Book Description

Serving as the foundation for a one-semester course in stochastic processes for students familiar with elementary probability theory and calculus, Introduction to Stochastic Modeling, Third Edition, bridges the gap between basic probability and an intermediate level course in stochastic processes. The objectives of the text are to introduce students to the standard concepts and methods of stochastic modeling, to illustrate the rich diversity of applications of stochastic processes in the applied sciences, and to provide exercises in the application of simple stochastic analysis to realistic problems.

* Realistic applications from a variety of disciplines integrated throughout the text
* Plentiful, updated and more rigorous problems, including computer "challenges"
* Revised end-of-chapter exercises sets-in all, 250 exercises with answers
* New chapter on Brownian motion and related processes
* Additional sections on Matingales and Poisson process
* Solutions manual available to adopting instructors ... Read more

Reviews (5)

Good book overall, organization is very poor
First, let me say that I found the content of this book to be, on the overall, wonderful and fairly well explained. Concepts are presented well and, unlike many other books on Stochastic Modeling, sigma algebra is avoided (this is a definant plus for making it into an undergrad or low-level grad textbook).

That having been said, this book has some of the worst organization I have ever seen in a textbook. Every chapter is divided into sections and at the end of each section there are questions which are separated into "Exercises" and "Problems"; this in-and-of itself is not as much of a problem as that everything is numbered the same way.

Therefore problem 5 in section 4 chapter 3 is numbered the same way (4.5) as exercise 5 in the same section and chapter is numbered the same way as exercise/problem 5 in the same section of any other chapter in the book. The only real difference between "Exercises" and "Problems" is that exercises tend to be answered in the back of the book.

There are also other organizational difficulties in the text itself--such as that it is never entirely clear where the examples are in the text: there are several things which are labeled as examples (and are), however, over half of the examples in some chapters seem to be simply thrown into the text without any special indicator that they are examples of what is being discussed.

While the content in this book is good, the organization is so wretched that I have to knock it down two stars.

A little too much waffle
Good points: A couple of good review chapters on basic probability theory (good for reference), lots of worked examples and exercises classified by level of difficulty, from the pissy-easy to the very challenging.

Bad points: The notation is strange at times. Very often, the treatment of limits is neither rigorous nor intuitively helpful, and a few things are repeated over and over (the axioms of a Poisson process, for example). In my view, a good paragraph of text is better than two pages (good or bad), and clarity and conciseness do not seem to be the authors' fortes. I'm sure this book would be in pretty good shape if it just lost some weight.

I was very surprised by not being able to find the law of large numbers written in a precise mathematical formula anywhere in the book, especially when its importance is stated in the introduction.

The material is not very nicely organized. This is the "chapter 3, section 4, subsection 2, subsubsection 6" type of book.

Having pointed out its defects, I have to say that I found this book to be a good and interesting introduction to stochastic processes. It's also one of the most "introductory" I've seen (the reader who complains about the level should know that, in most universities, an upper-division probability course is a prerequisite for a stochastic processes course).

Feedback for Academic Press: the format is not very attractive; even with all the waffle, that book could be half as thick. (Take example from Ross's "Stochastic Processes" or Rudin's "Principles of Mathematical Analysis.")

A very good introductory book
The book shows through examples the very vast collection of stochastic models without going too deep in the technical details. I consider the book a good introduction for undergraduate students with a calculus and probability course. Most adequately for engineers than mathematicians.

Taylor dares call this an introduction...
I took a course in Stochastic Processes using this book... this book attempts to review some of the statistics that you would need to understand the major topics of this course; however, your background in stats MUST be bulletproof else you will be quite lost in the woods. It helps if you have a very good instructor teaching the course without having to figure out the difference between his symbols and the authors' symbols! (NOTE: I took this course as a graduate student at Wayne State in Detroit... this course can be a career killer; I ended up dropping the course halfway into the semester!)

Very good explanation on all his topics
I think it's a very good book about Stochastic modeling; with comprehensive examples. It's a good book for introductory courses on this field. ... Read more

Book Description

In an elegant and concise fashion, this book presents the concepts of functional analysis required by students of mathematics and physics. It begins with the basics of normed linear spaces and quickly proceeds to concentrate on Hilbert spaces, specifically the spectral theorem for bounded as well as unbounded operators in separable Hilbert spaces.

While the first two chapters are devoted to basic propositions concerning normed vector spaces and Hilbert spaces, the third chapter treats advanced topics which are perhaps not standard in a first course on functional analysis. It begins with the Gelfand theory of commutative Banach algebras, and proceeds to the Gelfand-Naimark theorem on commutative C*-algebras. A discussion of representations of C*-algebras follows, and the final section of this chapter is devoted to the Hahn-Hellingerclassification of separable representations of commutative C*-algebras. After this detour into operator algebras, the fourthchapter reverts to more standard operator theory in Hilbert space, dwelling on topics such asthe spectral theorem for normal operators, the polar decomposition theorem, and the Fredholm theory for compact operators. A brief introduction to the theory of unbounded operators on Hilbert space is given in the fifth and final chapter.

There is a voluminous appendix whose purpose is to fill in possible gaps in the reader's background in various areas such as linear algebra, topology, set theory and measure theory. The book is interspersed with many exercises, and hints are provided for the solutions to the more challenging of these. ... Read more

Reviews (1)

Reed
This book is an excellent introduction to real analysis. It is written in a fairly informal style which allows the topics to sink in. If I were a student new to analysis, I would recommend buying this book along with one of the more formal texts (ex. Rudin). ... Read more

Book Description

This book provides a comprehensive treatment on modeling approaches for non-Gaussian repeated measures, possibly subject to incompleteness. The authors begin with models for the full marginal distribution of the outcome vector. This allows model fitting to be based on maximum likelihood principles, immediately implying inferential tools for all parameters in the models. At the same time, they formulate computationally less complex alternatives, including generalized estimating equations and pseudo-likelihood methods. They then briefly introduce conditional models and move on to the random-effects family, encompassing the beta-binomial model, the probit model and, in particular the generalized linear mixed model. Several frequently used procedures for model fitting are discussed and differences between marginal models and random-effects models are given attention. The authors consider a variety of extensions, such as models for multivariate longitudinal measurements, random-effects models with serial correlation, and mixed models with non-Gaussian random effects. They sketch the general principles for how to deal with the commonly encountered issue of incomplete longitudinal data. The authors critique frequently used methods and propose flexible and broadly valid methods instead, and conclude with key concepts of sensitivity analysis. Without putting too much emphasis on software, the book shows how the different approaches can be implemented within the SAS software package. The text is organized so the reader can skip the software-oriented chapters and sections without breaking the logical flow.   ... Read more

Book Description

The subject of dynamic equations on time scales continues to be a rapidly growing area of research. Behind the main motivation for the subject lies the key concept that dynamic equations on time scales is a way of unifying and extending continuous and discrete analysis.This work goes beyond an earlier introductory text "Dynamic Equations on Time Scales: An Introduction with Applications" (ISBN 0-8176-4225-0) and is designed for a second course in dynamic equations at the graduate level. Key features of the book: excellent introductory material on the calculus of time scales and dynamic equations * numerous examples and exercises * covers the following topics: the exponential function on time scales, boundary value problems, positive solutions, upper and lower solutions of dynamic equations, integration theory on time scales, disconjugacy and higher order dynamic equations, delta, nabla, and alpha dynamic equations on time scales * unified and systematic exposition of the above topics with good transitions from chapter to chapter * useful for a second course in dynamic equations at the graduate level, with directions suggested for future research * comprehensivebibliography and index * useful as a comprehensive resource for pure and applied mathematicians Contributors: R. Agarwal, E. Akin-Bohner, D. Anderson, F. Merdivenci Atici, R. Avery, M. Bohner, J. Bullock, J. Davis, O. Dosly, P. Eloe, L. Erbe, G. Guseinov, J. Henderson, S. Hilger, R. Hilscher, B. Kaymak¿alan, K. Messer, D. O'Regan, A. Peterson, H. Tran, W. Yin ... Read more

Book Description

Spectral sequences are among the most elegant and powerful methods of computation in mathematics.This book describes some of the most important examples of spectral sequences and some of their most spectacular applications.The first part treats the algebraic foundations for this sort of homological algebra, starting from informal calculations. The heart of the text is an exposition of the classical examples from homotopy theory, with chapters on the Leray-Serre spectral sequence, the Eilenberg-Moore spectral sequence, the Adams spectral sequence, and, in this new edition, the Bockstein spectral sequence.The last part of the book treats applications throughout mathematics, including the theory of knots and links, algebraic geometry, differential geometry and algebra. This is an excellent reference for students and researchers in geometry, topology, and algebra. ... Read more

Reviews (7)

An excellent introduction to Real Analysis
Marsden and Hoffman have done an admirable job combining clarity and rigor in a book appropriate to the level of an advanced undergrad class at a good university. The organization and tone of the work set it apart from the alternatives. The authors proceed from lesser rigor to greater within each chapter, presenting definitions, theorems, and worked examples before the proofs, which are placed at the end of each chapter. The authors address this somewhat unusual organization in their introduction:

"We decided to retain the format of the first edition, which gives full technical proofs at the end of each chapter but presents some idea of the main point in the text. This seems to have been well-received by the majority of readers... and we still believe that it is a sound pedagogical device for a course like this. It is not meant as a way to shun the proofs; on the contrary it is intended to give to views of the proof: on in the way working mathematicians think about it, (the trade secrets, so to speak), and the other in the way mathematicians write out formal proofs."

Marsden Hoffman is written in a slightly more conversational tone than other rigorous introductions to analysis. However, as a math major at Stanford, I felt like this only made the text more readable.

A side note: Though Marsden and Hoffman do make light of Cantor's quaint, 19th century definition of a set in their intro to set theory, they ultimately do so only to motivate the exposition of a formal, axiomatic view.

Reasonable textbook, some editions full of typos
The good part: The text contains the usual definitions, theorems and proofs in a spacious layout (LaTeX - what would you expect...), and also provides some intuition and insight (with pictures of open and closed sets, sin(1/x) etc). The main text is quite long (some find it too verbose, I liked it), and proofs are given after the main text, and don't clutter the exposition. There are also many worked examples, and exercises (with hints/solutions for odd numbered ones).

However, the book (in its 2nd edition, 7th printing) is riddled with typos. And these are not only the occasional harmless typo, no, there are errors at the heart of definitions and proofs. For example, when defining the limes inferior, the sign on infinity is wrong for degenerate cases. Confusing! The proof that Q is countable is wrong, too (though this is trivial to see, so no confusion here.)

Lamentably, this is no isolated case. There are about 36 (!) typos on the first 100 pages of the 7th printing (check the author's homepage for a list of errata). This is really too much for a such an expensive "elementary" textbook.

However, apparently there is a new printing as of May 2003 that fixes most of these problems. So, make sure you don't accidentally buy an old printing of this second edition.

From a grad student's point of view
The book is poorly written. And the author tries to claim the credit for a lot of previous work, without mentioning when, where or who invented the proofs or solutions. He sometimes mocks and makes fun of other people's definitions calling them "pitiful!." The language used seems to be intended to sound fancy and sophisticated, but to me it's plain annoying.
The answers to most examples are not provided promptly, instead they are piled together at the end of the chapter.. leaving the student to wander around constantly looking for what the author is trying to say.
I would not recommend this book for use as a text book, for it is (unlike what some reviews say) not easy to read, in fact most proofs and explinations are not formatted well, they are written as in an essay.. long sentences and in text format ex: (1/2) instead of an actual math font for the number one half.

Poorly written; to be avioded
This book has been used as the text for an undergrad analysis class at Stanford for a number of years. It is overly verbose, poorly organized, and terribly written. The language is imprecise, and relies too much on intuition than solid reasoning. Furthermore, the proofs often lack elegance.

A much better text is Rudin's Principles of Mathematical Analysis. Concise and eleganty written. The language is precise, and the proofs are often full of beautiful and clever ideas.

great for readers who want to learn the material.
It is always delightful and pleasure to read Marsden's book on such subject from his applied mathematics background: the author is always put readers perspective to understand important concepts and insights. This book will get the most benefit for those readers who are serious on the subject with non-traditional mathematical background. Although the book is over 700 pages, it covers more than enough a tradition real analysis course syllabi, the author put great efforts on informal illustations on the hardcore of the material (no-nonsense diagrams, layman's terms). I think if readers can follow this book thoroughlly, they will be more confident to attack Rudin's scholarly's work "Elementary Mathematical Analysis" and they should be feel very comfortable to Rudin's work as "cheat sheet" for this book, and for other scholarly quality works. ... Read more

Book Description

This new edition of an indispensable text provides a clear treatment of Fourier Series, Fourier Transforms, and FFTs. The unique software, included with the book and newly updated for this edition, allows the reader to generate, firsthand, images of all aspects of Fourier analysis described in the text. Topics covered include : ... Read more

Reviews (1)

Can be understood by an undergraduate physics major.
This is a book written for mathematicians, yet it is accessible to an upper level physics undergraduate. Much of the book explains concepts very well, at other times I was very frustrated. The DOS based software included with the book did not seem to work as billed on my systems. A high point of the book is Walkers 2 dimensional Fourier optics section. This section does an excellent job on a complex topic. ... Read more

Reviews (1)

Excellent summary of the most important PDEs!
I studied this book from cover to cover, and I found its explanations lucid and complete.F. John's writing style makes excellent reading, and the details he supplies are complete enough that anyone with only abackground in undergraduate multivariable calculus can understand thearguments.Like any good mathematics textbook, this one leaves the readerto work out his/her own steps at some points, but Dr. John always makes itclear which elements areneeded.This book will always have a place onthe shelf in my office. ... Read more

Book Description

Book Description

Hardbound. Twelve problems have been added to the first edition; four of them are supplements to problems in the first edition. The others deal with issues that have become important, since the first edition of Volume II, in recent developments of various areas of physics. All the problems have their foundations in volume 1 of the 2-Volume set Analysis, Manifolds and Physics. It would have been prohibitively expensive to insert the new problems at their respective places. They are grouped together at the end of this volume, their logical place is indicated by a number of parenthesis following the title. ... Read more

Book Description

Hardbound. ... Read more

Book Description

Are some areas of fast Fourier transforms still unclear to you? Do the notation and vocabulary seem inconsistent? Does your knowledge of their algorithmic aspects feel incomplete? The fast Fourier transform represents one of the most important advancements in scientific and engineering computing. Until now, however, treatments have been either brief, cryptic, intimidating, or not published in the open literature. Inside the FFT Black Box brings the numerous and varied ideas together in a common notational framework, clarifying vague FFT concepts.Examples and diagrams explain algorithms completely, with consistent notation. This approach connects the algorithms explicitly to the underlying mathematics. Reviews and explanations of FFT ideas taken from engineering, mathematics, and computer science journals teach the computational techniques relevant to FFT. Two appendices familiarize readers with the design and analysis of computer algorithms, as well.This volume employs a unified and systematic approach to FFT. It closes the gap between brief textbook introductions and intimidating treatments in the FFT literature. Inside the FFT Black Box provides an up-to-date, self-contained guide for learning the FFT and the multitude of ideas and computing techniques it employs. ... Read more

Book Description

If you want top grades and thorough understanding of numerical analysis, this powerful study tool is the best tutor you can have! It takes you step-by-step through the subject and gives you accompanying related problems with fully worked solutions. You also get additional problems to solve on your own, working at your own speed. (Answers at the back show you how you’re doing.) Famous for their clarity, wealth of illustrations and examples—and lack of dreary minutiae—Schaum’s Outlines have sold more than 30 million copies worldwide. This guide will show you why! ... Read more

Book Description

There has been a great deal of excitement over the last few years concerning the emergence of new mathematical techniques for the analysis and control of nonlinear systems: witness the emergence of a set of simplified tools for the analysis of bifurcations, chaos and other complicated dynamical behaviour and the development of a comprehensive theory of nonlinear control. Coupled with this set of analytic advances has been the vast increase in computational power available both for the simulation of nonlinear systems as well as for the implementation in real time of sophisticated, real-time nonlinear control laws. Thus, technological advances have bolstered the impact of analytic advances and produced a tremendous variety of new problems and applications which are nonlinear in an essential way.

This book lays out in a concise mathematical framework the tools and methods of analysis which underlie this diversity of applications.

The material presented in this book is culled from different 1st year graduate courses that the author has taught at MIT and at Berkeley. ... Read more

Reviews (1)

An excellent nonlinear systems book
As a Ph.D student I found this book very helpful and I would like to recommend this book everyone involved in nonlinear systems. I also have Vidyasagar's (i wish there were more example problems) and Khalil's nonlinear systems(mainly devoted to Lyapunov analysis) books which are also good but I found this book much explanatory than others. ... Read more

Book Description

This book is devoted to a theory of gradient flows in spaces which are not necessarily endowed with a natural linear or differentiable structure. It consists of two parts, the first one concerning gradient flows in metric spaces and the second one devoted to gradient flows in the space of probability measures on a separable Hilbert space, endowed with the Kantorovich-Rubinstein-Wasserstein distance.
The two parts have some connections, due to the fact that the space of probability measures provides an important model to which the "metric" theory applies, but the book is conceived in such a way that the two parts can be read independently, the first one by the reader more interested in non-smooth analysis and analysis in metric spaces, and the second one by the reader more orientated towards the applications in partial differential equations, measure theory and probability.

Reviews (1)

Splines are more than you thought
This is a very nice book about splines for all who needs interpolation of data and are getting a bit nervous about the somewhat improper behaviour of normal cubic splines, i.e., the ones you learned about in your undergrad exam. The author provides both illustrative examles with computer codes (in FORTRAN) and describes the necessary theoretical background. Compared with many other books, it is readable also for a non-mathematician, although some experience with numerical analysis will be most helpful. ... Read more

Book Description

The book offers an initiation into mathematical reasoning, and into the mathematician's mind-set and reflexes. Specifically, the fundamental operations of calculus--differentiation and integration of functions and the summation of infinite series--are built, with logical continuity (i.e., "rigor"), starting from the real number system. The first chapter sets down precise axioms for the real number system, from which all else is derived using the logical tools summarized in an Appendix. The discussion of the "fundamental theorem of calculus," the focal point of the book, especially thorough. The concluding chapter establishes a significant beachhead in the theory of the Lebesgue integral by elementary means. ... Read more

Book Description

This book offers the first comprehensive introduction to the debate on the foundations of mathematics in the 1920s. Most contemporary work in this field originates from the groundbreaking contributions of Hilbert, Brouwer, Bernays, and Weyl. This volume makes available the first English translations of 25 central articles on the debate by these major figures and many others. Each section of the book contains an introduction which provides the necessary historical and technical context for understanding the articles. ... Read more

Reviews (1)

A useful reading with additional commentary
This is a reading that contains 25 articles of major European mathematicians of the first half of the twentieth century. With two exceptions, all the papers are translated into English for the first time,most part of them from German, and some of them from Dutch and French. Alltranslations are fluent and, as far as I can tell (I can't check the Dutchoriginals!), they are sufficiently accurate. The book consists of foursections, which are devoted, respectively, to Brouwer, Weyl, Hilbert andBernays, and intuitionistic logic. Every section is preceded by a detailedstudy, in which the selected texts are presented in their historicalcontext. At the end of each introductory study there is a completebibliography of original sources and secondary literature. The properunderstanding of some of these articles presupposes some knowledge of settheory (both Cantor's naive theory and Zermelo's axiomatics)andmathematical analysis (essentially, the concept of continuity).Nonetheless, most of the contributions are accessible to readers with basicnotions of first order mathematical logic. Although the level of difficultyof the different articles is somewhat uneven, taken as a whole the bookoffers a very good text for graduate courses in philosophy of mathematics.It is also of considerable interest for scientists and historians ofscience.

The leit motiv of the book is the debate between Brouwer andHilbert - and their respective followers- about the foundations ofmathematics in the period between 1920 and 1931, that is, before the impactof Goedel theorems. The debate between formalists and intuitionists touchedupon not only logic, but also set theory and the fundamental concepts ofanalysis, such as that of the continuum. The idea of infinity has alwaysbeen at the center of the disputes. Should we accept in mathematics theexistence of infinite entities, such as set of points or cardinal andordinal transfinite numbers? Hilbert and the formalists answered that wecan, provided that our theories are logically consistent, that is, imply nocontradictions. Brouwer and the intuitionists, on the contrary, thoughtthat consistency is a necessary although not a sufficient condition formathematical existence. They demanded an effective method of constructionfor every mathematical entity, and this stringent condition lead them toreject some fundamental portions of set theory and classicalmathematics.

The outcome of the debate was rather inconclusive. Goedel'stheorems about the incompleteness of formal arithmetic and theunprovability of consistency for formal theories -such as set theory- putsevere limitations on Hilbert's program. On the other hand, intuitionistswere unable to reconstruct large fragments of elementary and highermathematics, and where they succeeded, the results were very complicatedand extremely awkward. Intuitionistic logic and Hilbert metamathematicalprogram are still alive, yet we now know that neither of them can beaccomplished in the way they were conceived in the 1920s. ... Read more

Book Description

What makes populations stabilize?What makes them fluctuate? Are populations in complex ecosystems more stable than populations in simple ecosystems? In 1973, Robert May addressed these questions in this classic book. May investigated the mathematical roots of population dynamics and argued-counter to most current biological thinking-that complex ecosystems in themselves do not lead to population stability. Stability and Complexity in Model Ecosystems played a key role in introducing nonlinear mathematical models and the study of deterministic chaos into ecology, a role chronicled in James Gleick's book Chaos. In the quarter century since its first publication, the book's message has grown in power.Nonlinear models are now at the center of ecological thinking, and current threats to biodiversity have made questions about the role of ecosystem complexity more crucial than ever.In a new introduction, the author addresses some of the changes that have swept biology and the biological world since the book's first publication. ... Read more