Probability and Computing: Randomized Algorithms and Probabilistic Analysis

Book Description

Assuming only an elementary background in discrete mathematics, this textbook is an excellent introduction to the probabilistic techniques and paradigms used in the development of probabilistic algorithms and analyses. It includes random sampling, expectations, Markov's and Chevyshev's inequalities, Chernoff bounds, balls and bins models, the probabilistic method, Markov chains, MCMC, martingales, entropy, and other topics. The book is designed to accompany a one- or two-semester course for graduate students in computer science and applied mathematics.

Customer Reviews:

Advanced probability topics without measure theory.......2007-08-18

This book is underestimated by two reviewers below. I totally do not agree with them. This book covers a wide range of topics in a very readable style. The contents in this book is complementary to the book of Motwani and Raghavan (but this book is much easier to digest).

It, without requiring any knowledge on measure theory, contains excellent introductions to many difficult topics in probability including

- concentration bounds (Chernoff, Azuma-Hoeffding, etc.)
- applications of stochastic processes such as queuing theory
- martingale (Wald's equation)
- coupling of Markov chains and their mixing times
- Shannon's source coding and noisy channel theorems
- Erdos' probabilistic method
- etc.

All of these topics are provided with excellent applications in computing.
The authors illustrate many clever tricks for proving theorems, and these tricks give insights to the readers as well.

Just unnecessary.......2007-05-17

This book, while written by two renowned computer scientists, is truly disappointing. In trying to discuss randomness and computation, this book just does a mediocre job on discussing randomized computation and also an equally poor job discussing relevant aspects of probability theory. Their approach is not novel and many of their examples can be found in other texts. If you really want to learn randomized computation, get Motwani et al's book on Randomized Algorithms. If you want to learn probability theory, get any advanced probability theory book like Spencer and Alon on the probabilistic method, one of Sheldon Ross's books, or even Grimmett and Stirzaker. Whatever you do don't get this weak hybrid of a book that will require you to get another book at some point to supplement your understanding.

Another poorly written text book.......2006-03-19

The authors must be smart guys. They obviously understand alot about this subject but make the mistake that you do too! As a result, the book is inadequate as a teaching tool.

They use only half to a third of the narrative they need to adequately explain a subject. They also like to leave out proof steps or not explain them. The problems at the end of chapters are poor as well, since the authors seem to have forgotten to teach the techniques needed to solve most them in the chapter they belong to.

I am sure to them it is intuitive.

Good Introductory Textbook.......2005-03-16

It's pretty easy to get computers to do things where the answer is yes or no, or 4 or 6, given that the inputs to the problem are known. It's much harder to get an answer to a problem where the answer is that their is a 62% chance that the answer is yes. Unfortunately, in real life it's this second class of problems that predominates.

This book is oriented to solving these kinds of real world problems. The exercises in the book are chosen from real world examples -- what we used to call story problems. This tends to give the student a better understanding of not only the mathematics and programming involved but experience in looking at problems with a view to understanding this approach to solving the problem.

This book is suitable for a one or two semester introductory class at the upper undergraduate or beginning graduate level.

Just a word about the illustration on the front of the book. At the end of the book Alice in Wonderland the queen is about to order Alice beheaded. Alice says, "You're nothing but a pack of cards." At this, the whole pack rose up into the air and came flying down around her. This illustration is by John Tenniel from the original book of 1899. A deck of flying playing cards is a good way to illustrate random and probability.

Applied Numerical Methods with MATLAB for Engineers and Scientists

Average customer rating:

Applied Numerical Methods with MATLAB for Engineers and Scientists
Steven C. Chapra
Manufacturer: McGraw-Hill Science/Engineering/Math
ProductGroup: Book
Binding: Hardcover

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ASIN: 007313290X

Book Description

Still brief - but with the chapters that you wanted - Steven Chapra’s new second edition is written for engineers and scientists who want to learn numerical problem solving. This text focuses on problem-solving (applications) rather than theory, using MATLAB, and is intended for Numerical Methods users; hence theory is included only to inform key concepts. The new second edition feature new material such as Numerical Differentiation and ODE's: Boundary-Value Problems.

Numerical Recipes in C: The Art of Scientific Computing

Average customer rating:

talk about outdated
A classic book of numerical algorithms
Very nice book
A classic, and still worth having
Great compilation of numerical routines for C programmers

Numerical Recipes in C: The Art of Scientific Computing
William H. Press , Brian P. Flannery , Saul A. Teukolsky , and William T. Vetterling
Manufacturer: Cambridge University Press
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Binding: Hardcover

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ASIN: 0521431085

Book Description

The product of a unique collaboration among four leading scientists in academic research and industry, Numerical Recipes is a complete text and reference book on scientific computing. In a self-contained manner it proceeds from mathematical and theoretical considerations to actual practical computer routines. With over 100 new routines bringing the total to well over 300, plus upgraded versions of the original routines, the new edition remains the most practical, comprehensive handbook of scientific computing available today.

Customer Reviews:

talk about outdated.......2007-06-27

this book was likely a looker back in the day, but its 2007 now. Need to have better details for non "C"-users. wish i had bought "Idiots Guide to C".

A classic book of numerical algorithms.......2006-12-24

This book, although published 15 years ago, is still very useful. In fact, its more recent counterpart "Numerical Algorithms in C++" is a mess, and I wouldn't recommend it to anyone. The explanations of the algorithms that occur in each section of this book are top-notch. It helps with such questions as "Sure you know how to evaluate an integral with pencil and paper, but how do you do it with a computer?" Everything from linear algebra techniques to integration and evaluation of functions to the FFT and spectral applications are explained clearly and coded up in C. The code is great too, with the exception of one problem that several reviewers have already mentioned - the author has a FORTRAN-like programming style in which each implementation has arrays going from 1 to n versus 0 to n-1. This does cause some implementation problems if you want to transfer the algorithms into another programming language. Overall, though, I can't think of one book that does all of the heavy lifting that this one book does as well as it does in the arena of numerical algorithms.

The book is now available online. Just type "Numerical Recipes" into Google and click on the Numerical Recipes Home Page to peruse the entire book free of charge. You might also find the "Numerical Recipes in C Example Book" useful. That book is simply the source programs that demonstrate all of the Numerical Recipes subroutines. Each example program contains comments and is preceded by a short description of how it functions. I know I found it helpful in many cases.

Very nice book.......2006-08-27

A must buy for students or researchers who need numerical methods. Comprehensive topics. A good place to start to deeper levels. Online book is good for quick look.

A classic, and still worth having.......2006-07-12

"Numerical Recipes" has been a staple in computing libraries for many years, and for good reason. It provides immediately usable implementations of all the workhorses of numerical computation, in production-quality form. Maybe there are better implementations out there, FFTW for example, but getting something to work correctly always comes before getting it to work fast. Numerical computation is a specialty, and vanishingly few of us are specialists. As a result, getting this much specialist knowledge for the price of a very few hours' wage, fully debugged and documented, is a great bargain.

I have to agree with the critics who point out that the Gnu Scientific Library (GSL) is more complete in some areas, and offers better licensing terms. This collection has its own strengths, though, and not just in documentation. The writeup, however, is the major interface between the software and us, the bio-ware. GSL's collection of 'man' (help) pages serves a purpose, but this book's exposition describes a lot more of the background and rationale for the routines. The code and man pages are self-evident statements of the implementation - but "what" is a very different question than "what else" or "why."

This one may not serve all needs. You'd be amazed how many it does serve, though. If you need more than a Matlab session for numerical computing, you need this.

//wiredweird

Great compilation of numerical routines for C programmers.......2004-12-17

I found this book indispensible in my effort to develop profitable trading systems for futures and options and in my research in factor analysis and, more recently, in chronic fatigue syndrome and fibromyalgia. Anyone who programs in C or C++ and works with mathematics must have this book. It covers a surprisingly wide range of algorithms: routines are included for everything from handling Julian dates and solving systems of linear equations to determining eigenvectors and singular value decompositions, solving differential equations, doing numerical integration (quadrature), not to mention calculating fast fourier transforms, lomb periodograms and maximum entropy spectral analyses. While not always state-of-the-art, the routines are quite reliable (when used correctly), clearly-written, and easy to understand and use. I would strongly recommend this book (and the companion software) to anyone who programs in C and is literate in mathematics. I always keep a copy nearby.

Jeffrey Owen Katz, Ph.D.
Author: "The Encyclopedia of Trading Strategies" (McGraw Hill, 2000)

Average customer rating:

Good book
Poorly written
It's engineering-oriented, not science-oriented.
At times, it is a difficult read
Not for beginners

Numerical Analysis
Richard L. Burden , and J. Douglas Faires
Manufacturer: Brooks Cole
ProductGroup: Book
Binding: Hardcover

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ASIN: 0534392008

Book Description

This well-respected text gives an introduction to the modern approximation techniques and explains how, why, and when the techniques can be expected to work. The authors focus on building students' intuition to help them understand why the techniques presented work in general, and why, in some situations, they fail. With a wealth of examples and exercises, the text demonstrates the relevance of numerical analysis to a variety of disciplines and provides ample practice for students. The applications chosen demonstrate concisely how numerical methods can be, and often must be, applied in real-life situations. In this edition, the presentation has been fine-tuned to make the book even more useful to the instructor and more interesting to the reader. Overall, students gain a theoretical understanding of, and a firm basis for future study of, numerical analysis and scientific computing. A more applied text with a different menu of topics is the authors' highly regarded NUMERICAL METHODS, Third Edition.

Customer Reviews:

Good book.......2007-07-18

If you are studying Maths and you just want to buy a book to read before you fall asleep, then don't choose this book. You need a lot of time to read and understand this book. You will enjoy more and more when you understand every lines in this book.

The problems in this book are close to what you have to know in order to pass the course. Numerical Analysis is actually more fun and interesting than other maths courses such as linear algebra, complex variables, probability (with me).

In my opinion, the worst part of this book is the CD. It will not help anyone who do not know how to code. Instead of giving the straight code (simple code that you will be able to keep track in every line), the author made the code become a program and the input is hard to understand. So if you are not familiar with coding, then you will have a hard time figure out how these codes actually work.
Actually, somehow I think the author wants to use Maple as his coding language, but in my class, we use Mathematica, so it's a little bit different in syntax.
However, these codes cover almost all of algorithms mentioned in the book.

Poorly written.......2007-03-09

This book has been, unfortunately, my first introduction to numerical analysis. I wish that I could have chosen a superior book myself, but this is the one prescribed by the university I attend.

The examples in this book are mostly short and insufficient, especially when they are most needed. The lack of good examples wouldn't be so much of a problem, however, if the text itself were better. Unfortunately, many topics are poorly explained. The notation used in this book is often awkward and confusing.

I'm used reading math textbooks and understanding them. Unfortunately, Numerical Analysis by Burden and Faires expects the reader to understand concepts that aren't even fully explained in the text. Avoid if you can.

It's engineering-oriented, not science-oriented........2007-01-25

There are two aspects for this topic. Would you like the deeper reason why a certain way works? Or would you like to have some impressions with a certain method and try to implement it? Not many books can balance these two aspects very well and Burden's book is more toward the latter. This can be observed that almost every method is with a pseudo code and many numerical examples are given (many are even in a step-by-step way).

So if one's background is from science such as math or physics, s/he probably regards this book as a failure. For engineering students, especially undergraduates, this book seems to stay at a good balance since it doesn't get too involved.

The pseudo codes are in general well written and helpful. I think it is the strength of this book. There are few books doing better in this aspect than this book. I have one impressive experience about it. Once a graduate student asked me a question and I told him Burden's book can solve his problem. He succeeded very fast and told me he even didn't know how that method works but just did programing based on the pseudo code. For education aspect, of course we don't encourage this kind of working. But for some situations, we need it.

On the other hand, this book is rather elementary than advanced. And I think it is intended for undergraduates, not graduates. This book was my textbook of numerical analysis when I was a junior. It also served as a textbook when I lectured to undergraduate students during pursuing my phd degree in engineering. I will still use it as the textbook next time whenever possible.

I should give it 4 stars or 4 and a half at most for this book. 5 stars are just out of viewpoint balance.

At times, it is a difficult read.......2006-10-25

I examined this book as part of my constant quest for better textbooks. In this case, the course is a one-semester course in numerical analysis. I have been using "Elementary Numerical Analysis Third Edition" by Atkinson and Han and am generally pleased with the results. The first point to make is that this book has more material than I could ever cover in one semester, so from my perspective it is unsuitable. However, if you have a two semester sequence in numerical analysis, then it has enough material so that it could be used both semesters.
There are twelve chapters:

*) Mathematical preliminaries
*) Solutions of equations in one variable
*) Interpolation and polynomial approximation
*) Numerical differentiation and integration
*) Initial-value problems for ordinary differential equations
*) Direct methods for solving linear systems
*) Iterative techniques in matrix algebra
*) Approximation theory
*) Approximating eigenvalues
*) Numerical solutions of nonlinear systems
*) Boundary-value problems for ordinary differential equations
*) Numerical solutions to partial differential equations

with an exercise set at the end of each section and the solutions to the odd numbered problems included at the end.
The level is more rigorous than Atkinson and Han, more of the results are first expressed in the form of theorems as opposed to the Atkinson approach of using worked examples. Once the theorem is presented, Burden then goes on to demonstrate by example. Burden uses Maple code to present the algorithms, which is generally understandable. Since the code is presented in snippets used to solve a specific problem, a lack of experience in Maple is not a serious hindrance. It is easy to infer the meaning of the Maple commands from the context.
However, it lacks the easy readability of the Atkinson book. There were many occasions when I stopped and had to think about what I had read. It eventually made sense, but I had to think about it before it was clear. I don't have that problem with the Atkinson book. Therefore, even if we made a change to a two semester sequence in numerical analysis, I doubt if I would adopt this book.

Not for beginners.......2006-10-17

Examples are few and offer little explaination.
I find this book so hard to follow.

On a good note: algorithms are clear.

MATLAB: An Introduction with Applications 2nd Edition

Average customer rating:

Great for learning the basics of MATLAB.
Reader
Very good introduction
The perfect introductory text for MATLAB
A truly excellent text!

MATLAB: An Introduction with Applications 2nd Edition
Amos Gilat
Manufacturer: Wiley
ProductGroup: Book
Binding: Paperback

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ASIN: 0471694207

Book Description

Assuming no prior MATLAB experience, this clear, easy-to-read book walks readers through the ins and outs of this powerful software for technical computing, including:

Generously illustrated computer screen shots and step-by-step tutorials applied in the areas of mathematics, science, and engineering
Clearly shows how MATLAB is used in science and engineering
Includes a completely new chapter on Symbolic Math
Thoroughly updated to match Matlab's newest release, Matlab 7

Customer Reviews:

Great for learning the basics of MATLAB........2007-08-18

I purchased this title because I am starting a numerical analysis sequence next year using Matlab and I knew only how to plot in 2D and do simple calculations at the command line. After studying from Gilat's text for the past month or so I feel very comfortable using Matlab for all the basics and I am ready to learn how to exploit the full power of the program.

Each chapter gives just enough mathematical background to provide anyone with at least college algebra/trig enough to understand what is going on.
Although this book does not cover any topic too deeply, it does cover the fundamentals of many aspects of Matlab in a way that allows the reader to move fairly quickly through the whole book without getting bogged down in any one area.

In the end you will know the basics about how Matlab operates: how to work with vectors and matrices, how to write simple programs and function files, how to plot and format data, how to fit data to a curve, and how to differentiate and integrate both numerically and symbolically, and a bunch of other great tools for solving problems.

Also, as the other reviewers mentioned, the book makes very good use of graphics to show how input and output should look, as well as what exactly each line means.

I would recommend this text to anyone wanting to learn the basics of Matlab.

Reader.......2007-04-23

If you plan to start with Matlab with no prior experience, this book beats most of the other available titles.Since an inside view of the book is not available on Amazon, I will for the benefit of others list out the chapters here.Ch1 begins with the necessary introduction,developing familiarity with the command window,display formats and precedence of operators.It moves on to Ch2 and Ch3 where arrays are introduced and the mathematical operations on them explained.Ch4 is about script files,Ch5 on elementary plotting techniques using in-built functions like plot and fplot.Ch6 introduces functions and Ch7 extends the previous material to formal programming techniques like loops and control structures.Ch8 explains curve fitting and interpolation,Ch9 is about three dimensional plots and special graphics.Ch10, the last one of the book uses Matlab to do symbolic math which cover elementary algebraic equations.The examples contained in the book are from elementary physics and engineering,so if you are looking for more advanced material that has been treated using Matlab,this might be a little less helpful.The numerical techniques again cover simple problems like projectile trajectory,flow of water from a vessel with a small hole punched in its sidewall,RC circuits, viscosity and so on.Relatively advanced topics like Fourier transforms and applications to signal processing are also left out.If you are done with this book or feel that the material isnt of much help, I will suggest that you might try "Numerical Computing with Matlab" by Moler(he is perhaps one of the architects of Matlab).This book(electronic version) is available for free from the mathworks website [...].Overall this book does a good job in explaining details and is also generously sprinkled with figures and screenshots.Please try it if you are first timer to Matlab.

Very good introduction.......2006-05-04

I had never used matlab when I started reading this book and I found it very easy to follow. I now have a good working understanding of the matlab basics and I recommend that anyone who's looking to get started with matlab pick up a copy.

The perfect introductory text for MATLAB.......2005-12-08

If you are completely new to MATLAB then you will find no better book to guide you through the basics. It is perfectly suited for teaching yourself several basic but still very interesting and useful programming techniques. Topics are presented to the reader in an order carefully determined to produce maximum benefit and knowledge. The book is short and very readable, with many example programs.

In short: if you want a FIRST introductory textbook for MATLAB, you can't beat this book. And it covers the latest version (Release 14).

A truly excellent text!.......2005-11-21

This book was written for teaching Matlab to freshmen in an introductory engineering course, so most of the examples are from first year physics and engineering. Nevertheless, after looking at all competing texts, I chose it to teach Matlab to sophomore geology majors, most of whom had not yet taken calculus or physics. I was very happy with the results; by the end of the semester the students were well on their way to being competent programmers, and I think they will find calculus and physics much easier because of their experience with this book.

I chose this text because it is very well written--you can tell the author has had long experience teaching the subject--and because of its many excellent examples. Most people learn faster by example than by theory, and the examples in this book are easier to follow than those of other texts. Each example shows the command window with a gray background and white insets, or call-outs, containing explanations. The pages are attractive.

In the main text, Matlab commands are set in Courier to clearly distinguish them from the discussion itself. Sections are fairly short and easy to follow, and at the end of each chapter there are many problems of gradually increasing difficulty. The solutions to some problems are given at the back of the book. The abundance of complete examples makes it easy to skip around in the book as soon as students are familiar with Matlab syntax. There are astonishingly few typos and none were serious. Cell arrays and structures are used only where needed for particular commands, a wise pedagogical decision. I particularly enjoyed the second edition's new chapter on symbolic math, as I had never used this part of Matlab in my own research.

The book is 7.5"x9.25" in size with 343 pages, and so is easy to carry around. It's inexpensive, as textbooks go nowadays.

Average customer rating:

Average Elementary Numerical Analysis Text
will need supplimentation
Maybe i'm just biased...
it makes numeric sense
A strict NO for starters

Elementary Numerical Analysis
Kendall Atkinson , and Weimin Han
Manufacturer: Wiley
ProductGroup: Book
Binding: Hardcover

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ASIN: 0471433373

Book Description

Offering a clear, precise, and accessible presentation, complete with MATLAB programs, this new Third Edition of Elementary Numerical Analysis gives students the support they need to master basic numerical analysis and scientific computing. Now updated and revised, this significant revision features reorganized and rewritten content, as well as some new additional examples and problems.
The text introduces core areas of numerical analysis and scientific computing along with basic themes of numerical analysis such as the approximation of problems by simpler methods, the construction of algorithms, iteration methods, error analysis, stability, asymptotic error formulas, and the effects of machine arithmetic.

Customer Reviews:

Average Elementary Numerical Analysis Text.......2007-07-10

Just so you know the source of this review and whether or not you should bother trusting me (hmm..maybe not?):
Ph.D. student in Statistics at Iowa State University.
B.S. Computer Science
B.A. Mathematics

Research areas: numerical analysis, analysis of large data sets, stochastic processes
Former research areas: truth maintenance systems, microarray analysis, parallel computing

Note: Not a plug. I like my job.

First off, the book's title is very appropriate. It requires extensive knowledge of calculus and linear algebra, but it uses a fairly non-rigorous "easy" approach to numerical analysis. It's not advanced enough for use in a graduate level class, even for non-majors, but it is very useful and appropriate for sophomore/junior undergraduates. Even though the approach is somewhat non-rigorous, the book doesn't avoid proofs, and though a more advanced mathematician or computer scientist would see holes, it's a book that surely feels complete to most undergraduate math/cs majors/minors.

The explanations and proofs are definitely not perfect. The proofs leave out steps that they assume readers should find obvious. Academic types like Atkinson who have spent years of research in this field often forget just how difficult these concepts are to undergraduates, so some of these "obvious" steps are not going to be obvious to all readers and should not have been omitted. Mixed in with the proofs are some straightforward explanations, but often they are not in layman's terms and I remember scratching my head at times. So I would give the explanations and proofs a C-/D+.

The author does a better job at the exercises. This is a difficult topic, so you don't want to have to work out problems that are too difficult, but some challenge is required to attain mastery of the subject. I think that this book accomplishes that goal. The problems are rarely overly difficult, and though most would be trivial to professors or professionals, they provide enough challenge to undergraduates who are new to the field. The author also does a good job at choosing problems which are relevant. This is nice since many (most, actually) mathematics books include many problems which look contrived and whose results seem meaningless. Anyways, I give the exercises an A.

The content is decent, but a LOT is left out. Traditionally, a two-semester sequence includes a class on numerical analysis as it relates to differential equations and a class on numerical analysis as it relates to linear algebra. Preceding discussion of either one of these topics is a necessary discussion of general iterative methods and analysis of computational error. This book covers all of those topics but none of them extensively. For a one-semester overview, the content is perfect and includes more than enough material. For a traditional two-semester sequence, this book is a bit skimpy. As stated before, the book is also not appropriate for graduate level classes. So if you haven't learned functional analysis, then don't worry--this book is for you. I give the content a B-/C+.

I was a bit disappointed with the computing examples. The examples were not poorly chosen, but there were not enough of them. Also, I think that they should have used a programming language which is easy to read even if you don't know the language. I give the computing examples a D+.

Even though I said that this book is inappropriate for graduate classes, it might serve as a nice reference for graduate students. I always skim through it as a review before certain classes. Though it can be nice as a refresher, a graduate student would probably be happier with something more rigorous like Peter Linz's "Theoretical Numerical Analysis: An Introduction to Advanced Techniques" (overview - very short) or Kendall Atkinson's (the author who wrote this book) "Theoretical Numerical Analysis: A Functional Analysis Framework".

Final note: To those who complain that it requires extensive knowledge of calculus, was that not a prerequisite at your school? The calculus required to understand this book and work the problems is not at a high school level, but it's nothing that a student who has passed college univariate and multivariate calculus shouldn't be able to handle.

2.5 stars

will need supplimentation.......2004-09-16

Of course this book assumes (advanced?) knowledge of Calc 1 & 2 as well as linear algebra and preferably Dif. EQ. These are all prerequisites for the course in which the book is used. That being said, it is quite annoying when the book *completely* skips over intermediate steps involving calculus leaving the student scratching his head. I find myself with my nose more in my Calc. books trying to figure out what the steps leading to the answer rather than learning Num. Analysis. Would have been nice if at least some intermediate steps were added to most problems, but hey, this is college and hand holding should not be assumed.

There are 3 main gripes which contribute to the low rating.

1. The Cost. For the price of the book, (considering the way the material is presented (see 2.) there should be a solution manual bundled with it. (see 3.)

2. The explanations of the material is cut and dry and not verbose at all, [which adds 2 stars to an original 0 rating] however, there is usually only one example for a topic, followed by 10-15 excercises associated with that topic. This often leads to pure frustration and having to "google" for supplimentary material to help me through the problems due to the fact that the example is far more elemantary than the excercises.

3. Lack of solutions. Coupled with the lack of GOOD examples is the lack of solutions for the excercises you just struggled to drudge through. Chapters that typically have 10-15 problems, some with sub-problems in them usually have 5 or so solutions in the back. (so if there is say question 1, parts a-h, question 2, question 3 a - k....there would be a solution for question 1 part c, question 3 part g...).

If you take this course and this is the required text, pray that your professor has great lectures and notes(neither of which my prof. has) or be prepared to spend many hours on google looking for other references.

Maybe i'm just biased..........2002-01-29

I'm biased because i had the good fortune to take Intro to Numeric Analysis from Ken Atkinson himself. I beta-tested this edition of the text, so my copy is in a loose-leaf binder.

Some reviewers have complained that the book is difficult because examples are in FORTRAN rather than C. I disagree. The real meat of the book is written in mathematical form; what source he provides is merely a convenience. When i took his class, most of the students (myself included) implemented in C rather than FORTRAN. No problem, because he was looking for correct results, not reviewing code.

And yes, this book assumes a solid knowledge of calculus, linear algebra, basic differential equations, and discrete logic. Did you think you'd be able to code mathematics without *understanding* it? If you understand the math in the first place, his implementations are very clear. If you don't understand the math, no amount of clarity will save you.

The real beauty, for me, was how he logically built a progression of topics, with each step providing the foundation for the next one. It was like seeing two years of college math in miniature.

it makes numeric sense.......2001-05-09

i had the pain to use this book for my undergrad. coursework for a 200 level class at Cal Poly. Contrary to the other reviewers, i believe the exercises are mediocre, and the material presented lack depth to provide a solid grounding to numerical analysis. Codes are inconveniently written in fortran-97? instead of the more readable pseudo-code. It may provide a good application supplementary for engineering students, but i strongly advise against it for mathematics undergrads. No fun. Lots of handwaving and smoking mirrors.

A strict NO for starters.......2001-04-22

The author presumes that the reader has an advanced knowledge of calculus even though the book is intended for use by undergrads.the content in the chapters of the book are not enough to solve the questions at the end of ech chapter.if you are looking for an introductory course in NA dont even think of using this book.

Average customer rating:

very nice conceptual overview
Not for the practitioner
Trash
Excellent Introduction, Sparse on Details
A Good Introductory Survey

Scientific Computing
Michael T. Heath
Manufacturer: The McGraw-Hill Companies, Inc.
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ASIN: 0072399104

Book Description

Heath 2/e, presents a broad overview of numerical methods for solving all the major problems in scientific computing, including linear and nonlinear equations, least squares, eigenvalues, optimization, interpolation, integration, ordinary and partial differential equations, fast Fourier transforms, and random number generators. The treatment is comprehensive yet concise, software-oriented yet compatible with a variety of software packages and programming languages. The book features more than 160 examples, 500 review questions, 240 exercises, and 200 computer problems. Changes for the second edition include: expanded motivational discussions and examples; formal statements of all major algorithms; expanded discussions of existence, uniqueness, and conditioning for each type of problem so that students can recognize "good" and "bad" problem formulations and understand the corresponding quality of results produced; and expanded coverage of several topics, particularly eigenvalues and constrained optimization. The book contains a wealth of material and can be used in a variety of one- or two-term courses in computer science, mathematics, or engineering. Its comprehensiveness and modern perspective, as well as the software pointers provided, also make it a highly useful reference for practicing professionals who need to solve computational problems.

Customer Reviews:

very nice conceptual overview.......2006-07-22

Wow, people seem to be really split on this book. I had Mike Heath for numerical analysis/scientific computing and he was an excellent instructor, one of the best lecturers I've ever had. (As a consequence, I have a hard time separating the book and the class, so judge accordingly.) The book is based on his lecture notes, though he added some material and didn't cover every topic in the book. Just reading the book is useful to give you an overview of the point behind different methods. The goal of the class for which this book was written is actually quite conceptual. It was to give scientists (that's me: a stats researcher who makes heavy use of numerical computation) and CS people in areas other than scientific computing a leg up. It was only a first class for people in scientific computing, the rough equivalent of intro Physics or intro Probability/Stats for people in those respective majors. However, you *won't* be prepared to "roll your own" from this book. In fact, at the beginning of the semester Heath was very careful to note that if you have the opportunity to use a library function for most numerical programming, you are nuts to roll your own. Why? Numerical algorithms are usually extremely complicated and the authors of the code often spend years developing careful expertise on them. Frequently the formulas used to elucidate a given method are NOT the ones used to implement it. You need error traps, tricks to handle ill-scaling and other special cases, etc. These are things that someone who has a one-semester, superficial understanding of a topic simply won't have. So consider the book on the goals it set: it is an overview of a field. If you want to learn more about any one topic, you have to dig deeper and consult references and other works, but this is a good place to start. For this, the book serves admirably.

Not for the practitioner.......2005-11-17

If you are interested in Scientific computing from the viewpoint of the end user that is the guy who uses the method to solve practical engineering problems then this book is lacking.

Not enough methods in this book to constitute an introductory survey of the field. Every chapter gets heavy dose mathematical treatment, apparently Heath loves his math but for the rest of us it doesnt translate into know-how. Know how to solve equations using computational techniques. Very few derivations to back his mathematical swagger, very few examples (if any) and fewer numerical schemes to solve problems. Many of the chapters receive cursory treatment such as PDE's get about 70 pages of print. Far too little to do anyone any good.

He does talk about interesting issues such as conditioning and error analysis and computer precision and memory issues but it is done from such a superficial viewpoint that one cannot use anything to improve ones code. Not recommended if you want to learn numerical methods even if you have an excellent professor to learn from. His chapter on FFT's was even more abstruse and there was hardly any methods with which to solve PDE's.

I had this for a graduate course in Numerical Methods but ended up using Hoffman's excellent book on Numerical Methods.

Trash.......2005-10-14

If you want to have a solid understanding of numerical computation, this book is definitely the last choice. Many theorems are given without any proof or even intuitions behind them in this book. Even when a proof is provided, it's often far from rigorous. The organization of chapters is the worst I have ever seen, revelant materials are scattered over several different locations rather than put together. Take the SVD for example, it is mentioned in the end of chapter 3, but reappears in chapter 4, which is very confusing. If you are new to this area, please don't read this book. It gives you many many facts without explanations, which I think is not a good way to learn new things. David S. Watkins' Fundamentals of Matrix Computations is a lot better and easier to understand. It also emcompasses many detailed treatments of various theorems. If you have bought Heath's book, don't be sad, at least it can serve as a coaster.

Excellent Introduction, Sparse on Details.......2004-11-20

While sparse on the details of many of the algorithms and theorems mentioned, as an introduction it covers a broad range of material-enough for two semesters of study. The writing is lucid, and when a proof of a theorem is given, it is easy to follow and explained in english afterward. Rationale is given for everything, which is a great benefit to a student not familiar with the nuances of sophisticated linear algebra.

A Good Introductory Survey.......2002-11-05

This book excels at presenting a reader with little to no knowledge in computer science and a mild mathematical background (knowledge of differential equations as a prerequisite) with the fundamental concepts regarding scientific computing. The presentation of pseudo-code algorithms helps smooth the transition from analytical (pencil and paper) thinking to numerical thinking. The algorithms are presented in a manner such tha anyone with access to dozens of possible environments can apply them, though they are by no means complete, thus requiring some thought into the processes. The material covered is 110% of what an engineer will want to know, 90% of what an applied mathematician will want to know, and 45% of what a numerical analyist will want to know. In all, a great book to begin a foray into numerical computing.

Matrix Computations (Johns Hopkins Studies in Mathematical Sciences)(3rd Edition)

Average customer rating:

Matrix Computations is an excellent guide to understanding and implementing Numerical Linear Algebra
bible
Gargantuan Copy and Paste Monument
Exactly what I needed
The bible of numerical linear algebra

Matrix Computations (Johns Hopkins Studies in Mathematical Sciences)(3rd Edition)
Gene H. Golub , and Charles F. Van Loan
Manufacturer: The Johns Hopkins University Press
ProductGroup: Book
Binding: Paperback

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ASIN: 0801854148

Book Description

Revised and updated, the third edition of Golub and Van Loan's classic text in computer science provides essential information about the mathematical background and algorithmic skills required for the production of numerical software. This new edition includes thoroughly revised chapters on matrix multiplication problems and parallel matrix computations, expanded treatment of CS decomposition, an updated overview of floating point arithmetic, a more accurate rendition of the modified Gram-Schmidt process, and new material devoted to GMRES, QMR, and other methods designed to handle the sparse unsymmetric linear system problem.

Customer Reviews:

Matrix Computations is an excellent guide to understanding and implementing Numerical Linear Algebra.......2007-09-30

This book is an excellent book for the student or researcher who needs to understand clearly the issues that arise in the developement of algorithms for the solution and analysis of linear systems. It gives a great explanation of how one operation like solving a linear system or doing just forward or backward solves can be mapped to basic BLAS primitives and how these variations have been implemented in popular libraries such as Lapack or BLAS and the archetectual reasons why one approach may be more optimized than another, row versus column operations, for example.

For the student it provides a nice walk through on the develpment of these algorithms and for the researcher provides a life long resource for reference to the many algorithms that are laid out here.

This book is clear and easy to follow and it is recomended for anyone who is serious about learning how to design and implement efficient linear algebra algorithms for a variety of archetectual and coding language environments.

bible.......2007-09-24

This book is a bible in matrix computation. While they have a lot of details on everything, though, the notations are rather complicated and hard-to-follow.

Gargantuan Copy and Paste Monument.......2007-05-07

Three stars are for:

(1) Relatively cheap price.
(2) Comprehensive but shallow coverage.
(3) Mass availability.

Hypothesis: The only three prematurely worn keys in Golub & Van Loan's keyboards must be: Control, C and V, since these form the shortcut for copy and paste operations.

There is no depth in this book when compared to classic matrix theory books, although I understand that this may distract from the possible use of the book as a reference manual. But as written, it is of little value in addition to Numerical Recipes; the latter has at least decent text this one does not have character, too much copying and pasting eliminated the book to form a skeleton.

What are the basis books for comparison?

1. Wilkinson, Algebraic Eigenvalue Problem. Super but expensive (>$100).
2. Marcus & Minc, A survey of Matrix Theory and Matrix Inequalities. Super but inexpensive (10$).
3. Horn and Johnson, Matrix Analysis, comprehensive, pretty good, and similarly priced to this ($30).

I am not suggesting that the content should mirror these books but the quality and depth should but despite being in its third edition, the book is full of errors both in pseudo-code and text.

The CTRL-C/CTRL-V effort is so insane that authors' could not help themselves to copy Wilkinson's theorem presentation sequence about the symmetric eigenvalue problem, but Wilkinson's commentary from his book (see Hoffman-Wielandt theorem in Golub & VanLoan second edition).

Whenever someone tells me that they learned something from Golub and Van Loan, I can not help myself to question what they thought they might have learned.

In almost all cases, Golub and Van Loan fans appear to know of a result through memorization without any clue about how it is derived and why it is important. So if this is your bible, then probably you do not deserve a job that requires critical thinking.

The books popularity tells something about the state of the academia: for example, the hotshots of signal processing republished Golub and Van Loan a few times to get their IEEE Fellow titles. Google for 'Multistage Wiener Filter', 'Relationship Conjugate Gradient MSWNF', 'Procrustes Rotations ESPRIT'. Definitely a field that does not appreciate critical thinking but fast copy and paste effort through graduate student slavery.

Exactly what I needed.......2007-03-08

I have been using "canned" programs for matrix calculations, but I needed to learn how they actaully work. This book provided exactly the information that I needed. This book is not for beginners--it requires a pretty good knowledge of linear algebra, but if you have that, this book will be most helpful in understanding sophisticated computational methods

The bible of numerical linear algebra.......2007-01-01

This book is the standard reference for all numerical linear algebra. It is a graduate-level applied math textbook written by practicing professionals for practicing professionals. If you are new to the topic you would probably prefer something like James Demmel's Applied Numerical Linear Algebra.

If you are interested in implementing the algorithms in this book, stop right now and first make sure that you can't use MATLAB or LAPACK instead, or even ScaLAPACK if you need a parallel implementation. Getting these algorithms right is hard, and the hard work has probably already been done by somebody else. LAPACK contains the accumulated wisdom of over forty years of research in numerical linear algebra, and MATLAB contains LAPACK. Don't re-invent the wheel.

On the other hand, if you want to understand how LAPACK works, or if you need to understand its numerical accuracy and stability, then this is the book for you.

Another reviewer has mentioned that this book contains numerous errata in the formulas. This is still true as of the third edition. Usually it is possible to detect and correct these errors by reading and understanding the surrounding text, but beware.

History: Fiction or Science? (Chronology, No. 1)

Average customer rating:

Calculations are only as good as your numbers
Pants on fire?
Accepted History & Chronology Must Be Changed.
Very Interesting
History as Science Fiction

History: Fiction or Science? (Chronology, No. 1)
Anatoly Fomenko
Manufacturer: Mithec
ProductGroup: Book
Binding: Paperback

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ASIN: 2913621058

Book Description

Recorded history is a finely-woven magic fabric of intricate lies about events predating the sixteenth century. There is not a single piece of evidence that can be reliably and independently traced back earlier than the eleventh century. This book details events that are substantiated by hard facts and logic, and validated by new astronomical research and statistical analysis of ancient sources.

Customer Reviews:

Calculations are only as good as your numbers.......2007-08-03

Yes, we can all agree that mainstream history is nearly 100% BS due to politics, economics, ego, problems with dating techniques, and various conspiracies. Agreed. But, I've been researching the distinct possibility that human history (in terms of civilizations) are much more ancient than we've been told, so coming across this book was very interesting to me. I wondered how Fomenko could be wrong (if at all) because he is very persuasive in his presentations. Then it dawned on me. If at previous times in prehistory, due to the various catastrophies that are well documented (comets, asteroids, planetary disruptions, plasma discharge, pole reversals, etc) the Earth was in a different position in relation to the sun, different tilt on its axis, different orbit, different rotation (in terms of velocity and DIRECTION), and the continents were in different positions, then would this not cause the ancients to see the sky (constellations) differently? In other words, is Fomenko making erronious assumptions about the physics of the Earth in pre-history, which then corrupt his data with regards to dating the relevant astrology? The last event to seriously disrupt our planet occured roughly 3500 years ago, according to other good researchers, so is it possible Fomenko has been confused by this? The vastly different physics of our planet in the not so distant past may explain this confusion, which is not to say the "mainstream" version of history is correct; on the contrary. I am not an expert in these fields, but wanted to see if this idea could spark discussion.

Pants on fire?.......2007-07-19

Will people ever read before spamming? Yes, Jesuits could not rewrite world history alone, they had help. Anyway, Dr Prof Acad A.Fomenko does not point to jesuits as the driving force of world wide history manipulation in published volumes 1,2,3;, actually he barely mentions the poor devils. Check it with 'Search inside' feature, please. China is rarely mentioned either, in fact, Dr Fomenko is completely eurocentric. Right, his theory contradicts all mainstream schools of history, because in their actual state they are all built on blatantly erroneus chronology. You don't need a mysterious cabal (conspiracy) to falsify history, the falsification is its modus operandi. It is inherent to history(ians) to falsify (distort) events, as it is inherent to humans to boast as it is inherent to power (authority) to legimize itself by referrring to glorious past made to its own order. Dr Prof Fomenko and team have identified scores of instances of such manipulation in Russian, European, etc.. history, and delivered valid statistical proof thereof. His own 'reconstruction' is completely another story. Forget c14 as a valid method of dating. W.Libby has initially discovered a brilliant method of INDEPENDENT dating. Too bad, c14 method has become a joke after a forced marrige with dendrochronology with consensual chronological scale inbuilt. Radiocarbon method can't stand blind tests, but is so very productive as a rubberstamp.

Accepted History & Chronology Must Be Changed. .......2007-04-09

There is no doubt that history as most know it is a sham, & institution's version of History both University & Church is fradulent & inaccurate. Everything was established with an agenda, The real "Dark Ages" are now when we have access to incredible amounts of information past authorities & more important 'common folk' didn't have but our institutions & educators are slow to evolve because of what has ignorantly & arrogantly been taught for too long. This is on many subjects not just Chronology.

For anyone to question "Why would a Mathematician have anything credible to say of History?" The answer is from Dr. Fomenko's preface in the book: "It would be worthwhile to remind the reader that in the XVI-XVII century Chronology was considered to be a subdivision of Mathematics." These volumes could possibly be some of the most important works to date & should be read by everyone with an interest in History, especially professors & educators who have a duty to the public. I have read both books & must say that 'Chronology 1' has some very eye opening & revolutionary information. Even if these volumes are part true the implications are profound & opens the doors to further investigations & questions which must be done. I speak several different lanquages & must say the logic Dr. Fomenko uses with "inflection" of words & words being read from left to right in one region & right to left in another then written backwards, the removal of vowels & get down to basics of words, or different cities & locations having the same name etc. is correct. Vowel usage has always been optional & varied, actually complicating linquistics & study. The first thing one has to understand is that words never had a fixed spelling in history like we do now, the spelling of words was mutable & regional, as well as names & titles of people were vast, varied & changed, NOTHING WAS FIXED or understood linear. Matters of Life & Death as well as financial profiteering yesterday & today were & are made with ignorant, illogical & conspiratorial views of history & reality, it's time people get closer to the Truth & society collectively grow up.

Very Interesting.......2007-03-07

It is a good proposal and I believe it will mature into something even better in the future. I think it deserves to be read.

History as Science Fiction.......2007-01-10

Anatoly Fomenko has written a very intriguing book, full of pictures, charts, and computer 'proof' of his thesis: backwards of AD900 we don't really know what happened or when. Between AD900 and AD1600 there is more certainty, but there is still a lot of fuzzy ground, and things don't get reliable until we get past the 1600's where the printing press made it very difficult for the perpetrators of this timeline manipulation to change anything that had been committed to print. The Dark Ages did not happen. Books were burned for a reason. One organization has doubled the actual length of its existence by expanding the real chronology. Read why.

I had always wondered why Christ died about AD33 and yet men waited until the 11th century to form the Knights Templar, the Cathars, etc and go after the Holy Land by force. Why the 1000 year gap? Turns out there wasn't more than a 10-12 year gap and he proves it using astronomy. This also implies that the planet is not as old as we have been told, and current Christian and other creationist scientists are already championing that idea without being aware of Fomenko's book. The two groups, creationist scientists and the Russian mathematical analysts corroborate each other. Fascinating.

Of course, all this flies in the face of what we have been told traditionally is the 'proper' chronology of western civilization, and most readers will experience 'cognitive dissonance' in reading this book. It means that our history going backwards from AD1600 becomes progressively more incorrect and unreliable until it cannot be trusted at all... in the space of 700-800 years.

Naturally, the curious, open-minded reader will want to know WHO did this, WHY, and did any of the events we think of as really ancient ever happen?
Dr. Fomenko is a respected scientist/mathematician at Moscow State University who has already answered these questions to the satisfaction of his initially skeptical colleagues. Most of them are now believers, a few still refuse to believe (the usual diehards), and of course the western press has ignored Fomenko's work -- for obvious reasons when you read the book. The ones who perpetrated this chronology ruse have a lot to answer for. They are still with us. That's why this book is a well-kept secret.

I gave the book a 4-star rating because I was unable to check out some of his claims; those I checked were as he said. But if even 1/3 of his claims are true, this punches a big hole in what we think is our history, the meaning of western civilization, our educational process (for repeating the ruse as gospel), and the trustworthiness of the organization that perpetrated this ruse, well-intentioned or not.

This book relates to current research into a Young Earth paradigm, to John Keel's discoveries about our planet, and Fr Malachi Martin's insights (in his now out-of-print books). We are indeed sheep who are manipulated and kept ignorant -- for a reason. While knowing what these men have to say may be the "booby prize" (as in: 'what can you do with this knowledge?'), it will provide interesting reading. Didn't someone say: "...and the Truth will set you free."?? For you to judge if this book contains the truth.

Introduction to Numerical Methods and MATLAB: Implementations and Applications

Average customer rating:

Okay for a text
Useful Book

Introduction to Numerical Methods and MATLAB: Implementations and Applications
Gerald W. Recktenwald , and Gerald Recktenwald
Manufacturer: Prentice Hall
ProductGroup: Book
Binding: Hardcover

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ASIN: 0201308606

Book Description

From the Back Cover: The outstanding pedagogical features of this book are: o use of numerical experiments as a means of learning

why numerical methods work and how they fail; o a separate chapter reviewing the basics of applied

linear algebra, and how computations involving

matrices and vectors are naturally expressed in MATLAB; o use of a range of examples from those that provide a

succinct illustration of a basic algorithm, to those

that develop solutions to substantial problems in

engineering; o consistent use of well-documented and structured code

written in the MATLAB idiom; o a library of general purpose routines—-the NMM

Toolbox-—that are readily applied to new problems; o a progressive approach to algorithm development

leading the reader to an understanding of the more

sophisticated routines in the built-in MATLAB toolbox.

Customer Reviews:

Okay for a text.......2006-03-18

This book is okay for a text book, however there arent many examples, and the examples that are there are very simple. There are solutions for some problems online, though most of them are very basic and don't help very much.

Useful Book.......2004-08-28

This is a nice book for scientists and engineers. There are MATLAB programs already written that you can download from the webpage very easily, and modify for your specific use. I am no programmer, so having programs I can easily modify is a plus. This is meant to only be a review of linear algebra, so if you are trying to learn that subject, you will probably need to supplement this text with another book. This is not terribly in-depth on the MATLAB either. But it is a very useful handbook of plotting and interpolation methods, and how to choose the best methods for your particular set of data.

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