I first noticed this book during the time that I spent at UC Berkeley as an undergraduate applied mathematics major. It was being used for Stat 101, and though I was not taking that course, I bought it because it looked even from casual inspection to be very well laid out, covering important and interesting issues in basic probability.

The strongest feature of this book from my point of view is its conciseness. Much is presented in as short a time as possible, and because of that the book is much more readable than many others of its level. In addition to conciseness, the authors (in my edition Hoel, Port, and Stone) have made a commendable effort to present the reader with clear and concrete definitions, compact theorems (many proven), and abundant useful examples. In the back of the book nearly all of the solutions of the chapter exercises are given, unlike many books where answers to only the odd problems are given. I believe that this book is ideal for self-study, and that much use of it could also be made as a textbook for an undergraduate course in probability. The exercises are not very difficult, but they are by no means trivial, and much can be learned from them. At the end of a close study of this book the reader would be ready to enter into a program of undergraduate level mathematical statistics, or into a further study of probability with the confidence inspired by a firm understanding of the most fundamental and key concepts in probability theory.

This was the book used in the standard upper-division probability course at UC Berkeley when I took it 18 years ago. In my opinion it is still the best. I have since taught the subject myself and was forced to use other books, with many more pages and fancy pictures than Hoel's book. Yet those books do not do anywhere near as good a job of teaching probabilistic *thinking* as well as Hoel. This is what causes the most problems for students of probability, and Hoel does it the right way in Chapters 1 and 2, which are key. The basic explanations are clear and concise, with many instructive examples.

My professor back then told us that if we want to learn probability, then do every exercise in this book. She was absolutely right. The exercises are excellent. Do them, and you will learn a lot.

This used to be *the* book on elementary calculus-based probability theory at most universities. I don't understand why it seems to have fallen out of favor. Perhaps because of its size (it is fairly compact, as it should be) and age, though I fear that it may be because it is a bit more demanding (but worth it) than many of the newer books.

This classical text is complete and detailed. I'm an undergraduate and used the book after acquiring the basics of multiple integration as an introduction to the calculus of probability. Plenty of exercises (answers provided) which not only help you understanding the theory but are also complementary to the text. (This is a "non-measure" text on probability theory.) Well written!!!! (see also Hoel at al., 'Int. to Stochastic Processes', and Taylor, 'An Int. to Measure and Probability',(Springer-Verlag)).

Optimization by Vector Space Methods, by David Luenberger, is one of the finest math texts I have ever read, and I've read hundreds. Many years ago this book sparked my interest in optimization and convinced me that the abstract mathematics I had been immersed in actually would be applicable to real problems. Since then, Luenberger's book has inspired several of my graduate students. I merely lent them my copy, and Luenberger did the rest; he drew them in by carefully laying the foundation for an elegant theory, with just the right mix of formalism and intuition, and opened their eyes to the beauty and practicality of abstract mathematics. Anyone with an interest in higher-level mathematics (beyond multi-variable calculus, say) would benefit from exposure to this finely-crafted book. I daresay, the rampant math anxiety that is so prevalent in the West would be substantially reduced if more authors would take such meticulous care in presenting their material.

The format of Luenberger's book is also extremely appealing in a way that I cannot quite put my finger on. The typography and illustrations are inherently crisp and inviting; they draw you in. There is nothing at all superfluous or gratuitous in this book. It is utterly to-the-point, methodical, and above all, clear. The techniques are developed starting from an elementary treatment of vector spaces, then proceeding on to Banach spaces and Hilbert spaces. Along the way, Luenberger introduces convexity, cones, basic topology, random variables, minimum-variance estimators, and least squares, among many other things. There is a recurring theme of duality, which can be used in a way analogous to the inner product of a Hilbert space. In particular, the familiar projection theorems of Hilbert spaces can be echoed in simpler normed linear spaces using duality, which Luenberger motivates and covers beautifully.

The book also covers some of the standard fare of functional analysis, such as the Han-Banach theorem, strong and weak convergence, and the Banach inverse theorem. However, Luenberger never wanders too far off into abstract nonsense; around every corner lay tantalizing application of these ideas to optimization. Luenberger first explores optimization of functionals then covers constrained optimization, which builds upon concepts such as positive cones and Lagrange multipliers. The optimization methods themselves have endless applications in fields such as computer vision, computer graphics, economics, and physics. Indeed, the list is effectively endless as optimization techniques pervade math and science.

I'm certain that the appeal of this book is helped immeasurably by the inherent beauty of the subject matter. Hilbert-space methods are lovely in themselves--they possess a structure that engages one's geometric intuition while at the same time admitting convenient algebraic properties. Once you are in the habit of phrasing problems in abstract settings such as Hilbert spaces, it forever changes how you look at things; you cannot help but look past the clutter to the essence of a problem (or, at least try very hard to do so). While this material is not nearly as abstract as, say, category theory, it nevertheless hits a high point in mathematics--a point more people ought to experience.

If you've had some exposure to optimization methods, or need to apply them in the context of computer vision, graphics, or finance, to mention just a few areas, then I urge you to take a look at Luenberger's fine book. It too hits a high point in clarity of mathematical writing. Combine beautiful theory with endless applications and lucid writing, and you have a winner of a book.

I owe Dr Luenberger a million thanks for writing this book. As his student, I think he is the master of putting complex issues in simple words. Your faithful student..Jayanth Krishnan

When I decided to change my career path from B-school to mathematics, I know that only with taking calculus and linear algebra courses is definitely not enough for me to get into a decent math graduate program. I spent an afternoon in a local bookstore to find a book for functional analysis and Hilbert space which is comprehensible for me at that time. I found Luenberger. I was obsessed with its clarity and simplicity without sacrificing too much rigor. Especially for those finance student who want to learn some advanced math for quant finance but may not have enough background to deal with, Luenberger's book is a really good starting point!

This was the BEST algebra/trig help I possibly could have received besides one on one with a professor. I used this book to refresh before taking placement exams, although, I was extremely impressed with the simplistic approach that would make 1st time learning easy as well. All steps are clearly laid out, and the book builds on itself very smoothly. At the end of each chapter there are MANY practice questions with answers in the back, and I did not encounter any errors. Excellent refresher or reference book. HIGHLY recommended above ANY other algebra/trig book.

I am a college student in California, I found this book and bought it for my 10th grade sister who is currently studying algebra. She has had an amazing improvement in the last few month in her mastery of algebra...this book has helped her a lot! I recommend this book to all students who want to learn algebra in an easy and quick way

I am a high school math teacher and many of my students keep this volume handy for quick review. In some cases they use it to get ahead of the others in the class. I have found this book to be excellent coverage of fundamental high school mathatematics.

As I just got a copy of the third edition I can now say that many of my comments on the second edition still hold. The book is authoritative, clearly written and very much applications oriented. Conover has done a good job of updating it with recent developments. He provides a nice introductory treatment of bootstrap among other things.

I own the second edition. So my comments refer mainly to it. Conover writes very well and covers all the commonly used nonparametric tests. He does a great job of handling the special treatment when there are many ties in a rank test. He also provides many important statistical tables. My understanding of the third edition is that it continues to cover the nonparametric procedures that have stood the test of time and that popular modern methods like bootstrap are also covered.

This is a very impressive book. All concepts are introduced in an elementary fashion, with derivation following only after an example of the technique. The explanations are lucid and the extensive lists of references very helpful. I would heartily recommend this book to anyone interested in robust estimators and nonparametric methods.

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In the early 1970s I was working on practical forecasting methods to apply to the U.S. Army supply depot workloads. Exponential smoothing was the commonly used "automatic" technique (once smoothing constants have been determined) that had great advantages over the informal methods used by the Army. Then someone told me that Box-Jenkins techniques were more general and powerful. I got a copy of the first edition published in 1970 and found that I could read and understand it even though I had little statistical training. I had a bachelors degree in mathematics. I got to appreciate the book even more when I took a short course from George Box, George Tiao and David Pack based on the book. I began to grasp some of the key ideas of stationary and nonstationary time series and learned about model selection, diagnostic checking and estimation. This started my interest in becoming a statistician and gave me the practical side of time series analysis first. I later specialized in it and got a Ph.D. in statistics.

Gwilym Jenkins died many years prior to this edition and Box's colleague Greogory Reinsel took on the task of helping to revise and update it.

It retains its original flavor. It is an applied book with many practical and illustrative examples. It concentrates on the three stages of time series analysis: modeling building, selection, estimation and diagnostic checking and how to iterate the process toward a good solution. The ARIMA time series models are what are considered. The theory of stationary and nonstationary time series is introduced to motivate interpretation of autocorrelation and partial autocorrelation in the model identification phase. Operator notation is introduced and used throughout the book to simplify equations. For me it helped simplify things and illuminate some concepts. But many readers found it difficult and confusing. the book is very systematic and practical. Many of the examples are real examples from Box's work in the chemical industry and his consulting during his career at the University of Wisconsin and also the consulting experience of Gwilym Jenkins in England.

The publishers and some amazon reviewers say that this edition is a major revision. The second edition published in 1976 was criticized for being essentially a reprint of the first. Although there is a new chapter 12 on intervention analysis and outlier detection it mainly is an expansion of ideas already discussed in the first edition. Theoretical results are kept aside in appendices as in previous editions.

This is not an up-to-date text on the theory of time series. It deals strictly with the time domain approach and does not include recent advances including nonlinear and bilinear models, models with non-Gaussian innovations and bootstrap or other resampling methods.

To get a balanced approach that includes the theory for frequency and time domain approaches the book by Shumway, the latest edition of the Brockwell and Davis text and the latest edition of Fuller's text are appropriate. For a graduate course I taught at UC Santa Barbara in 1981 I used the first edition of Fuller's book. Anderson provides a thorough account of the time domain theory. Excellent texts that specialize in the frequency domain approach are Bloomfield's second edition and the two volume book by Priestley. Brillinger's text is also worthwhile for those interested in spectral theory (frequency domain statistics).

Although there are many things that is text does not cover, it remains the classical text on a rich class of time domain methods that are still very practical. This is a text I bought for reference even though I still have the first edition.

Box-Jenkins is THE definitive, foundational text in time series analysis. Mastery of this volume requires extensive graduate level understanding of mathematical statistics. While difficult even for intermediate statistical practitioners, this text is necessary for any professional who examines time series data and well worth the considerable effort to acquire mastery.

This book was used in my "Introduction to Ordinary Differential Equations" class when I was a senior at Louisiana State. I found it to be one of the better texts in differential equations that I have come across. The first chapter is mainly the prerequisite calculus, then the next chapter jumps into first order equations. Then unlike most other books, he jumps straight into second order problems. the biggest plus in the book is the ready use of complex analysis throughout, something which most books avoid altogether, thus allowing the student to get only a partial understanding of the theory needed to solve more advanced problems. Answers are included at the back of the book, problems are clear and well-explained, and there are enough advanced topics covered later in the book (including celestial mechanics) to keep the course interesting for students of all kinds.

I took an undergraduate ordinary differential equations class and felt I grasped the subject quite well. I wanted an inexpensive text that I could review the subject with and I decided that I would give Coddington's book a try. I was really pleased with the order in which the text was presented which differed from the course I had taken. The author's seem to put things in a very logical order versus some texts I have seen which really confuse you by the order in which the subjects are presented. Another point that I have to make is the depth that the book has. I learned much more in reviewing this text than I ever did in any diff eq class. It shows the distinction between linear and non-linear diff eq's and covered many other methods which I had not learned previously. This is a great text as a "refresher" or as a course text. I just wish I would have previously used this text to learn ordinary differential equations.

This book is a holy bible for introduction to differential equations. It is easy to understand and the problems are quite challenging. Dr Coddington knows how to explain the material by systematically order(Easy to tough). His book is not easy to figure out if you just sit without paper,pen and think. But once you are understand his book, no one can teach you differential equations for undergarduate level. Other suggested reading are Theory of ordinary differential equations, Linear ordinary differential equations by Earl Coddington(Both of them), Ordinary Differential Equations by Fritz John,and Ordinary Differential Equations by Edward L Ince. Once the most important statement is: YOU KNOW DIFFERENTIAL EQUATIONS IF YOU UNDERSTAND WHAT IS GOING ON IN CODDINGTON'S AND FRITZ JOHN BOOKS.

In order to pursuit my interest in economics and finance, I search some Statistics texts for help. With the training in science and no background in statistics, I found this book comprehensive. It is rigorous but accessible, well organised with appropriate coverage. The examples are relevant and helpful. Moreover, the author always keeps students in mind. The only downsides are no answers to problems and no bibliography. As a whole, it is a great book.

One of the most beautifully written books in mathematical statistics with the right mix of rigor and simplicity. A must read book before jumping into econometrics.

One of the most beautifully written books in mathematical statistics with the right amount of rigor and simplicity. A new generation book, a book for the 21st century economists,statisticians,business professionals. A must read book before jumping into econometrics.

This text is a leisurely development of the major concepts in measure of probability theory. There are many useful examples that are sprinkled throughout the text that motivate the discussion. The solutions to the problems are also provided. This book is suitable for advanced undergraduate. Although I don't have any major complaints about the book, there already exists a much better book with many more exercises, diagrams, and much more thorough development and extension of the principal concepts. That book is Jones' "Lebesgue integration on Euclidean space", which I cannot recommend highly enough.

This is an excellent reference book for measure theory as it applays to probability.

Highly accessible and clear intro to measure and Lebesgue integration. Can relax with this book while waiting for the train after work. Only minor negatives are: (1) not enough exercises and (2) there are typos but Springer Verlag doesn't provide any errata list whatsoever.

For a non math major (or stats major) user, this book offers an easy way to have works done quickly. But be cautious, an first-class cookbook does not necessarily yeild a first-class meal on your table.

This is an excellent first book for nonparametric statistical methods. It is a cookbook, but is a good introduction to the many nonparametric techniques for assessing data. These are oftentimes much better suited for your data than the standard stuff you get in intro to statistics. The book by David J. Sheskin or by Conover should your next book.

This is (together with Empirical Methods for Artificial Intelligence by Paul R. Cohen) the best of the statistics books I read.

This is a great helpful tool for students to use! I was struggling in my stats class and this book helped a great deal. It is set up with many helpful hints and practice problems! Bravo Schaum's

As per all Schaum's thjis is also excellent. Like many of the others I have, especially the Concrete Book, this one too, worn out. Since it was required for a course that I took for an elective, would you beleive Economic Statistics. An easy A for math majors and Engineers; no real hard core economics covered.

Had this course over thirty years ago; upon recomendation of a friend. Professor did ask one question regarding economics; "which one of these bell curves represents percent of total income". Most wrongly (as I did) the symettric one as opposed to the correctly skewed to the left one.

Nom more economics, then. Pure probability, Stats, and Fun. Since the prof was a sports and gaming fan, as am I, this is my favorite math.

The downside, was the prof was veiwed as biassed against women, because his one-point (out of 500) bonus question was always sports trivia. I actually usually hit them, although I remember, the one test before Memorial day 1970, that if were after I would have known that the Late Tony Hulman alwasys said "Gentlemaen, start your engines".

But I digress. Get this book, agree -- cheap thorough and worth it. My favorite and most practical branch of math; so buy, learn and beat the lotto, cards, horses, and slots.

I have used this book to teach myself statistics and probability theory in a relatively short period of time. The essentials are well laid out and reinforced with plenty of examples and exercises. I would recommend using a Schaum outline authored by Murray Spiegel for becoming proficient in problem solving in that particular area. I got started this way after reading the book, Indiscrete Thoughts by Gian Carlo Rota.