Product Description
Review of previous editions

‘Such a text — and this is the only one of this type I know of — should be the basis of all instruction in Mathematical Programming. Journal of the Royal Statistical Society

‘An excellent introduction … for students of business administration and people who want to see the utility of operations research. European Journal of Operational Research

‘It will be appreciated very much by practitioners who already have knowledge in the field of mathematical programming. Mathematical Programming Society Newsletter Model Building in Mathematical Programming Fourth Edition H. Paul Williams Faculty of Mathematical Studies, University of Southampton, UK

This extensively revised fourth edition of this well-known and much praised book contains a great deal of new material. In particular sections and new problems have been added covering Revenue Management. Hydro Electric Generation, Date Envelopment (efficiency) Analysis, Milk Distribution and Collection and Constraint Programming. The book discusses the general principles of model building in mathematical programming and shows how they can be applied by using simplified but practical problems from widely different contexts. Suggested formulations and solutions are given in the latter part of the book together with computational experience to give the reader a feel for the computation difficulty of solving that particular type of model. Aimed at undergraduates, postgraduates, research students and managers, this book illustrates the scope and limitations of mathematical programming, and shows how it can be applied to real situations. By emphasizing the importance of the building and interpretation of models rather than the solution process, the author attempts to fill a gap left by the many works which concentrate on the algorithmic side of the subject. ... Read more

Customer Reviews (6)

The best book on *practical* model building
That's it.It's the best book for learning modeling in a practical fashion.The learning from this book is practical and you'll learn to build practical and useful models.

Great OR book
This is an excellent book if you want to go deep understanding the true meaning of basic math programs.

Excellent
If there is anything that I would hold against my favorite Operations Research books - it would be the lack of emphasis on model and structure. Williams' book fills in that gap and is an essential companion to every Math Prog book. It is not a cookbook where one can look up a particular problem and the possible ways to model it. Instead, it takes a systematic and very sensible approach to modeling.
The three chapters on Integer Programming Models are amazingly easy to understand and were a real help during a graduate course in the subject. The huge number of practical examples in Parts 2, 3 and 4 of the book is the real value of the book. I would be hard-pressed for space to describe the range of problems that are modeled in Part 2... Part 3 covers a good deal of discussion on these formulations and Part 4 follows it up with solutions. Though solutions are not discussed in detail, they are a great help for someone who has worked hard through the problems and needs a verification of the solutions.
Another useful section in the book is a chapter on the interpretation of Linear Programming solutions. For a person without a Math Prog background (say, a manager), this kind of material is very useful. In fact, it once served as a good refresher for me in a hurry... and an excellent one at that.
The only sore point is a very limited discussion on nonlinear models.

The Best Book of Its Kind
This is one of the only books I have ever encountered that focuses on the practical aspects of model formulation.This is a frequently overlooked aspect of optimization, but models that are well formulated will often result in superior performance.It is particularly strong in the formulation of mixed-integer problems, with a variety of tips for linearizing variable products and for incorporation of logical constructs.It also shows how to model SOS1 and SOS2 variable types.One other area that I found to be particularly useful was a section covering convexity analysis.This was the only book that I've read that did a good job of explaining the concepts and ramifications of problem convexity.Finally, the examples in the book cover a wide range of practical problems.Most are fairly simple, but do a good job of illustrating important techniques.

I highly recommend this book for linear and mixed-integer modelers.However, if you don't use these types of solvers in your work, the book is less likely to be valuable.

Good book for every one
Some books are good for mathematicians, some books are good for managers. This book is different. Williams did a good job to combine both mathematic and application perfective in a single book. Even you have only high school background, this book is readable. For senior researchers or grad students or strong math background person, this book is still enjoyable to recall your fundamental of math modeling. The references are not quite updated, however.Also, this book should added some current optimization tools.Even though the title is model building, not solving, it won't be harmful to have the metaheuristics (only introduction) or KKT. ... Read more

Product Description
A comprehensive, nonmathematical guide to the practical application of linear programming models—for students and professionals in any field

From finding the least-cost method for manufacturing a given product to determining the most profitable use for a given resource, there are countless practical applications for linear programming models. This self-contained book and disk set provides everything you need to know to apply linear programming to real-world situations—how to prepare input, how to interpret output, what to do if the model will not solve, and how to make your results useful and usable—while entrusting the hard-core arithmetic to the user-friendly computer package on disk. Written in clear prose that stays away from the complex mathematics underlying the technique, Introduction to Practical Linear Programming contains:

• A complete introduction to problem structure, assumptions, applications, and other core concepts
• A detailed, step-by-step guide to model construction (from a problem description to a useful model) and interpretation of output
• Linear programming examples and exercises from a range of real-life areas, including agriculture, manufacturing, finance, and advertising
• Important techniques for troubleshooting and error identification
• Procedures for testing how good your model is—how robust are the results?—and more

Product Description

In 1958, Ralph E. Gomory transformed the field of integer programming when he published a short paper that described his cutting-plane algorithm for pure integer programs and announced that the method could be refined to give a finite algorithm for integer programming. In January of 2008, to commemorate the anniversary of Gomory's seminal paper, a special session celebrating fifty years of integer programming was held in Aussois, France, as part of the 12th Combinatorial Optimization Workshop. This book is based on the material presented during this session.

50 Years of Integer Programming offers an account of featured talks at the 2008 Aussois workshop, namely

- Michele Conforti, Gérard Cornuéjols, and Giacomo Zambelli: Polyhedral Approaches to Mixed Integer Linear Programming

- William Cook: 50+ Years of Combinatorial Integer Programming

- Francois Vanderbeck and Laurence A. Wolsey: Reformulation and Decomposition of Integer Programs

It includes a DVD containing a recording of the three original lectures as well as a panel discussion with six pioneers.

The book contains reprints of key historical articles together with new introductions and historical perspectives by the authors: Egon Balas, Michel Balinski, Jack Edmonds, Ralph E. Gomory, Arthur M. Geoffrion, Alan J. Hoffman & Joseph B. Kruskal, Richard M. Karp, Harold W. Kuhn, and Ailsa H. Land & Alison G. Doig.

It also contains written versions of survey lectures on six of the hottest topics in the field by distinguished members of the integer programming community:

- Friedrich Eisenbrand: Integer Programming and Algorithmic Geometry of Numbers

- Raymond Hemmecke, Matthias Köppe, Jon Lee, and Robert Weismantel: Nonlinear Integer Programming

- Andrea Lodi: Mixed Integer Programming Computation

- Francois Margot: Symmetry in Integer Linear Programming

- Franz Rendl: Semidefinite Relaxations for Integer Programming

- Jean-Philippe P. Richard and Santanu S. Dey: The Group-Theoretic Approach to Mixed Integer Programming

Integer programming holds great promise for the future, and continues to build on its foundations. Indeed, Gomory's finite cutting-plane method for the pure integer case is currently being reexamined and is showing new promise as a practical computational method. This book is a uniquely useful celebration of the past, present and future of this important and active field. Ideal for students and researchers in mathematics, computer science and operations research, it exposes mathematical optimization, in particular integer programming and combinatorial optimization, to a broad audience.

Product Description
A practical, accessible guide to optimization problems with discrete or integer variables

Integer Programming stands out from other textbooks by explaining in clear and simple terms how to construct custom-made algorithms or use existing commercial software to obtain optimal or near-optimal solutions for a variety of real-world problems, such as airline timetables, production line schedules, or electricity production on a regional or national scale.

Incorporating recent developments that have made it possible to solve difficult optimization problems with greater accuracy, author Laurence A. Wolsey presents a number of state-of-the-art topics not covered in any other textbook. These include improved modeling, cutting plane theory and algorithms, heuristic methods, and branch-and-cut and integer programming decomposition algorithms. This self-contained text:
* Distinguishes between good and bad formulations in integer programming problems
* Applies lessons learned from easy integer programs to more difficult problems
* Demonstrates with applications theoretical and practical aspects of problem solving
* Includes useful notes and end-of-chapter exercises
* Offers tremendous flexibility for tailoring material to different needs

Integer Programming is an ideal text for courses in integer/mathematical programming-whether in operations research, mathematics, engineering, or computer science departments. It is also a valuable reference for industrial users of integer programming and researchers who would like to keep up with advances in the field. ... Read more

Customer Reviews (6)

Good book and fast delivery.
The book's sent to me a bit early than expect...that's good. But the cover is quite old and there are still a label of the library on the book.

This is the classic introduction textbook for integer programming
This book provides the overview of the integer programming. It is good to be an introduction integer programming textbook.

Very good!
It has all the major subjects in IP and uses a mathematical approach very clear.

Integer Programming
It's not good for the beginners who never have basic knowledge about linear, nonlinear, and integer programming. Too difficult to understand because it contains only theories.

One of the most interesting books I've used
This book features great contents. Integer programming is one of the most interesting subjects and this book captures the beauty of it through the use of nice explanations and a neat and organised notation. The author carefully describes the algorithms used to solve some of the classic integer programming problems. The theorems are generally followed by proofs and the contents are presented in a very comprehensive order. ... Read more

Product Description
The book presents a unified treatment of integer programming and network models with topics ranging from exact and heuristic algorithms to network flows, traveling salesman tours, and traffic assignment problems. While the emphasis of the book is on models and applications, the most important methods and algorithms are described in detail and illustrated by numerical examples. The formulations and the discussion of a large variety of models provides insight into their structures that allows the user to better evaluate the solutions to the problems. ... Read more

Product Description
Linear models are central to the practice of statistics and form the foundation of a vast range of statistical methodologies. Julian J. Faraway's critically acclaimed Linear Models with R examined regression and analysis of variance, demonstrated the different methods available, and showed in which situations each one applies.

Following in those footsteps, Extending the Linear Model with R surveys the techniques that grow from the regression model, presenting three extensions to that framework: generalized linear models (GLMs), mixed effect models, and nonparametric regression models. The author's treatment is thoroughly modern and covers topics that include GLM diagnostics, generalized linear mixed models, trees, and even the use of neural networks in statistics. To demonstrate the interplay of theory and practice, throughout the book the author weaves the use of the R software environment to analyze the data of real examples, providing all of the R commands necessary to reproduce the analyses. A supporting Web site at www.stat.lsa.umich.edu/~faraway/ELM holds all of the data described in the book.

Statisticians need to be familiar with a broad range of ideas and techniques. This book provides a well-stocked toolbox of methodologies, and with its unique presentation of these very modern statistical techniques, holds the potential to break new ground in the way graduate-level courses in this area are taught. ... Read more

Customer Reviews (2)

Not so hot for teaching principles, okay for case studies
As an introduction to the general linear model this book by Julian Faraway is disappointing. Every time he introduces a new topic, the topic is quickly dismissed.I wish that he would create concise paragraphs that explain the concept he is introducing.Instead, he quickly launches into R code. I just don't find his writing style illuminating.

However, as a book of case studies, R code, and worked examples, this book is pretty good.So, learn the principles from someone else (I've been using Agresti's book on categorical data analysis and a book by Quinn & Keough) and then apply them in the R setting using the examples from Faraway.

This is coming from the perspective of a statistics graduate student.As an introduction to the subject of categorical data analysis and other linear model derived techniques I believe that it falls a bit short.

Flawed but well-explained
"Extending the Linear Model with R" is a "sequel" of sorts to the impressive "Linear Models with R" also written by Faraway.It assumes a basic knowledge of R (you don't have to be an expert) and a decent understanding of linear models.If you don't have that background, then I would start with the before-mentioned "Linear Models with R".If you read and understood that book, then you should be more than prepared for this one.

This book covers extensions of the linear model including Generalized Linear Models (GLM's), Mixed and Random Effects Models, Nonparametric Regression Models, Additive Models (including GAM's - Generalized Additive Models), and it contains a brief introduction to Regression Trees and Neural Networks.The biggest focus is on Generalized Linear Models.The book is fairly thorough, though not exactly comprehensive, in covering the topic of GLM's and specific commonly used GLM's.The material is very well-explained and easy to follow and they do a good job at integrating code, examples, and graphs in a way that facilitates understanding of both statistical concepts regarding GLM's and also the implementation of these concepts in R.The code is especially useful and it covers most things in R that you will need for this topic, at least those available from CRAN.The book is not very rigorous regarding theory, but that only makes the book easier to read and more practical.However, I do have one complaint regarding this section.The author spends several chapters discussing various commonly used GLM's and THEN finally gets around to defining what a GLM is and covering the basic theory.This seems backwards to me and for this reason I wouldn't read the chapters in order.Also, due to the late coverage of some of the basic theories, we don't get to see the implementation and analysis of certain sub-topics (e.g. leverage and influence) in the early examples.

Mixed and Random Effects models are second in terms of attention received.The organization is better and the explanations and code integration continue to be handled well.Nonparametric Regression and Additive Models only receive one chapter apiece, but both chapters are extremely informative and they are well-explained like the rest of the book.I was especially happy to see the coverage of GAM's (it's very short but useful) since it is a moderately recent topic (1990) and many similar books only make a brief mention of them (hey, GAM's exist) if they are mentioned at all.The chapter on Regression Trees is short, but again they make sure to cover many of the important sub-topics with clarity.The Neural Networks chapter is skimpy and you won't learn much, but it was an unexpected bonus so I can't take off points for that.

Do note that this book takes a regression approach throughout, so look elsewhere for an ANOVA perspective.The book is short with plenty of room left to talk about other topics.Thus, I would have liked to see a second part devoted to an ANOVA approach since I'm the kind of person who hates having to thumb through countless books, but they are open about the book's scope so I can't really complain.

Okay, one more complaint.I would have greatly liked to see an appendix of the R functions used throughout the book with short descriptions and references to where in the book you can find the function being discussed.R Help isn't bad, so it's not a tragic omission, but it still would have been nice.

In summary, this book is extremely useful if you plan on using extensions of linear models with R.Flaws aside, it receives my recommendation. ... Read more

Product Description

Incorporating a number of the author’s recent ideas and examples, Dynamic Programming: Foundations and Principles, Second Edition presents a comprehensive and rigorous treatment of dynamic programming. The author emphasizes the crucial role that modeling plays in understanding this area. He also shows how Dijkstra’s algorithm is an excellent example of a dynamic programming algorithm, despite the impression given by the computer science literature.

New to the Second Edition

• Expanded discussions of sequential decision models and the role of the state variable in modeling
• A new chapter on forward dynamic programming models
• A new chapter on the Push method that gives a dynamic programming perspective on Dijkstra’s algorithm for the shortest path problem
• A new appendix on the Corridor method

Taking into account recent developments in dynamic programming, this edition continues to provide a systematic, formal outline of Bellman’s approach to dynamic programming. It looks at dynamic programming as a problem-solving methodology, identifying its constituent components and explaining its theoretical basis for tackling problems.

Product Description
Algorithmic Principles of Mathematical Programming investigates the mathematical structures and principles underlying the design of efficient algorithms for optimization problems. Recent advances in algorithmic theory have shown that the traditionally separate areas of discrete optimization, linear programming, and nonlinear optimization are closely linked. This book offers a comprehensive introduction to the whole subject and leads the reader to the frontiers of current research. The prerequisites to use the book are very elementary. All the tools from numerical linear algebra and calculus are fully reviewed and developed. Rather than attempting to be encyclopedic, the book illustrates the important basic techniques with typical problems. The focus is on efficient algorithms with respect to practical usefulness. Algorithmic complexity theory is presented with the goal of helping the reader understand the concepts without having to become a theoretical specialist. Further theory is outlined and supplemented with pointers to the relevant literature.
... Read more

Product Description
Presents a computational theory for robust control that highlights the fundamental limitations and capabilities of linear controller design for plants with uncertainty. DLC: Automatic control. ... Read more

Customer Reviews (3)

Not useless
I think that the other reviews posted here do not give a fair evaluation of the book. (These reviews are also so similar that one wonders why the second reviewer felt it necessary to post...) It is true that the L1 method has not received as much attention as other robust control techniques, such as the H-infinity theory, but it is a viable alternative, and has been used to design real-life controllers, such as those for high-purity distillation columns.One of the merits of this approach, as J. Ball noted in his review of this book for SIAM Review (Vol.41, No.4) is that it is easier to incorporate time-domain constraints (e.g., overshoot, settling time, maximum deviation from desired tracking) than in some other robust control approaches.Other features of controller performance can be analyzed as well, because the design approach is amenable to detailed analysis.This book is not meant to be a treatise on linear programming or on functional analysis, and shouldn't be criticized on those grounds. Contrary to the statements ofthe earlier reviewers, the material of this book should be of some interest to researchers: there are open problems in this area that are discussed in an article by Bamieh and Dahleh in the book "Open Problems in Mathematical Systems and Control Theory" (Springer, 1999), and articles on the relationship of infinite-dimensional convex analysis with this area have been recently published in IEEE Trans. Auto. Control. Potential readers should compare this book with the later "Computational methods for controller design" (Springer, 1998) by Elia and Dahleh, which covers some of the same topics.

The book gives no insight into the subject.
This book is primarily about one approach to the control of plants with uncertainties: The L1 (ell one) theory.Unfortunately it is not a very useful book: there is probably not one real life plant that carriers a controller designed by thismethod.This is not surprising since the L1 objective is of little interest in general.

The book is essentially a watered down version of a few topics ininfinite dimensional optimization and functional analysis.TheL1 theory is simply an application of the Hahn Banach theorem toan idealized formulation of the control problem. The problem is then reduced to an infinite dimensional linear program, which, with truncation is reduced to a finite dimensional one.The objective function, however, is not very useful.One can simply use the constraints to obtain a feasible solution to the LP, but the resulting design is difficult to comprehend, and it is difficult to specify margins with this method.

So for the control engineer, the book is not very useful.For the mathematicians, it gives little insight into control issues, and talks only of known mathematics.

The does not provide insight into the subject of Control
With the exception of one chapter, this book is about a narrow and unproven approach to control system design: The L1 theory. There is almost surely no real life plant that carries a controller based on this design.Additionally, the authors present a mathematical treatment of an engineering subject, butthe treatment fails to give the experienced control engineer any insight.

From the point of view of mathematical control theory, the book is simply a watered down version of a few topics in infinite dimensional optimization and functional analysis.It is based onan application of the Hahn Banach theorem to a formulation of thecontrol problem.It also contains a lot of mathematical facts, but it does not tie them well to control theory. So the mathematician will get little insight into the subject of control.

Here we have a book that is neither useful to the engineer, nor to the mathematician. ... Read more

Customer Reviews (2)

Wealth of easy-to-understand modeling/algorithmknowledge!!!
Do not look at the date of this book (1977).It still provides the foundation of applied mathematical programming used today.And it is still used today in modeling courses as the main reference because it covers topics from A to Z in a practical and easy-to-understand manner.

Not only does this book show you how to model a wide array of problems, it explains the mathematical algorithms/techniques behind the modeling.And it combines the theory with tonnes of examples!!!

After reading this book, I finally have a true understanding of several topics such as linear programming, duality theory, sensitivity analysis, network/dynamic programming, integer programming, non-linear programming, and my favorite, modeling/solving large-scale problems (via column generation, decomposition, etc..)

The best thing about the book is that advanced topics do not seem advanced any more!!!I wasted my $$$ on too many Operational Research books that over-complicate topics; this book should be on every mathematical programmer's book shelf.

Many thanks to Bradely, Hax, and Magnanti for a job well done!

this book has to be in your reference library
Its true that no single linear programming book has everything you need. Bradley's book is excellent for problem formulation and exercises.

I keep it along with Katta Murty's and James Ignizio. ... Read more

Product Description

Product Description
The aim of stochastic programming is to find optimal decisions in problems which involve uncertain data. This field is currently developing rapidly with contributions from many disciplines including operations research, mathematics, and probability. Conversely, it is being applied in a wide variety of subjects ranging from agriculture to financial planning and from industrial engineering to computer networks. This textbook provides a first course in stochastic programming suitable for students with a basic knowledge of linear programming, elementary analysis, and probability. The authors aim to present a broad overview of the main themes and methods of the subject. Its prime goal is to help students develop an intuition on how to model uncertainty into mathematical problems, what uncertainty changes bring to the decision process, and what techniques help to manage uncertainty in solving the problems. The first chapters introduce some worked examples of stochastic programming and demonstrate how a stochastic model is formally built. Subsequent chapters develop the properties of stochastic programs and the basic solution techniques used to solve them. Three chapters cover approximation and sampling techniques and the final chapter presents a case study in depth. A wide range of students from operations research, industrial engineering, and related disciplines will find this a well-paced and wide-ranging introduction to this subject. ... Read more

Customer Reviews (3)

Insufficient detail
The author is certainly well recognized in the field. However, I found the book a bit difficult to read. I felt the author could have described things in greater detail and depth. That is, he seemingly left a lot for the reader to infer and derive for himself.

Formalism doesn't equal good introduction.
Given that there are not many books in the area of stochastic programmingBirge et al have written a book that will be a necessary reference for thetime being. The first third of the book does provide a good introduction tothe basics of SP but after that a level of formalism dominates that makesone wonder if she is reading from an arcane optimization journal. The latertwo thirds of the book is really nothing more than an amalgam of resultspulled from the literature (journals). As such, little motivation isprovided for the major results that are for the most part just juxtaposedon after another. One wonders why such a journalistic style would be usedfor an introductory text. After all the subject should not be presented asa springer-verlag MATH text in a field like algebraic topology where atheorem-proof format is legimate.Thus, until a better introductory textcomes along that blends more of the practical engineering aspects with thetheory we must be content with the current state of the art.

A must own guide to Stochastic Programming
Introduction to Stochastic Programming is a must own book for anyone working in OR, IE, MS, etc.As stochasticity becomes more and more important in the field, this book becomes increasingly valuable. "Introduction" is a bit of a stretch.It starts from ground zeroof Stochastic Programming, but is very heavy on the math.If you aren'tsolid with your LP and probability, then a brush up is definately in order. This book is not for the faint of heart.Nevertheless, Birge and Louveauxdo an OUTSTANDING job.The examples are clear, easy to follow (assumingyou're not math phobic) and very relevant.They go through differentformulations of stochastic programms (recourse, chance constrained, etc.). The book discusses formulation, algorithms, and applications. There are notmany books out there on Stochastic Programming...and this is really theonly one you need to own. ... Read more

Product Description

Popular in the first edition for its rich, illustrative examples and lucid explanations of the theory and use of hierarchical linear models (HLM), the book has been reorganized into four parts with four completely new chapters. The first two parts, Part I on "The Logic of Hierarchical Linear Modeling" and Part II on "Basic Applications" closely parallel the first nine chapters of the previous edition with significant expansions and technical clarifications, such as:

* An intuitive introductory summary of the basic procedures for estimation and inference used with HLM models that only requires a minimal level of mathematical sophistication in Chapter 3
* New section on multivariate growth models in Chapter 6
* A discussion of research synthesis or meta-analysis applications in Chapter 7
* Data analytic advice on centering of level-1 predictors and new material on plausible value intervals and robust standard estimators

While the first edition confined its attention to continuously distributed outcomes at level 1, this second edition now includes coverage of an array of outcome types in Part III:

* New Chapter 10 considers applications of hierarchical models in the case of binary outcomes, counted data, ordered categories, and multinomial outcomes using detailed examples to illustrate each case
* New Chapter 11 on latent variable models, including estimating regressions from missing data, estimating regressions when predictors are measured with error, and embedding item response models within the framework of the HLM model
* New introduction to the logic of Bayesian inference with applications to hierarchical data (Chapter 13)

The authors conclude in Part IV with the statistical theory and computations used throughout the book, including univariate models with normal level-1 errors, multivariate linear models, and hierarchical generalized linear models.

Customer Reviews (7)

THE Book - dense but important
Basically if you buy this book, you don't need anything else on HLM. It's comprehensive, as the technique stands. But you can't learn HLM from this book - you'll need a teacher.

If you want to learn HLM, this book will not help you.
The book is not bad. But need so much improvement. I send a letter to the authors with my comments.
For example:

A basic topic such as "assumptions" is not clear presented. You have to "discover" them on your reading.

You will find things like "as we can see this will create a problem" ok. but what kind of problem, why are these a problem?

I got the book, and for each chapter I read, I had to go online to look for additional information, and clarifications.

It is clear that the authors are experts and the topic, and things are "so clear and obvious" for them, but the people that is reading the book might have problem following it.

Conclusion. After 2 weeks I decided to return the NEW book and get a USED one.

I also got the "manual" for the HLM6 software, dont bother. It is not a good manual. Actually, it is not a manual because it does not teach you how to use the software, it does not explain its different options, it just show you some examples. You can find similar things online. I returned the manual as well.

Near-bibilical status
The second edition of this texbook by Raudenbush and Bryk has achieved near-biblical status in the world of multi-level modeling.It is quite comprehensive, and the chapter on centering, an unexpectedly important and complex topic, is the best I"ve seen.

Nevertheless, Raudenbush and Bryk make what I take to be a serious error when they fail to acknowledge the strengths and weaknesses and breadth and limitations of their likely audience.For all but the best trained mathematical statisticians, this book is inaccessible and, for the reader, money poorly spent.Raudenbush and Bryk must know that most sociologists, political scientists, program evaluators, policy analysts, and numerous others will find their book too difficult to use as a self-teaching tool.Thus, in fairness to those trying to keep up with important methodological developments, the authors should, at the very least, conspicuously acknowledge the demands their book places on the reader.

For most readers, there are much better ways to a make a start on multilevel modeling.If one wants to, he or she can then work toward meeting the demands imposed by Raudenbush and Bryk.

The classic text on Hierarchical Linear Modeling
This is a must-have book for anyone who is serious about understanding multilevel/hierarchical linear modeling.

pre-req: mid-level stats experience
I had taken a class in HLM before, and I bought this book to refresh myself on the details.It takes a good deal of attention to detail and concentration to really get the full measure from this book, although it's all in there.Despite the authors' best efforts, there is a good bit of stats jargon in the book, so a reader who is not familiar might have some difficulty.If you're at a point where learning HLM is a logical next step, you'll be fine and I recommend this book.However, if your over-eager faculty advisor told you to learn HLM, despite your minimal experience in stats, you're better off enrolling in a class or workshop. ... Read more

Product Description
The first of the two volumes of the leading and most up-to-date textbook on the far-ranging algorithmic methododogy of Dynamic Programming, which can be used for optimal control, Markovian decision problems, planning and sequential decision making under uncertainty, and discrete/combinatorial optimization. The treatment focuses on basic unifying themes, and conceptual foundations. It illustrates the versatility, power, and generality of the method with many examples and applications from engineering, operations research, and other fields. It also addresses extensively the practical application of the methodology, possibly through the use of approximations, and provides an introduction to the far-reaching methodology of Neuro-Dynamic Programming.The first volume is oriented towards modeling, conceptualization, and finite-horizon problems, but also includes a substantive introduction to infinite horizon problems that is suitable for classroom use. The second volume is oriented towards mathematical analysis and computation, and treats infinite horizon problems extensively. The text contains many illustrations, worked-out examples, and exercises. ... Read more

Customer Reviews (3)

Understated and overstated all at once
After having been exposed to (and purchased) a number of books by Dr. Bertsekas on an eclectic array of topics, I have little doubt about his superb acumen and mastery of many, many subject areas involving applied mathematics.This book is no exception.Further, the legibility of Bertsekas' books score much higher the other two members of the GMTM (the Greek Math Triad of MIT), namely Bertsimas and Tsitsiklis, whose writings are highly esoteric in the purest form of the Archimedian tradition.

However, despite applaudable efforts to make the book more accessible to those on a lower IQ scale than the top-shelf MIT doctoral students, Bertsekas' 2-volume set on DP & Optimal Control still falls short in two key areas: (1) Visualization; and (2) Inconsistency in flow.

Being a product of the multi-media era, I and many of my fellow students are highly-dependent on visualization tools.In my opinion, what is NOT conveyed through lines and lines of cryptic (and author-specific) symbolism and mathematical formulation CAN be effectively conveyed through the strategic (and reasonably-ample) use of graphs and diagrams.Once the reader has a general idea of the gist of the concepts, then the specifics can be stated using precise mathematical language.But until then, the formulations are subject to open and erroneous interpretation (much the same way that few students are able to decipher the true essence of Symphony No. 40 by merely staring at the musical notes on sheets of paper).A picture is worth a thousand Greek symbols.

Inconsistency in flow refers to the fact that certain basic concepts are overstated in the book, while some of the more critical concepts (particularly those involving not-so-obvious algebraic steps in the proofs) are deemed "trivial" by the author, and apparently skipped for the sake of keeping the book to a manageable size.My suggestion is to err on the side of over-inclusion by keeping the proofs to a minimal in the actual text, but making the proofs (with all "trivial" elaborations) available online through the publisher's website (or via an included CD-ROM).

The aforesaid aside, the book is one of the best efforts in providing a comprehensive and modern analysis of DP/MDP, and its later editions do have the potential to claim 4.5-5 stars.In the interim, I recommend Powell's Approximate DP book as a less painful way of learning what I personally consider to be one of the most important topics in combinatorial optimization.

not what i expected
This book has so many unnecessary material in it. This makes you tired if you want to read it as your course book. I think Bertsekas, is more busy to write as many as book he can instead of making them readable.

Best book I've used so far.
This book does a very good job presenting both deterministic and stochastic optimal control.The author does a particularly good job in presenting the derivation of the Bellman equation and its relation tovariational formulations for deterministic optimal control. Thereare also many very good problems with which the reader can test herunderstanding, and the author has made many solutions available on his webpage.Problems range from testing theoretical understanding to determinigoptimal policies for various control problems.There are even someexercises which ask the reader to develop parallel codes to solve someproblems, so I think there is something in this book for everybody. Richard Bellman once said that there is considerably more to optimalcontrol than just locating the eigenvalues of some matrix in the complexplane.I believe that Bertsekas has remained faithful to Bellman's viewwith the broad range of problems which he attacks through dynamicprogramming. I am currently doing a PhD thesis in mathematics studyingBellman equations, and I cannot think of a better source for intuitionabout control problems than Bertsekas' book.He even does a nice job inpointing out where he has omitted technicalities in the mathematicaltreatment for those who wish a very rigorous approach to control. Ifthere is a better book out there, I am not aware of it. ... Read more

Product Description
Undergraduate linear algebra is both beautiful and replete with real world applications and connections to the rest of mathematics. The purpose of the present volume is to enrich the understanding of linear algebra for a wide audience by placing a broad collection of short items in the hands of teachers, students, and others who enjoy the subject. Because undergraduate linear algebra is so fundamental to the mathematics curriculum, it is often taught by non-specialists and specialists alike. "Linear Algebra Gems" offers to all teachers clever ways in which core ideas can be presented to their students.

Most articles are accessible to those with modest preparation in linear algebra, including beginning students. However, many items will also contain pleasant surprises even to those well-versed in the subject. The editors have combed through the literature, and have selected from original submissions, to find expository articles and problems to enrich the reader's understanding. The seventy-three articles selected are organized into nine sections, with over 120 problems grouped into subject categories as a tenth section.

Contributors to the volume include experts in the field and long-time teachers of linear algebra. The book was prepared as part of a broad contract with the National Science Foundation to improve undergraduate linear algebra education. The editors hope that many readers will find enjoyment from this collection. ... Read more

Customer Reviews (1)

If you need some small sparks of new material in your linear algebra classes, this is the book for you
Years ago, I taught the two-semester calculus sequence for several years in succession. While that made it easy and routine for me to present the topics in lecture, I also recognized the potential for becoming stale in focus. It is easy to repeat yourself year after year, after all your audience changes, so there will be no complaints.
In order to avoid this "rusting in place", it is necessary for the teacher to search for and find new, different and interesting ways to present the material. In the area of linear algebra, where the same potential for stagnation exists, this book will solve the problem. It contains sets of very short proofs, applications and operations of the fundamental principles of linear algebra. In most cases, you will not find them in linear algebra books, so they will give you new ways to present the material.
Fortunately, technology is generally not a part of these short bursts. Since the goal is to teach what linear algebra is and what it can be used for, using a symbolic mathematics package would be a hindrance to the understanding. If you teach linear algebra and are looking for some new sparks, this is the place to look.
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