Book Description
The leading authority on system dynamics explains this approach to organizational problem solving, emphasizing simulation models to understand issues such as fluctuating sales, market growth and stagnation, the reliability of forecasts and the rationality of business decision-making. The CD includes modeling software from Vensim, ithink, and PowerSim.
Customer Reviews:
One of the best SD books with connection to practical work.......2007-10-06
"Business Dynamics" is a great book leading the newcomer -as myself- into the field of SD and the experienced system dynamicist can use it as a knowledge pool.
Even though the book is rather expensinve -and heavy alike- it covers great wisdom of John Sterman (he is by the way a scholar of the founder of the field, Jay W. Forrester) and is more than worthwhile buying if you are strongly interested in the field.
I was lucky to meet John and Jay this summer during a specific SD workshop at MIT and the yearly System Dynamics Society Conference and could chat with both of them (they are both very practicably using SD with a strong academic background). Learning and getting more experienced in System Dynamics and the use for daily problem solving is a dynamic and evolving process of wisdom with lots of feedback ("Business Dynamics" can help a lot in getting deeper insights.
Best regards
Ralf
Excellent.......2007-08-29
Excellent guide to systems thinking, clear examples, clear thinking and very interesting conclusions reached. highly recommended
buen libro.......2007-02-22
como parte de la materia lo llevo, me salio mas barato que en mexico y me es util para mi carrera
Amazing.......2007-01-12
The definitive book on Business dynamics !
It may look dificult to follow, but it isn`t really easy to read and follow !
The cd brings good examples.
Edward Garrity, Professor of Information Systems.......2007-01-04
Sterman's book is far and away the best and most comprehensive book on system dynamics for business. Although the title is "Business Dynamics" it really is a text on applying system dynamics to both business and larger social issues/systems.
If you are a strong student of business and systems then this is the book for you. It is highly recommended if you are interested in learning the most you possibly can regarding system dynamics and how to model systems. However, if you are searching for an introduction to this area - watch out. The book is actually quite advanced - it is used at MIT and other graduate business programs at top universities.
What is amazing about this book is that it blends absolute precision, correctness and detail with practical modeling advice and insight and it is written in a relaxed style with numerous examples. It is one of the best examples of clear writing about a complex topic. Dr. Sterman's years of system work has allowed him a level of clarity that is unsurpassed in the business and systems area.
As mentioned earlier, the book can be overwhelming and I would recommend a newcomer to this area to pick up several books first, to provide a more gentle introduction. This is not a contradiction of what I wrote earlier, it is simply that the book packs so much information in its pages, and it is still very long.
Highly recommended.
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.
Customer Reviews:
needs complete student manual.......2007-09-28
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.......2006-06-16
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.
If you like a well written, applied, operational kind book........2005-09-28
If you like mathematics but prefer an operational approach instead of the abstract approach, you will like this book.
An ideal complement to Calculus books (like Piskunov, Thomas Jr., etc.) that do not emphasize Complex Variables.
Clear explanations. Many examples. Relatively fast to read, that is, you will not stop the reading trying to demonstrate those boring "easy to show statements".
Pleased.......2005-07-05
The book was in great shape and I liked the math help websites included.
Excellent intro. to complex analysis!.......2004-06-19
This course was my first exposure to the mathematical field of analysis at the undergraduate level, and our school ditched Gamelin's book used two years ago in favor of this book. Just to give you an idea of the difference a book makes (it was the same teacher for both courses, mind you): when Gamelin was used, EVERYONE dropped out of the course; when Brown/Churchill was used, only one person dropped the course and half the class received A's!
Truly, this is a remarkable shift, and this book had a lot to do with it. I thought the organization was flawless (note: you will have to go through the book in order, as many examples depend on previous material), and starting from the beginning with the definition of a complex number was definitely the way to go, as about 1/3 of my class had never seen a complex number before. I loved the fact that there were many examples worked out (never explicitly showing people how to do the end-of-section exercises, but showing them the methods for where to go) and the major theorems were alloted many pages for clear proofs with diagrams and detailed explanations (an entire section was devoted to a proof of the Cauchy-Goursat theorem!). Also, the choices of problems were superb, with some routine exercises meant to get you thinking along the right tracks followed by some very difficult ones. Basically, enough to challenge even the ablest math student, but enough for the average one to get a grasp on the concepts as well.
The book also provides an advantage for the instructor as to what applications to teach. Granted, chapters 1-6 cover almost all the theory, but 7-12 are all applications (7 is "usually" considered theoretical as well, but it is called "applications of residues!") in physics, advanced calculus and geometry, and engineering. So, a professor could choose to emphasize only the theoretical parts and save the apps. for independent study (which my prof. did) or could teach the relevant theories coupled with some of the applications (conformal mapping with fluid flow and heat flow, for example). It truly is a versatile book.
I noticed a complaint on here about not having enough examples or worked-out proofs. Well, to that individual (and any others who might be having the same problem), this book is meant for an upper-level undergraduate course, which means that there are going to be less examples worked out in great detail, the proofs may just be thumbnail sketches, and the problems will not have a quick reference page in the chapter for a formula or method like in calculus, for example; even though the book is versatile, a lot of the learning still falls on the student's shoulders.
My one and only gripe is that the book didn't take a lot of time to spell out how to perform a delta-epsilon proof for limits, which is one of the basic proofs in analysis. But, luckily, I had a very patient instructor who was willing to walk it through with me (most of the rest of the class had already had real analysis, so they didn't need to go over it). But, still, it's not enough to take it down a star, in my opinion.
They say this book is among the canon of undergraduate mathematics, and I can certainly see why. What a great introduction to complex analysis! This book will definitely be accompanying me to grad school!
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:
The exercises are not very good.......2007-09-11
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.......2006-05-03
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 !.......2006-04-16
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.......2006-01-20
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.......2005-05-01
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.
Book Description
This book provides a comprehensive introduction to complex variable theory and its applications to current engineering problems and is designed to make the fundamentals of the subject more easily accessible to readers who have little inclination to wade through the rigors of the axiomatic approach. Modeled after standard calculus books--both in level of exposition and layout--it incorporates physical applications throughout, so that the mathematical methodology appears less sterile to engineers. It makes frequent use of analogies from elementary calculus or algebra to introduce complex concepts, includes fully worked examples, and provides a dual heuristic/analytic discussion of all topics. A downloadable MATLAB toolbox--a state-of-the-art computer aid--is available.
Complex Numbers. Analytic Functions. Elementary Functions. Complex Integration. Series Representations for Analytic Functions. Residue Theory. Conformal Mapping. The Transforms of Applied Mathematics. MATLAB ToolBox for Visualization of Conformal Maps. Numerical Construction of Conformal Maps. Table of Conformal Mappings. Features coverage of Julia Sets; modern exposition of the use of complex numbers in linear analysis (e.g., AC circuits, kinematics, signal processing); applications of complex algebra in celestial mechanics and gear kinematics; and an introduction to Cauchy integrals and the Sokhotskyi-Plemeij formulas.
For mathematicians and engineers interested in Complex Analysis and Mathematical Physics.
Customer Reviews:
Excellent Book!.......2006-04-23
First let me say that this book was an introduction to the subject for me. After reading the first six chapters, and working through most of the problems, I have to say this book is great. I highly recommend this to anyone who is learning on there own. In particular, the chapter on residues is excellent. The chapter on series is also good, although I would have liked more worked examples for proofs involving uniform convergence. Also, a little more emphasis on the Arguement would have been nice. Nevertheless, 5/5 for this one, it is extremely well written and the authors really provide motivation for the theorems to come. This is definitely one of the best math books I have read. Great buy, worth every penny.
Good Introductory Book.......2004-01-28
This was the book that I learned Complex Analysis from. Definitely made the subject accessible to pretty much any reader. Plenty of exercises: some more theoretical, some more applied. It skillfully straddles the gap between being a theoretical math book and a math book for people with more applied aims (such as engineers). Most topics are covered thoroughly, though certain more complicated subjects such as winding number are left out for simplicity.
This book definitely prepared me for tackling the dense, theoretical, and exceptional "Complex Analysis" by Ahlfors. I'd recommend it as an introductory book for anyone trying to get into the subject who is intimidated by Ahlfors, as well as for anyone who is only interested in the essential commonly-applied tools.
down to earth book for people like you and me.......2001-12-10
I have just finished a class using this book, and on the whole its done a good job. I didn't find it in any way super special or anything, but I could read it and understand it. As far as math books go that is pretty good. Lots of exercises with answers in the back, which is what you need. Usually there are worked out examples of the most standard problems, but not always, e.g. there is no example of residue calculus with a Log function.
Book Description
This is an advanced text for the one- or two-semester course in analysis taught primarily to math, science, computer science, and electrical engineering majors at the junior, senior or graduate level. The basic techniques and theorems of analysis are presented in such a way that the intimate connections between its various branches are strongly emphasized. The traditionally separate subjects of 'real analysis' and 'complex analysis' are thus united in one volume. Some of the basic ideas from functional analysis are also included. This is the only book to take this unique approach. The third edition includes a new chapter on differentiation. Proofs of theorems presented in the book are concise and complete and many challenging exercises appear at the end of each chapter. The book is arranged so that each chapter builds upon the other, giving students a gradual understanding of the subject.
This text is part of the Walter Rudin Student Series in Advanced Mathematics.
Customer Reviews:
I love this book!.......2006-11-08
I love this book, even though I have not absorbed more than a small portion of it yet. I find this to be a much better book than the "baby Rudin", which struck me as dry, overly concise, and without motivation. This book provides ample motivation, and although it proceeds in great generality, proceeds at a reasonable pace.
The best thing about this book, however, is the spirit of it--the integrated approach to analysis that Rudin takes is unique and greatly appreciated--Rudin is, like Lang, a testimony to the fact that the best mathematicians do not draw artificial lines between different areas within mathematics. Rudin presents the material in ways that connect to other areas of mathematics and will help the reader become a better mathematician, even if she never directly uses any of the material contained in this volume.
I would not recommend this book as a first exposure to measure theory or complex analysis--it is advanced and requires a great deal of background to fully understand and appreciate. But I think this is a book that any serious mathematician should add to their collection and eventually work through. People wanting to learn measure theory might look to the book by Inder K. Rana, or to the classic book by Royden. For more elementary treatments of complex analysis I would recommend the classic by Ahlfors, Theodore Gamelin's book, or the book by Greene and Krantz.
My 2 cents.......2006-10-11
There are some excellent reviews here for this outstanding book, so I will try to avoid repetition. In preparation for my qualifying exams in graduate school, two of my colleagues and I did all of the exercises in Rudin (give or take a couple, no more). What I found striking at the time was how Rudin took three subjects -- measure theory, functional analysis, and complex analysis -- and weaved them together seamlessly. It is not that I believed them to be separate subjects, but until then I hadn't realized just how they all fit together. Really, this book is superb.
A word of warning, though. Rudin's prose is concise, and his proofs leave you wondering if you'd ever be able to reproduce them on your own. It is what we in the business are used to call 'elegant'. It pays to work in groups, persevere, and go over everything twice or more. Good luck.
Necessary, Necessary, Necessary.......2006-07-24
While I would not recommend this text to someone wishing to teach herself real and complex analysis, having this book in your personal mathematics library is a must for anyone seeking to further her education in higher mathematics. It's one of the most commonly used undergraduate texts, referred to by some as the "Bible". If you can afford it though, I would recommend that you pick up a copy of Baby Rudin to use as a reference.
The first two chapters in combination with Bartle's text on Lebesgue Integration and Measure makes for a killer introductory course in Measure Theory.
Oh, and if you can solve the problems in Rudin's book, you can do pretty much anything, so it's a major confidence booster!
Real and Complex Analysis (Higher Mathematics Series) .......2006-03-03
The approach in this book is formal, yet not intuitive and neither natural for a beginning graduate student who have yet developed some level of mathematical maturity.
Concise and concrete proofs, chanllenging exercises are given in the text. The book is fruitful in many ways, however you must have considerable mathematical maturity in order to benefit from this text.
It is a pleasure to have this book on my shelf.
A start in math........2004-09-22
I am a fan of Rudin's books. This one "Real and Complex Analysis" has served as a standard textbook in the first graduate course in analysis at lots of universities in the US, and around the world.
The book is divided in the two main parts, real and complex analysis. But in addition, it contains a good amount of functional and harmonic analysis; and a little operator theory.
I loved it when I was a student, and since then I have taught from it many times. It has stood the test of time over almost three decades, and it is still my favorite. I have to admit that it is not the favorite of everyone I know.
What I like is that it is concise, and that the material is systematically built up in a way that is both effective and exciting.
Some of the exercises are notoriously hard, but I think that is good: It simply means that they serve as work-projects when the students use the book. And this approach probably is more pedagogical as well.
After surviving some of the hard exercises in Rudin's Real and Complex, I think we learn things that stay with us for life; you will be "marked for life!"
Review by Palle Jorgensen, September 2004.
Book Description
I used to think math was no fun
'Cause I couldn't see how it was done
Now Euler's my hero
For I now see why zero
Equals e
[pi] i+1
--Paul Nahin, electrical engineer
In the mid-eighteenth century, Swiss-born mathematician Leonhard Euler developed a formula so innovative and complex that it continues to inspire research, discussion, and even the occasional limerick. Dr. Euler's Fabulous Formula shares the fascinating story of this groundbreaking formula--long regarded as the gold standard for mathematical beauty--and shows why it still lies at the heart of complex number theory.
This book is the sequel to Paul Nahin's An Imaginary Tale: The Story of I [the square root of -1], which chronicled the events leading up to the discovery of one of mathematics' most elusive numbers, the square root of minus one. Unlike the earlier book, which devoted a significant amount of space to the historical development of complex numbers, Dr. Euler begins with discussions of many sophisticated applications of complex numbers in pure and applied mathematics, and to electronic technology. The topics covered span a huge range, from a never-before-told tale of an encounter between the famous mathematician G. H. Hardy and the physicist Arthur Schuster, to a discussion of the theoretical basis for single-sideband AM radio, to the design of chase-and-escape problems.
The book is accessible to any reader with the equivalent of the first two years of college mathematics (calculus and differential equations), and it promises to inspire new applications for years to come. Or as Nahin writes in the book's preface: To mathematicians ten thousand years hence, "Euler's formula will still be beautiful and stunning and untarnished by time."
Customer Reviews:
An excellence introductory book on advanced mathematics such as Euler's Identity, Irrationalioty, Fourier Series.......2007-09-22
The primary topic of Nahin's "Dr. Euler's Fabulous Formula" is the complex number or more appropriately the Euler's identity: e power to (it) = cos(t) + isin(t). Nahin called this book the second half of his complex number series. The first book in the series is named "An Imaginary Tale: The Story of square root of minus one." The second book is called "Dr. Euler's Fabulous Formula." The primary topics of the second book are: Fourier series, which is covered on Chapter 4; Fourier Integrals on Chapter 5; the application of complex numbers on electronics Chapter 6.
The book has six chapters, which contains both pure and applied mathematics materials. Other than the three chapters mentioned above, the other three chapters are (i) Complex Numbers, (ii) Vector Trips, and (iii) The Irrationality of pi square. Chapter one is about the assortment of non elementary complex numbers such as applying complex number on obtaining the sum of a real series. Chapter three provides a detail proof of the irrationality of the number pi square using Euler's Identity. On the applied side: Chapter two demonstrates the application of complex number on mathematical modeling. Since Nahin is an eminent electrical engineering professor, his book also provides plenty of material on (a) partial differential equations (PDE) such as wave equation on chapter four, and (b) electrical engineering material such as baseband, carrying frequencies, antennas, radio receivers and speech scrambler on chapter six.
This is an excellence introductory book not only on pure complex numbers usage in mathematics such as summing a series but also on the usage of PDE, Fourier series, and Fourier Integral in physics and engineering.
Good clear explanation of Fourier series.......2007-04-11
Dr Eulers fabulous formula fits a niche between books for non mathematicians (too simple) and books only understood by mathematicians. It provides the best explanation of Fourier series and integrals that I have read. Its explanation of imaginary numbers is excellent, but not as good as Feynman in his lectures on physics. I reccomend it for those who want to understand how Fourier series work.
excellent for fourrier series and fourrier transform exposition.......2007-03-29
A very readable book. Many concepts developed around Euler's magic formula are clearly explained. Including a lucid exposition on the calculus of the sum of classical series such as the value of zeta function for several positive integer values of its argument. Paul Nahin excels in describing the origin and the development of fourrier series and fourrier integrals from Bernoulli to Fourrier and more. Anyone interested in this field will find something interesting in this book to learn. The reason I didn't rank it five stars is that I found explanations often too lengthy while the addition of a chapter on distribution theory could fill the gaps in mathematical rigor and make the transition from fourrier series to fourrier integrals more logical. I should add that the lack of rigor in transition from fourrier series to fourrier integrals, as described by P. Nahin, is inherent to the more fundamental problem of transition from discrete to continuous. Indeed, in mathematics, this is a very slippery terrain. In functional analysis, mathematicians go round this problem by introducing distribution theory. P. Nahin mentions only the name of distribution theory without any decription. I think a chapter on this theory would make the book a must have.
Excellent expository book.......2007-03-25
Paul Nahin's book, "Dr. Euler's Fabulous Formula," is an excellent expository treatment of Euler's formula (you say, "which one?") e^i*theta = cos(theta) + i*sin(theta) and its profound, and far-reaching, ramifications. Dr. Nahin also gives an extensive informal discussion of Fourier series, Fourier transforms, the Dirac Delta Function, and what electrical engineers would call "signals and systems theory." Some mathematical purists may criticize the lack of pure rigor. However, this book is an "expository" book, not a rigorous "textbook." Ideally, I recommend that you read Dr. Nahin's book in conjunction with your standard college textbook. That way, you will get the best of both worlds. Your textbook will give you the disciplined rigor. Dr. Nahin's book will give you the "Aha... insight!" I read Dr. Nahin's book before taking a graduate level course in electrical engineering (EE) Signals and Systems. I breezed through the EE course with perfect scores on my exams, and I give a lot of credit to Dr. Nahin. When you study mathematics, you really need BOTH disciplined mathematical rigor AND intuitive insight and understanding. Beware, however, that this book has LOTS of mathematics in it. The book is loaded with serious mathematics. Don't read this book if you want something for the intelligent layperson. Read this book if you love mathematics, if you are an engineering or mathematics student, or if you like industrial-strength mathematics. Paul Nahin may single-handedly save Americans from mathematical illiteracy. He does something that the mathematical community does not do well... "market and sell" mathematics.
Errata please.......2007-02-14
Like all of Paul Nahin's books, I really like this one.
However, as with so many books an Errata would help. Mathematical and mathematical finance books are getting so expensive, that unless authors or publishers have a URL for Errata, readers esp. of mathematical books will wait for [sometimes years] for a second corrected edition of books.
I could be wrong about these but it seems these are typos:
p. 30 lines 5 & 6 curly bracket should only be around the 2 * cos(x/2) term
p. 121 second equation should be t=(v+u)/(2*c)
p. 121 '* (1/(2*c)' missing at end of the line
p. 123 line 17, first word should be 'bother' not 'other'
p. 127 line 3 and 4, it seems that the 'icnPI/l' [not the ones in the cos() or sin() terms] term after the 'B' and before the '2*cos' respectively, should not be there. Or am I missing something ?
p. 128 4th line from bottom should be 1753 not 1733
p. 143 2nd line before last equation should be '... (x- i * y)...'
p. 144 equation under 'In summary, then...' cases are reversed
p. 216 seems 1/(2*PI) is missing from right side of first equation, i.e. from "...G(u)G(omega-u)...du"
Book Description
This thorough and detailed exposition is the result of an intensive month-long course sponsored by the Clay Mathematics Institute. It develops mirror symmetry from both mathematical and physical perspectives. The material will be particularly useful for those wishing to advance their understanding by exploring mirror symmetry at the interface of mathematics and physics.
This one-of-a-kind volume offers the first comprehensive exposition on this increasingly active area of study. It is carefully written by leading experts who explain the main concepts without assuming too much prerequisite knowledge. The book is an excellent resource for graduate students and research mathematicians interested in mathematical and theoretical physics.
Customer Reviews:
Detailed overview of the subject.......2005-05-16
Mirror symmetry has become an established branch of mathematics and mathematical physics, and research in the subject has resulted in brilliant developments. This sizable book contains essentially some (polished) lecture notes of a seminar series in mirror symmetry that was given in the spring of 2000. This reviewer only studied Part 5 of the book, entitled "Advanced Topics" and so only that part will be reviewed here. In addition, space constraints then dictate only a small portion of this part can be reviewed. Needless to say, any reader who intends to tackle this book will need a substantial background in modern mathematics and advanced physics, and a sizable commitment in time. The time spent is well worth it though, as both the mathematics and physics behind mirror symmetry has to rank as one of the most fascinating research topics in the last two decades.
In the chapter entitled "Topological Strings" the authors consider the functional integration of worldsheet geometries. This project involves essentially the integration over the complex structures of Riemann surfaces. Referring to this procedure as "quantum gravity", they do not address it in-depth, but instead focus on the coupling of topological sigma models to worldsheet gravity, which is called `topological string theory' in the literature. The authors first consider the case where the target is a Kahler manifold whose first Chern class is zero, since for this case the quantum cohomology ring is less easy to obtain, i.e. it can obtain contributions from holomorphic maps of any degree. Even for the case where there is no coupling to gravity, the degree 0 contribution is related to the classical intersection number. The contributions from higher degree result in the deformation of the classical cohomology ring into the quantum cohomology ring. The authors then ask whether there are any other correlators that will give nontrivial (non-zero) invariants in genus 0. Posing this question leads to the WDVV equation and the genus 0 topological string partition function. The n-point correlation functions of topological strings can then be defined as the nth partial derivatives of this function. For higher genus cases, the correlators are all zero, but the authors show the connection between the higher genus partition function and holomorphic anomalies. The case of three-dimensional Calabi-Yau manifolds is special, if one concentrates on the integration over the complex structures of the worldsheet. When the complex dimension of this moduli space is 3(g-1) then there are isolated points where holomorphic maps exist. Defining a topological string theory for Calabi-Yau threefolds is straightforward, as the author shows, and proceeds analogously to the case of topological field theory. A measure is defined on the moduli space of Riemann surfaces of genus g that cancels the axial charge anomaly. A genus g (>1) topological string amplitude, which is a section of a bundle over the moduli space of Calabi-Yau manifolds, is then obtained from this procedure. Modulo the presence of holomorphic anomalies, the authors show that the definition of topological string amplitudes is consistent with the topological symmetry. The origin of these holomorphic anomalies is discussed in fair detail by the authors, having their origin in the boundaries of the moduli space.
The rigorous mathematical formulation of mirror symmetry is of course of great interest to mathematicians. Because of its origin in string theory and quantum field theory, mirror symmetry has not yet received this kind of rigor. Chapters 37 and 38 of this book discuss some of the approaches that attempt to put mirror symmetry on a more rigorous foundation. One of these involves the use of `derived categories,' an approach that was recommended by the mathematician Maxim Kontsevich. The discussion in these chapters takes place in the context of D-branes, and Kontsevich conjectures that mirror symmetry is the equivalence of two categories: the derived category of coherent sheaves, and the category of Lagrangian submanifolds with flat U(1) connections. Specifically the equivalence entails the equivalence between the bounded derived category of coherent sheaves or `B-cycles' and the category of A-cycles with compositions defined in terms of holomorphic maps from disks. This latter category is derived from the Fukaya A-infinity category, as is shown by the authors. They discuss in detail this category, being essentially a generalization of a differential, graded algebra, especially how to obtain the compositions. In chapter 37, the authors give an explicit example of the equivalence of these categories for the case of the elliptic curve. The elliptic curve is interesting in this regard in that it is its own mirror, i.e. the complex parameter is mapped to the complexified Kahler parameter by the mirror map.
The derived category has sometimes been a stumbling block to those who want to understand the Kontsevich conjecture. The authors do not attempt to give the reader the needed insight into this kind of category, but merely take it to be a collection of all holomorphic bundles and coherent sheaves. Sheaves in this category can be subtracted from each other using a map between them. Physically, this subtraction corresponds to the annihilation of branes and anti-branes via a tachyon. Derived categories though are straightforward to think about if one views them from the standpoint of algebraic topology. Derived categories are rich enough to include notions of localization and triangulated objects (i.e. "complexes") and maps (i.e. morphisms) between these objects. This is a kind of "homology" but what is of main interest are homotopies between the morphisms. The class of homotopic morphisms between two complexes forms an abelian group and one can then obtain a category consisting of complexes as objects and classes of homotopic morphisms as morphisms. A cohomology functor can then be defined on this category, along with graded objects and differentials between them. The homotopic category can be given a "triangulation" and morphisms in this category that give rise to isomorphisms in cohomology are given special status, called `quasimorphisms.' The localization of this category with respect to quasimorphisms is called a derived category.
Average customer rating:
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- A Must Read for the Serious Investigator
- "On S'engage Et Puis On Voit!"
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The Logic of Failure: Recognizing and Avoiding Error in Complex Situations
Dietrich Dorner
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ASIN: 0201479486 |
Customer Reviews:
Interesting.......2007-07-04
Dense, detailed and often fascinating. Fluid writing despite translation from German. Those who are used to jumping to conclusions will find much to learn here regardless of the overall malfunction. Unfortunately, the promise shown initially is not fully delivered for several reasons. The author makes frequent use of his simulations, tests, and models and asks much of the reader who has only read a brief introduction to them. In the later chapters, it's more tedious to follow along with his constant references; furthermore, the book essentially becomes an argument for the use of computer-simulated research rather than a distilled analysis of failure. The last chapter feigns a comprehensive summary, but drifts away as the author ponders the process of determining the point of failure. I could take it, then, as either (i) a technical, interesting but inconclusive study of the reasons for failure which focuses on a mere handful of examples; or (ii) an outdated, abstract examination of the process for examining failure, which does not consider alternative approaches and isn't thorough enough to be worthwhile.
If you're interested in note-taking and then drawing your own conclusions, then this book should be an excellent read as it's filled with detail. For others, it delivers a few very fascinating chapters about our cognitive biases and then fails to draw them together cogently.
Meh........2007-05-27
Things are complex. Watch the behaviors of items in a system closely. Get a computer to model the cause and effect relationships. Things don't always respond like you would expect. That's the book in a nutshell... I ended up speed reading the book instead of word for word because I couldn't handle all of the excessive examples, nor the continued reference back to his computer simulation "real" models (and I *like* computers!).
good so far.......2007-01-10
This was recommended to me at work. Interesting analysis of why problem-solving approaches to social problems so often fail, and why they so often fail so miserably. Basically, there are two types of problem-solvers. Successful problem solvers make one small change, then observe the result. Unsuccessful problem solvers decide on a strategy ahead of time, implement all changes at once, and either stick to their strategy no matter how badly it is failing or scrap their strategy entirely and introduce a brand new one, without transition. Interesting case studies to illustrate the point that logic without logical use of empiricism is ineffective, and common.
A Must Read for the Serious Investigator.......2007-01-04
Dorner provides great insights into why we humans are not as smart as we think we are. He shows how our slowness in thinking, our inability to process large amounts of information at any one time, our arrogance, and short sightedness all contribute to ineffective problem solving. While he attempts to provide ways to avoid these stumbling blocks, he falls short on this mission. A much better read for how to avoid these pitfalls can be found in Apollo Root Cause Analysis.
"On S'engage Et Puis On Voit!".......2006-12-22
Napoleon said "On s'engage et puis on voit!" Loosely translated that means "One jumps into the fray, then figures out what to do next," a common human approach to planning. This discussion (page 161) takes on the adaptability of thought and cautions decision makers about the risks of overplanning in a dynamic, multivariate system. Using examples from Napoleon as well as more concrete examples such as the quotation about soccer strategy (also on page 161,) Dietrich Dörner, the brilliant German behavioral psychologist (University of Bamberg) has created a masterwork on decision making skills in complex systems; I find it to be highly complimentary to Perrow's work and also highly recommend his equally brilliant "Normal Accidents."
A strength of this work is that Dörner takes examples from so many areas including his own computer simulations which show the near-universal applicability of his concepts. One of Dörner's main themes is the failure to think in temporal configurations (page 198): in other words, humans are good at dealing with problems they currently have, but avoid dealing with and tend to ignore problems they don't have (page 189): potential outcomes of decisions are not foreseen, sometimes with tragic consequences. In one computer simulation (page 18) Dörner had a group of hypereducated academics attempt to manage farmland in Africa: they failed miserably. In this experiment Dörner made observations about the decision makers which revealed that they had: "acted without prior analysis of the situation; failed to anticipate side effects and long-term repercussions; assumed the absence of immediately negative effects meant that correct measures had been taken; and let overinvolvement in 'projects' blind them to emerging needs and changes in the situation." (How many governmental bodies the world over does this remind you of?)
I am a safety professional, and am especially interested in time-critical decision making skills. Dörner's treatment of the Chernobyl accident is the most insightful summation I have seen. He makes the point that the entire accident was due to human failings, and points out the lack of risk analysis (and managerial pressure) and fundamental lack of appreciation for the reactivity instability at low power levels (and more importantly how operators grossly underestimated the danger that changes in production levels made, page 30.) Dörner's grasp here meshes the psychology and engineering disciplines (engineers like stasis; any change in reactivity increases hazards.) Another vital point Dörner makes is that the Chernobyl operators knowingly violated safety regulations, but that violations are normally positively reinforced (i.e. you normally "get away with it," page 31.) The discussion about operating techniques on pages 33 and 34 is insightful: the operators were operating the Chernobyl Four reactor intuitively and not analytically. While there is room for experiential decision making in complex systems, analysis of future potential problems is vital.
In most complex situations the nature of the problems are intransparent (page 37): not all information we would like to see is available. Dörner's explanation of the interactions between complexity, intransparence, internal dynamics (and developmental tendencies,) and incomplete (or incorrect) understanding of the system involved shows many potential pitfalls in dynamic decision making skills. One of the most important of all decision making criteria Dörner discusses is the importance of setting well defined goals. He is especially critical of negative goal setting (intention to avoid something) and has chosen a perfect illustrative quote from Georg Christoph Lichtenberg on page 50: "Whether things will be better if they are different I do not know, but that they will have to be different if they are to become better, that I do know." A bigger problem regarding goals occurs when "we don't even know that we don't understand," a situation that is alarmingly common in upper management charged with supervising technical matters (page 60.)
Fortunately Dörner does have some practical solutions to these problems, most in chapter six, "Planning." One of the basics (page 154) is the three step model in any planning decision (condition element, action element, and result element) and how they fit into large, dynamic systems. This is extremely well formulated and should be required reading for every politician and engineer. These concepts are discussed in conjunction with "reverse planning" (page 155) in which plans are contrived backwards from the goal. I have always found this a very useful method of planning or design, but Dörner finds that is rare. Dörner argues that in extremely complex systems (Apollo 13 is a perfect example) that intermediate goals are sometimes required as decision trees are enormous. This sometimes relies on history and analogies (what has happened in similar situations before) but it may be required to stabilize a situation to enable further critical actions. This leads back to the quote that titles this review: 'adaptability of thought' (my term) is vital to actions taken in extremely complex situations. Rigid operating procedures and historical problems may not always work: a full understanding of the choices being made is vital, although no one person is likely to have this understanding; for this reason Dörner recommends there be a "redundancy of potential command" (page 161) which is to say a group of highly trained leaders able to carry out leadership tasks within their areas of specialty (again, NASA during Apollo 13) reportable in a clear leadership structure which values their input. Dörner then points out that nonexperts may hold key answers (page 168); though notes that experts should be in charge as they best understand the thought processes applicable in a given scenario (pages 190-193.) This ultimately argues for more oversight by technicians and less by politicians: I believe (and I am guessing Dörner would concur) that we need more inter- and intra-industry safety monitoring, and fewer congressional investigations and grandstanding.
This is a superb book; I recommend it highly to any safety professional as mandatory reading, and to the general public for an interesting discussion of decision making skills.
Customer Reviews:
Hated it........2007-07-10
Used this book as an undergraduate... hated it... I kept using a little thin old edition of "Complex Variables and Applications" by Churchhill to actually teach math using english.... Ironically the instructor who was teaching out of his notes followed churchhills presentation closer then this text.
The treatment of this subject in this text is just so horrid for a FIRST LOOK AT COMPLEX THEORY. No elegance to it what so ever...
elegant treatment.......2006-05-18
The book reveals complex analysis as a very elegant and lovely branch of mathematics. The level of rigour is not that of Marsden's other book, Elementary Classical Analysis. Instead, Basic Complex Analysis can be usefully read by non-maths majors, especially those in physics and engineering.
Key ideas are well covered. Starting with the Laurant series, which generalises the Taylor series. Then, from this, the idea of contour integration is examined. Giving rise to the Residue Theorem and the winding number. All because the only term that does not integrate to 0 is 1/z, which gives the complex log and its imaginary argument is the only thing left. So simple and powerful. Amazing that an essentially arbitrarily intricate contour integral can be given by the residues at the enclosed poles! Yet the text's derivation should get straightforward to follow for most readers.
If you are going onto advanced physics, like quantum electrodynamics, then this theorem is used extensively.
The book also covers important subsequent ideas. Especially conformal mapping and the Schwartz-Christoffel transformation. The treatment of conformal mapping, though, is only a hint of the richness of analysis available here.
The numerous problems are also good for the student to tackle.
Very good book, actually.......2006-05-13
When I first started with this book, I was not a fan. However, the book grew on me over time. Marsden and Hoffman do a very good job of blending both theoretical and computational aspects of complex analysis. They do a very good job of motivating and explaining the proofs, and they do not leave out any details (this is both good and bad - it can distracting, but as long as you pay attention, you will never get lost). The illustrations in the text are for the most part illuminating and useful, and the worked examples at the end of each section are not bad as well.
I did have a few minor problems, though. While many of the exercises are good, some of them seemed rather trivial. The chapter on conformal mapping could use some work. The binding on mine started to come apart by the end of the semester, although that may have been my fault.
Quite Dry.......2004-02-11
This is the second book that I have read beside the Vector Calculus by Marsden and Hoffman. This book rushes you through with an introductory chapter and go right into the heart of complex analysis. The author assumes you to have a great professors that can explain things in detail when you can't quite understand what is written in the text. Unfortunately I did not have a great instructor.
The examples of the book are quite simple, compare to some end of section problems.
Overall this book has no surprises as it is quite dry, got bored from reading it. If it was not a required text book for a 3rd year complex analysis course, i wouldn't recommend it to anyone. There are many other books out there that are better written.
A versatile introduction to the subject........2002-03-06
I used an earlier edition of this text as an instructor 20 years ago. The students in my class at the time were equally divided among the fields of mathematics, physics, and engineering. The book proved to be quite useful for all of them. Marsden skillfully strikes a balance between the needs of math majors preparing for graduate study and the needs of physics and engineering students seeking applications of complex analysis.
The book is clearly written and well-organized, with plenty of examples and exercises. My only significant criticism of the first edition was the author's tendency to label many examples of contour integration as theorems. Technically, there is nothing wrong this, but I found that some of my students tended to memorize the statements of these "theorems" rather than focus on the methods of integration discussed (for example, "Pac-Man" integrals with branch cuts along rays other than the positive real axis). Nonetheless, this is a fine text that has--not surprisingly--continued to be widely used for over two decades.
Book Description
One of the most diverse branch of mathematics, complex variables proves enormously valuable for solving problems of heat flow, potential theory, fluid mechanics, electromagnetic theory, aerodynamics and moany others that arise in science and engineering. As taught in this exceptional study guide, which progresses from the algebra and geometry of complex numbers to conformal mapping and its diverse applications, students learn theories, applications and first-rate problem-solving skills.
Customer Reviews:
good reference book..........2007-05-23
more of a handbook with the important theorems and formulas.
the examples and excercise are well conceived.
This book no longer need a review.......2007-01-12
This book no longer need a review. It is so popular among the academics and the students for its lucid way of treating complex variables I used this book as my reference for complex variables for the graduate mathematical methods course. This book helped me a lot with lots of examples and interesting exercise problems. It is also very good for students who wants to have a fast glance at the concepts. Overall, I would strongly recommend this book to any student who wants to learn complex variables in the most simple way with all kinds of examles to solve problems and score high grades.
Great cheap text on complex variables for the mathematician.......2006-08-13
Complaints seem to abound in regard to how this Schaum's outline is too theoretical and has too few problems involving applications. You must remember that this particular outline was meant to complement an undergraduate mathematics course in complex variables, not an applied physics or engineering course using complex variables. Thus, the purpose of this book is to develop the calculus of functions of a complex variable.
This is one of those Schaum's outlines that has sufficient explanation, figures, and examples that it can double as a cheap textbook on the subject. However, remember that the emphasis is on theorems and proofs of theorems versus applications. However, there are some sections of the outline that are excellent at illustrating some applications of the subject matter. In particular, chapter 9, "Physical Applications of Conformal Mapping" contains applications from physics using those equations that are defined by a potential, including the electromagnetic field, the gravitational field, and, in fluid dynamics, potential flow, which is an approximation to fluid flow assuming constant density, zero viscosity, and irrotational flow. By choosing an appropriate mapping, the outline demonstrates clearly how one can transform the inconvenient geometry of one set of these equations into a much more convenient one. The equations are solved in this new "convenient" geometry, and then transformed back into the old one. One example of a fluid dynamic application of a conformal map that is detailed is the Joukowsky transform.
If you are not looking for a book to complement a mathematics course on complex variables and you are looking for something more applied, you might look at "Complex Variables: Introduction and Applications". That book has the first part dedicated to theory and the second part dedicated to applications at a reasonable price.
too theoretical.......2005-02-27
I bought this thinking it would help me understand complex variables, complex integration and differentiation. As another customer commented there are wayyyy to few solved concrete problems, all of the solved problems are proving some theorem. This is useless. I can look those proofs up elsewhere. What I expected was concrete solved problems, there are very very few of those. All in all I am rather dissapointed with this book. Not recommended unless you are looking for many proofs of just theorems.
Good mixture of examples and theory........2004-06-02
I like this book very much. First, you can go through solved examples or you can try to solve them yourself and compare your solution against the presented one. If you want to get deeper, there are theorems to be proved and again, proofs are shown or indicated, you will not be left alone. Then the book presents number of examples to be solved.
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