mathematical optimizations
341099
Very clear and exhaustive. A lot of examples. A good mathematical background is obviously required. Every programmer involved in projects on a domain requiring mathematical optimizations should have it on its desk.
4610469
I'm a recent Ph. D. graduate in Operations Research and during the last 4 years this book has been one of my main tools in both my studies and academic research. This book is a comprehensive introduction to nonlinear programming and is divided in two parts.; Part I covers the main theoretical considerations and Part II covers many important optimization methods. I would say that the main feature of this book is that it manages, in a clear  and concise way, to take the reader from the very basics of optimization to advanced and current topics of nonlinear optimization. In particular, it covers the theory and methods of convex optimization of non-differentiable functions where the important concepts of subdifferentials and conjugate duality come into play. From my opinion, these are necessary tools for any aspiring researcher in optimization theory and I haven't seen yet a more understandable and concise presentation of these subjects. Another area where this book shines is in it's examples and applications. Contrary to many mathematical introductory books, I would say that every example of this book is non-trivial and of some theoretical or applied value. It is in these examples and applications where the reader can see the real value of the developed theory and methods. Believe me when I say that more than once you'll be referring back to the examples to get ideas for even your own research.  All said, I really enjoyed this book and value highly it's contents.
1138588
Es un libro muy bueno, si te gustan las matemticas lo disfrutars al mximo. Te ensea a ver las matemticas de una nueva forma muy apasionante e interesante. Recomendado al lim x->0 (1/x)
4938221
Its a great book; some chapters may be too hard for thse who do not have mathematic expertise. Sure I'd recommend this book.
261323
This is an excellent review of the math of pursuit and escape paths. I have not read the book completely, but I concentrated my reading on a couple of problems I was mostly interested in: The Lady in the Lake problem, and the Lion-and-Man problem. These two problems are strictly connected, and have more immediate geometric explanations than the equations of the problems presented in the book. However, these alternative explanations are missing in the book; too bad because they add a lot to the understanding and intuition of the problems. In one case actually, (Lion-and-Man problem), I believe the outcome of the problem  is different from the one provided. This doesn't detract from this enjoyable book, which is well written, with very approachable, step-by-step math passages.
1850006
As a finite element software developer, I find this book is so designed that it is relatively easy to understand by any level of graduate student. The first few chapters on 1-dimensional finite element equation formulation  is the best I have ever seen so far in the "sea" of finite  element text. Other than that, the overall content of the book is rather  "light". It should be read by all users who use finite element.
740881
LINEAR ALGEBRA, Third Edition, is one of the better books on linear algebra. The material is presented in an abstract and mathematically rigorous fashion. The focus of the book is on the ideas and proofs behind the linear algebra -- its treatment of applications to physics and computer science is almost nonexistent. Topics covered include vector spaces, linear transformations, systems of linear equations, determinants, inner product spaces, eigenvalues and eigenvectors, and canonical forms.
For the aspiring engineering or computer science student, this book is not for you. Basic matrix theory is enough for those fields, and this book is littered with rigorous proofs. There are many other textbooks that present linear algebra from more of an engineering or computer science perspective. As an alternative I recommend that you take a look at "Matrix Analysis and Applied Linear Algebra" by C.D. Meyer.
The style of this book is written in the traditional theorem-proof-example style and is thus geared more towards aspiring mathematicians, especially those who enjoy theory and pure mathematics. Many of the examples demonstrate less than obvious inferences and can be very useful, but of course the meat of the book lies in the comprehensive build-up of linear algebra theory from a mathematically sophisticated point of view.
In summary, a highly recommended purchase for mathematicians. Computer scientists and engineers should look elsewhere though.
3356520
Dano is a key reference for those who are interested in the history of the application of linear programming to solve the problems of a variety of industries. The survey of applications primarily covers up to the 1960's. The information and sample problems in this book are hard to find elsewhere.
4284361
I can't say more than what already been said by other reviewers. To recap,
F = {all excellent combinatorial optimization books}
cost(this_book) <= cost(y) for all y in F.
;)
1190001
This book strikes a good balance between applications and mathematical rigor. Useful for practitioners of numerical inversion as a reference and a gateway to the original mathematical works.
1782575
This book by Hildebrand along with its companion Methods of Applied Mathematics are a perfect match for students of Science and Engineering. It is a must for this era where the blind use of mathematical software is prevalent masking the intricacies of the method.
The details of the  method employed in the software should be understood to have any faith in the software output.
1598996
Would recommend this book to anyone who is looking to understand the operational and mathematical constructs involved in this area.
2898721
The book is pitched to a student majoring in maths. The level of proofs given correlates with such a presumed background. It is well suited for a 3rd or 4th year undergraduate or possibly a graduate student. Take the introductory discussion of random variables. The treatment delves quickly into aspects like Borel sets and sigma algebras. This is something that presumes a thorough acquaintance with those and related concepts.

A neat feature is the many graphs. The topic inherently lends itself to this, unlike some other branches of maths like combinatorics. The book gives the reader quick graphical understanding of the numerous probability distributions.

Some chapters also offer vignettes. Short typically historical notes that might describe how the field has charged, usually in response to the massively cheaper computing power. This has made such items as hardcopy random number tables defunct.
3829867
The problem of finding the shortest route given a list of locations that need to be visited and a map is an old problem that arose out of practical need.  The computational complexity of it though is quite extraordinary as the number of potential routes that need to be examined grows exponentially.  The innocuous question of finding the best route has led teams of mathematicians and computer scientists to tackle the problem and whether a polynomial time solution to the problem (more or less a solution for which the computable time can be tackled on a reasonable human scale) is a clay millenium prize problem who's solution will gain the winner 1 million USD.  In Pursuit of the Traveling Salesman is an overview of the problem and a readable history of some proposed computational solution methods.

The book starts with the history of the problem and introduces similar problems in graph theory as a background.  It discusses early thoughts about the problem and how it was proposed and who started to think about it, it is interesting to note that focus on it was geographically broad with it being of practical importance for surveying crops in india (by minimizing the officials journeys when sampling crop yields).  The book introduces the reader to how the traveling salesman is relevant in practice in order management, circuit board architecture, food delivery, star gazing, and organizing data that needs fast retrieval.  Minimizing distances between points is important for many activities, thus the traveling salesman problem has many applications.

The author then focuses on solution methods.  This is done in a non-mathematical way, though the ideas are mathematical by nature.  The author focuses on intuition and brings the reader up to speed with pictures and well chosen intuitive language.  The algorithmic ideas are definitely readable and though many subtleties will be missed, the general ideas of techniques are communicated well.  The author also introduces the reader to Linear Programming with well chosen examples and the reader gets a basic grasp of quite technical ideas.

The primary contents of the book to me are in description of the algorithms that are primarily used for solving problems and their history.  But the author also includes a background about complexity, why the problem of P/NP is important and what solving it means.  The author also includes some nice artistic examples of the traveling salesman and discusses how human intuition does a good job of coming close to solutions using basic heuristics.  I definitely enjoyed reading this and it was the perfect mix of visual example with written description.  One comes through it appreciating the subtelty of what seems to be a simple problem, but is anything but.  Highly recommended for those interested in some light math.
1748941
This textbook is a highly mathematical treatment of the modeling of Mobile Fading Channels.  In fact, the reason I give the book 4 stars instead of 5 is that an unprepared reader could get lost in the mathematics when all they might be looking for is a basic understanding of fading channels.

Again, this book is about "modeling" fading channels.  Fading channels are essentially stochastic processes.  However, when a computer model is developed, the best that can be hoped for is a "pseudorandom" process, which the author calls a "deterministic" process as it is based on calculated outcomes of a function.

Keeping in mind that this book is essentially mathematical, I like the overall structure of the book.  Chapter 3 describes Rayleigh and Rician processes as a starting reference.  Chapter 4 is an introduction to deterministic processes and Chapter 5 details several methods by which to compute deterministic processes.

Chapters 6 and 7 are the heart of the text.  Chapter 6 describes frequency non-selective stochastic and deterministic channel models.  Chapter 7 does the same for frequency selective channels.  In this latter case the behavior of the channel varies with frequency.

Finally Chapter 8 wraps up treatment of the subject by describing some fast channel simulators.

All in all, the text is overall a sound mathematical description of the problem of developing computer models of mobile fading channels.
610778
This book was an interesting read on how to use estimation to solve or help with everyday problems.  This book is more suitable for those that have a casual interest in math.  It is also a good book for those that problem solve on a daily basis and looking to improve their skills.  However, hardcore math enthusiasts or logicians will probably not get much from the book or find it to elementary.  Otherwise, a good read.
1901764
This book worth 4.5 stars.
It is a comprehensive review of Extremal Combinatorics, though the book mainly presents connections between Combinatorics and Theoretical Computer Science.
The book is up to date and has chapters on current techniques and research topics.
The down sides of this book are:
1. There are a few typos and ambiguities throughout the book which often make it hard to read.
2. Each excersice follows immediately by a hint, which often give a glimpse to the solution. Hint section would be more preferable.