comprehensive as a reference for more advanced students, nor would it be a great choice for a graduate or advanced course. ... Read more

Book Description
Complex Analysis with Mathematica offers a new way of learning and teaching a subject that lies at the heart of many areas of pure and applied mathematics, physics, engineering and even art. This book offers teachers and students an opportunity to learn about complex numbers in a state-of-the-art computational environment. The innovative approach also offers insights into many areas too often neglected in a student treatment, including complex chaos and mathematical art. Thus readers can also use the book for self-study and for enrichment. The use of Mathematica enables the author to cover several topics that are often absent from a traditional treatment. Students are also led, optionally, into cubic or quartic equations, investigations of symmetric chaos, and advanced conformal mapping. A CD is included which contains a live version of the book, and the Mathematica code enables the user to run computer experiments. ... Read more

Customer Reviews (1)

A true delight
What a wonderful and delightful book. The author has taken a well-worn topic and infused it with insight and energy. Best of all, the author communicates simply and clearly. He has brought graduate complex analysis to the masses; I wish that I had a book like this as an undergraduate. It is also a great read: the kind of pick you could pick up and go cover to cover with. However, you'll probably want to be at your keyboard trying out his many examples. The unique thing about this tome is that it is well-written, it is mathematically ambitious and it is an invaluable reference for how to use Mathematica. Also, as we have come to expect from Cambridge, this book has excellent production quality. ... Read more

Book Description
Second Edition features the latest tools for uncovering the genetic basis of human disease

The Second Edition of this landmark publication brings together a team of leading experts in the field to thoroughly update the publication. Readers will discover the tremendous advances made in human genetics in the seven years that have elapsed since the First Edition. Once again, the editors have assembled a comprehensive introduction to the strategies, designs, and methods of analysis for the discovery of genes in common and genetically complex traits. The growing social, legal, and ethical issues surrounding the field are thoroughly examined as well.

Rather than focusing on technical details or particular methodologies, the editors take a broader approach that emphasizes concepts and experimental design. Readers familiar with the First Edition will find new and cutting-edge material incorporated into the text:

• Updated presentations of bioinformatics, multiple comparisons, sample size requirements, parametric linkage analysis, case-control and family-based approaches, and genomic screening
• New methods for analysis of gene-gene and gene-environment interactions
• A completely rewritten and updated chapter on determining genetic components of disease
• New chapters covering molecular genomic approaches such as microarray and SAGE analyses using single nucleotide polymorphism (SNP) and cDNA expression data, as well as quantitative trait loci (QTL) mapping

Molecular biologists, human geneticists, genetic epidemiologists, and clinical and pharmaceutical researchers will find the Second Edition a helpful guide to understanding the genetic basis of human disease, with its new tools for detecting risk factors and discovering treatment strategies. ... Read more

Customer Reviews (2)

Good for context and historical understanding
It's a good book for historical context and perspective from true experts in the field. The field of human genetics advances at the speed of light - if you want up tothe minute information, read journal articles.

Already out of date
I bought this book on the recommendation of a professor but it really isn't that good of book. It is already out of date as it focuses primarily on linkage analysis with only a cursory look at association studies. Moreover most of the coverage of association is family based studies and not the more common case-control design.

Finally, I bought this book b/c it mentions that it covers multiple comparisons - my area of research. It doesn't at all! There is a slight mention that multiple comparisons can be a problem but that is it!

There are much better books out there... ... Read more

Book Description
"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 (6)

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.

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.

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.

Very Good quality and speed
I got this book very quickly and it's really very good. Thanks

a good book
An ideal text for a first-year graduate students in mathematics studying Compex Analysis. And this depend how the professor present the material. The exposition is complete and very clear, including a lot of optional material for the curious.which could be very useful to those preparing for a qualifying exam in analysis at the PhD level. Overall, recommend text.
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