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CK-12 Foundation’s Probability and Statistics (Advanced Placement) FlexBook introduces students to basic topics in statistics and probability but finishes with the rigorous topics an advanced placement course requires. ... Read more

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October 19th 1987 was a day of huge change for the global finance industry.  On this day the stock market crashed, the Nobel Prize winning Black-Scholes formula failed and volatility smiles were born, and on this day Elie Ayache began his career, on the trading floor of the French Futures and Options Exchange.  
 
Experts everywhere sought to find a model for this event, and ways to simulate it in order to avoid a recurrence in the future, but the one thing that struck Elie that day was the belief that what actually happened on 19th October 1987 is simply non reproducible outside 19th October 1987 - you cannot reduce it to a chain of causes and effects, or even to a random generator, that can then be reproduced or represented in a theoretical framework.

The Blank Swan is Elie's highly original treatise on the financial markets - presenting a totally revolutionary rethinking of derivative pricing and technology. It is not a diatribe against Nassim Taleb's The Black Swan, but criticises the whole background or framework of predictable and unpredictable events - white and black swans alike -, i.e. the very category of prediction.
 
In this revolutionary book, Elie redefines the components of the technology needed to price and trade derivatives. Most importantly, and drawing on a long tradition of philosophy of the event, from Henri Bergson, to Gilles Deleuze, to Alain Badiou, and on a recent brand of philosophy of contingency, embodied by the speculative materialism of Quentin Meillassoux, Elie redefines the market itself against the common perceptions of orthodox financial theory, general equilibrium theory and the sociology of finance.
 
This book will change the way that we think about derivatives and approach the market. If anything, derivatives should be renamed contingent claims, where contingency is now absolute and no longer derivative, and the market is just its medium. Also, the book establishes the missing link between quantitative modelling (no longer dependent on probability theory but on a novel brand of mathematics which Elie calls the mathematics of price) and the reality of the market. ... Read more

Customer Reviews (10)

Please Concentrate
I love the books "The Black Swan", "Fooled by Randomness", and "Against the Gods".Those are great books, insightful, and easy to read.

However, since I have only average intelligence, I have to read each sentence in this book two or three times, and then think about it.So this is a very slow read for me.I'll illustrate what I mean.For example, on page 5 we have the sentence, "Contingency is the writing/trading thread that we keep pursuing despite the fact that the context has been saturated by replication."That's a great sentence.Unfortunately, it took me two days of thinking before I understood it.This is an interesting book, but it is not a leisurely read for the average Joe.

And you thought The Black Swan was vacuous ...
According to Ayache the "philosophical work I am producing and even the pre-philosophical plane of immanence that I am trying to stretch out with the help of my conceptual personae and my league of friends (the bank, the quants, Sydney, Taleb the Levantine and Derman the South African ...) are the prelude to the science and to its plane of reference". Ayache is certainly one of the lighter craft in the Talebian flotilla, drifting higher into meta-philosophy. This is related to "the necessity of meta-contextual ascent"perhaps, which might explain why he can often be found "gliding over my plane of immanence". Ayache would like us to imagine "that you are so much impressed by what you have read (impressed beyond memory or, rather, impressed in the direction opposite of memory)".

I don't know what that means, even though The Blank Swan is the Australian version of The Black Swan - a language I understand quite well, and homage to regime switching models - the topic of my doctoral thesis.We shall not wonder why an unnamed Australian bank "never connected with us" when Ayache was attempting to sell them a "purple gastropod".

As noted by one of Ayache's astute reviewers here, "the writing style is difficult and [you] need to read [it] a few times [for it] to sink in" but most interestingly, Taleb has explained that "This, of course, is just the beginning, so one has to be understanding about the speculative aspect of the effort". Rather than reject this torrent of nonsense for what it is, the teacher has invited us to "view this as a gutsy look at the end of probability and how we will need to envision the world once we get rid of this artificial, antiquated tool."God help us all if that's the case.

Market Of Or With Future?
I have a German tongue and I am not a philosopher. How can I write a review?
I have read this book with the eye of a quant finance mathematician.
In short, it is a must-read book for quant finance people (change or even influence the way we think about derivatives) and an enjoyable-read for people who like unconventional highly original thinking and writing styles. Some might say, not for holiday reading, but I am not so sure. For reading books that I could not write, I often chose a "beach".
Yes the thoughts behind this book are challenging.

My compilation of the utilities I "take": in this book Dr. Ayache gives deep insight into the materialization of contingency as a price. A contingent claim (derivative) is not a contingent claim, if it is not dynamically replicable (this has much to say about , say, CDOs being not a contingent claim).
Probability is not a theory for predictive modeling but explanation and its incarnation in a model (like Black Scholes) is a guide (I would even say it was a game rule unmasked 1987 as unreliable in its innocent form). Looking back requires recalibration. I let speak Ayache here: " ..... It is only because the dynamic trader has to be hedging continuously his position in the option and therefore is following the option continuously; it is only because of this that he is basically entitled to compute something we call implied volatility - and implied volatility is the simplest instance of recalibration ... recalibrating the BS model to the option market price ...."
So, if price is the absolute, everything else is about inverting. And inverse problems often are ill-posed and challenging for mathematicians.

But I also have read chapters as nice-to-have: especially the Sidney chapters, flying with thoughts.

Unreadable
On page 196, the author has a quote:"I, too, seek an unreadable book ... a book incapable of being read straight through, even, to bring reading to stop"That this quote should so absolutely summarize this book, cannot be by chance.Trying to read The Blank Swan straight through is a frustrating experience and needlessly so in my view which is the reason I rated it 3 stars.As it stands, it is a book that needs to read in small quantities and not in chronological order, but I believe this is how the author intended it.Further too this point, there are a few aspects of this book that make it very tiresome to read.First, it is highly repetitive.On a banal level, the author refers to "the last part of the book" about 50 or more times in the first two parts of the book (there are four parts).In some cases, the author will start a paragraph saying "As will be shown in the last part of the book", only to finish the paragraph "(see the last part)".These are are not word for word quotes, but capture the meaning.The book is also repetitive in that it addresses the same topic from a very slightly different point of view multiple times.This means you have to read essentially the same thing over and over again, only at the end to get 90% of the same message.As a historical process, it's clear to see why the book feels so repetitive, because many of the chapters were published separately before coming together as a book.

To continue to the content of the book, I think the effort is worthwhile, for those predisposed, to understand what is being written.It is mostly a book on philosophy and not the markets or derivatives.But it does make a few points about the market which can help someone gain insight into its behavior.To speak to the philosophy, the book borrows most of its foundation from Gilles Deleuze and to a lesser extent Quentin Meillassoux and Alain Badiou.The author may say the latter are more important to his work, but to the user of this philosophy rather than the creator, the work of Deleuze in my view is more important.A problem with the book arises here because the philosophical concepts are not well explained.They assume a knowledge not only of Deleuze et al themselves, but also of philosophy in general.This means the book inhabits a nebulous middle ground in terms of its intended audience.

The meaning in all this is that a reader of this book should expect to have to read several other books in order to really understand what the author is talking about.Herein lies my biggest criticism of the content of this book.If you take the time to read Deleuze, Meillassoux, Badiou; and to add one to the list, Bergson; and also to read a few of their popularizers such as De Landa, your time will have been better spent than reading this book.There just isn't enough synthesis here to make the whole of The Blank Swan, better than the sum of its parts which is these philosophical works.

In light of the above criticisms, I have still given the book three stars.The reason is that there is a lot here and forming a full picture of it could in fact take a year or more at my pace.I fault the author for making the reader really assemble the concepts in the book themself, but better to have what is here than nothing at all.

In need of summary, let me end the review with a few comments.This is not a simplistic book, it will take much mental effort and time to get anything out of it.In addition, it can be tiresome to read because it is needlessly repetitious.Certain investor types will get something out of it, but not a specific formula for a particular investment strategy.On the other hand, this book with change my portfolio and what more can be said?I hope this helps a little in judging whether to read the book.It's probably some time before a full review of this book can be written, at least by me.

It takes courage to cut so many trees for this book. Nice cover picture though
EA believes he possesses the instinct of a scientific revolutionaire, when all he is doing is to fiddle with the concept that probabilities change over time. Really sad to see such a thick book on such a thin topic. The style is arrogant. Read Nobel Prize Engle if you want to look at dynamic correlations, don't waste a penny for this man who thrives on the thought that some people might think he is a genius. The quant finance community is not so stupid as you believe Mr EA! ... Read more

Product Description

Presenting probability in a natural way, this book uses interesting, carefully selected instructive examples that explain the theory, definitions, theorems, and methodology.Fundamentals of Probability has been adopted by the American Actuarial Society as one of its main references for the mathematical foundations of actuarial science. Topics include: axioms of probability; combinatorial methods; conditional probability and independence; distribution functions and discrete random variables; special discrete distributions; continuous random variables; special continuous distributions; bivariate distributions; multivariate distributions; sums of independent random variables and limit theorems; stochastic processes; and simulation. For anyone employed in the actuarial division of insurance companies and banks, electrical engineers, financial consultants, and industrial engineers.

Customer Reviews (14)

There are better alternatives to this.
The bad part is that I had to buy this book for my Probability course, and I will probably end up throwing it away after the course ends. There are exercises in each chapter I have covered so far which have little to do with the material in the chapter. I have also found material which is introduced with little or no continuity. The language is rigid, and the flow of thought is not linear. Overall, it makes the learning experience less efficient, and more frustrating; it increases the load on the student, who is forced to make the connections himself, instead of presenting them in the text, as appropriate, or introducing them via exercises which connect with the current chapter material.

The good part is that there are books out there which, in my personal opinion, and using my understand-o-meter, are much better.

Very good and concrete introduction!
I am a graduate in statistics. The textbook I used is the Introduction to probability by bertsekas and Tsitsiklis while I used this book for supplementaryand I found it excellent! It provides some brief history about probability and most improtant, concrete process of the proof of theorms, many of which are very attractive to me!

Too Much Talking
The author of this book just can't shut his mouth! He babbles on and on about all kinds of nonsense, because he doesn't know how to bring the material clearly, concisely, and in logical order. Don't get me wrong: it's pretty good textbook, and relatively rigorous too. It's just that this book is smiply too long. If Mr Ghahramani wants to illustrate concepts with an endless stream of babble and examples, at least give some sort of overview at the end of paragraphs. Don't burden the reader with the task of seperating what is important from what is meant more as an illustration in case you didn't understand the theoretical concepts.
What's perhaps even more irritating, though, is the absense of a study aid with answers. This makes it virtually impossible to use it for self-study. There are (ironically) very concise answers to the odd-numbered questions at the end, but I prefer to check my answers immediately and learn from any mistakes I may have made.
I may have fired away a bit too strongly at the beginning. Instructors might even be delighted by this book; its division of questions into easy and difficult is also useful. However, I'd scout the market a little more closely before using "Fundamentals of Probability" in a course.

NOTE: I MEANT TO GIVE THIS PRODUCT 2.5 (OR 3) STARS, BUT I CAN'T CHANGE THE ONE STAR SHOWN FOR SOME REASON

It's actually somewhat readable.
This book is all right for a math book.Every time I forget something in probability, I can go back to this thing and find exactly what I'm looking for.I guess it could be more rigorous, but I think that would ruin it's understandability.It could definitely use more examples, but I say that about every book.I'm sure it contains its share of typos, but I'm so used to seeing typos in math texts I don't give them a second thought.

This book can sure help you with figuring out how to compute odds in poker, so check it out.

Good book on probability for all but mathematicians...
This book is probably not rigorous enough for a serious mathematics student in probability/statistics, although I am basing this partly on the fact that I (EE Ph.D.) can read and understand this book whereas I can hardly get through a page in a book like Mathematical Statistics by Wilks without extensive background reading. Ghahramani's book has many interesting examples, such as Polya's problems on estimating the number of misprints in a book when two proofreaders each catch a certain (differing) number of mistakes (estimating an unknown frequency). It is quite readable. My only real criticism, and this is not unique to Ghahramani's book, is that "a picture is worth a thousand words" i.e. it is lacking in figures - e.g. if you are going to talk about the central limit theorem, it would be more easily grasped to students to show how the sums of some non-normal distributions quickly approach a normal through a figure or two. [...] ... Read more

Product Description
Probability Models is designed to aid students studying probability as part of an undergraduate course on mathematics or mathematics and statistics. It describes how to set up and analyse models of real-life phenomena that involve elements of chance. Motivation comes from everyday experiences of probability via dice and cards, the idea of fairness in games of chance, and the random ways in which, say, birthdays are shared or particular events arise. Applications include branching processes, random walks, Markov chains, queues, renewal theory, and Brownian motion. No specific knowledge of the subject is assumed, only a familiarity with the notions of calculus, and the summation of series. Where the full story would call for a deeper mathematical background, the difficulties are noted and appropriate references given. The main topics arise naturally, with definitions and theorems supported by fully worked examples and some 200 set exercises, all with solutions. ... Read more

Customer Reviews (1)

Not Great...but better than some
If you are taking this class as an undergrad I would caution that it is extremely hard if not impossible and the book is not much help. The examples are not terribly detailed and they are overly difficult to follow. Good Luck:) ... Read more

Product Description
Virtually every engineer and scientist needs to be able to collect, analyze, interpret, and properly use vast arrays of data. This means acquiring a solid foundation in the methods of data analysis and synthesis. Understanding the theoretical aspects is important, but learning to properly apply the theory to real-world problems is essential.The second edition of this bestselling text introduces probability, statistics, reliability, and risk methods with an ideal balance of theory and applications. Clearly written and firmly focused on the practical use of these methods, it places increased emphasis on simulation, particularly as a modeling tool, applying it progressively with projects that continue in each chapter. It also features expanded discussions of the analysis of variance including single- and two-factor analyses and a thorough treatment of Monte Carlo simulation. The authors clearly establish the limitations, advantages, and disadvantages of each method, but also show that data analysis is a continuum rather than the isolated application of different methods.Probability, Statistics, and Reliability for Engineers and Scientists, Second Edition, was designed as both a reference and as a textbook, and it serves each purpose well. Ultimately, readers will find its content of great value in problem solving and decision making, particularly in practical applications. ... Read more

Customer Reviews (11)

Review by a student user!
This book is mainly targeted for technical professionals such as scientists and engineers. It is well structured each chapter begins with table of contents of its own which I personally like because it adds to clarity of the material and one can easily locate the relevant topic easilywithin a chapter without having to waste time. Furthermore, it introduces new topic with theory and relatively good explanation of the equations which are followed by good examples. There are lots of graphs and tables which is great because it aids visual learner like myself and the majority of us are visual learners.
There is an additional feature included in this book that one does not find in engineering books and that is to emphasis the application of the theory to real world projects. This is supplemented by the introduction of projects that continue throughout the book to aid students learn the content. This book can be used by the students or professionals to aid them in problem solving or decision making depending on the users need. Often engineers and scientists have to make a decision based on an incomplete set of data, this book provides tools and method to aid such decision. Furthermore, the topics and methods covered in the text aid in decision making and also in determining likelihood of an event occurring. These types of information are often needed to make an educated guess, if the data is missing or hard to obtain. It also goes over the probability, that is likelihood of something occurring, an event based on the historical data.
I would have liked to see more and variety of examples after the introduction of a new topic. Furthermore the book doesn't contain answers to any of the problems that appear at the end of each chapter which is an issue. Most engineering books contain answers to at least odd number of problems but this book contains none. It is reasonably priced however I feel that color should have been used in the text to add a visual appeal to the book. Moreover, most books contain a CD to explain complex engineering problems and that component can be added for this text as well.
This book is great because it lays a foundation for engineering students and provides them with a great background in interpreting and analyzing data. Overall content wise this book is excellent which can be easily made better by adding the components that I mentioned above. I sincerely hope that this review aids in making this text better.

Probability, Statistics, and Reliability for Engineering and Scientists Review
I found this book to be helpful in learning probability and statistics. It is generally well written with clear examples of what to do. Some of the text gets a little wordy however and is hard to follow. The examples are usually easy to follow, and I appreciate the consistency of examples from chapter to chapter, and examples that are useful for real life application. The consistency of chapter organization is also a plus. I found it easier to read through a chapter knowing the basic outline of it and what to expect from section to section. The table of contents at the beginning of each chapter is a quality that in my experience is unique to this book. It is helpful to get a feel for the chapter before you start reading, or to quickly jump to the section that you need to find. It is also useful because it is easy to get lost in the numbering of the sections each with a 3 digit identifying number. The problems are mostly well written and applicable to the chapters. They don't follow the examples as closely as I would have hoped, but that probably makes for a better teaching tool. The simulation problems look interesting for more real world application. However, the book would benefit from a section with selected answers in the back. These are useful to let the reader know if they are on the right track or not. Overall this is an excellent textbook that is very well organized, it is hard to follow at points, but its strengths ultimately outweigh its weaknesses.

Good Reference Book
The purpose of this book is to inform engineers and scientist of how to use probability, statistics, and reliability in their respective field.
This book is well organized by chapter and subsections using numerals. Its organization first introduces a new concept, then proceeds to describe it in further detail, and finally gives applicable examples of how to use these methods.

This book can provide to be a useful tool and reference to its intended audience. It is easy to find different methods and each method is well introduced with its intended purpose. I personally felt the book could be gaged for a broader audience with a small amount of added descriptive detail. For someone familiar with probability, statistics, and reliability methods and someone using this book as a reference, I feel the book is very effective. Not being an expert and not having a large amount experience in the study of probability, statistics, and reliability, I believe it would be beneficial for the book to provide a few less-technical descriptive terms. As a very basic example: The book defines the use of the cumulative mass function in this way: "The cumulative mass function is used to indicate the probability the random variable X is less than or equal to xi." This is a good definition for someone familiar with the concepts and should not be omitted. For a novice, the inclusion of an additional sentence for clarity might help. To drive the point home it might include a following sentence such as, "For example, the cumulative mass function is the chance of picking a card out of a deck that has a number on it less than or equal to 3." This describes an action the reader can relate to. As the chapters move into more and more technical detail, a plain language, nontechnical description of what the general subject is can be very helpful for a novice reader.

Overall, this book is a well written resource for scientists and engineers. With the addition of a few nontechnical details, I believe the book will be able to reach a broader audience and be more applicable to students and the less informed reader.

Book Review
Probability, Statistics, and Reliability for Engineers and Scientists, written by Bilal Ayyub and Richard McCuen, is a very thorough textbook that covers all the important parts of probability and statists needed for engineers. It gives many accurate and applicable examples to its readers. All the examples are worked through very nicely, making it easy to follow for someone very new to the subject.

I would prefer if the examples are better highlighted and recognized as examples, to stand out more and draw the attention of the users that are searching for only examples. That being said, maybe adding some color, although might be more expensive, may help identify them. Also, if the spacing were a little larger in between sections it would not be as visually overwhelming.

The graphs are large and labeled really well and are often a great tool for the students to further their understanding of the material.

I like how equations are clearly written out and given a lot of room in between and after the text, making them easy to comment on with hand written notes in the margins. I also like how the equations are each numbered, making them easy to reference. I would prefer if the textbook were a little larger with respect to its surface area, thereby being overall thinner. I think this design would make the textbook more comfortable to hold and read through.

The amount of examples and review problems for each chapter make it really helpful to prepare for exams. I think it would be more beneficial if there were selected answers/solutions in the back of the book. I am often hesitant to do problems when I am not sure if they will be right, than again as it is now, it encourages students to study in groups. There are clearly arguments for both sides.

Before each new topic there is a very helpful in depth description and background of the topic to be stated that really helps the reader get the entire context of the topic. Without these sections I feel that I would be very lost.

As it says in the beginning of the text, the purpose of this book is to "1) introduce probability, statistics, reliability, and risk methods to students and practicing professionals in the engineering world and the sciences, 2) emphasize the practical use of methods, 3) establish the limitations, advantages, and disadvantages of the methods". Based on my observation, I think the goals set for this text were well achieved.

I do really like the textbook, and I think I get a very thorough understanding of the material, while seeing real life application. I would say it is a textbook worth keeping after this course as a reliable reference.

Comprehensive, Concise and Well-Written
One of the greatest facets of the textbook is the clear and concise writing style.The authors present the subject manner in a way that is both easy to understand and comprehend.A strong emphasis was placed on incorporating "real world" case studies within each chapter.This allows the reader to understand the significance and relevance of the subject material in applied engineering.Examples include [but are not limited to] building/construction design, and natural hazards.

The structure and setup of each chapter aids in achieving greater reader comprehension.Each chapter begins with an introduction, providing a brief synopsis of the material to be covered.The format is deductive in nature, beginning with general topics and moving towards specific focus areas.This format is particularly organized and systematic.

An important feature of the textbook is the incorporation of the derivation of particularly useful equations.All too often, in many textbooks, the derivation of equations is left out, leaving the reader with the "final equation" only.I believe that the inclusion of derivations allows for greater comprehensiveness.

In terms of improvement of the textbook, a larger number of pictures and diagrams [when necessary] may help, although it may be difficult to add.Additionally, the availability of a soft-cover copy would reduce the cost of the textbook.

In summary, this is an excellent source of information for understanding probability, statistics, and reliability. ... Read more

Product Description
Probability and Statistics with Applications: A Problem Solving Text is an introductory textbook designed to make the subject accessible to college freshmen and sophomores concurrent with their study of calculus. It is organized specifically to meet the needs of students who are preparing for the Society of Actuaries and Casualty Actuarial Society qualifying examination P/1. Sample actuarial exam problems are integrated throughout the text along with an abundance of illustrative examples and 799 exercises. Additionally, the chapters on mathematical statistics cover all of the learning objectives for the statistics portion of the Casualty Actuarial Society Exam 3L syllabus. Here again, liberal use is made of past exam problems from CAS Exams 3 and 3L. The book provides the content to serve as the primary text for a standard two-semester advanced undergraduate course in mathematical probability and statistics. ... Read more

Customer Reviews (1)

Great book with a lot of examples.
The book is very well written. I find it often leads me to a conclusion or formula based on my own reasoning, rather than shoving the formula into my face and then proving it. The examples are the real show stealer though, and often clarify just how one would use a formula in real (though a more interesting) life.

I recommend for anyone looking for an introductory book to probability. ... Read more

Product Description
The first seven chapters use R for probability simulation and computation, including random number generation, numerical and Monte Carlo integration, and finding limiting distributions of Markov Chains with both discrete and continuous states. Applications include coverage probabilities of binomial confidence intervals, estimation of disease prevalence from screening tests, parallel redundancy for improved reliability of systems, and various kinds of genetic modeling. These initial chapters can be used for a non-Bayesian course in the simulation of applied probability models and Markov Chains. Chapters 8 through 10 give a brief introduction to Bayesian estimation and illustrate the use of Gibbs samplers to find posterior distributions and interval estimates, including some examples in which traditional methods do not give satisfactory results. WinBUGS software is introduced with a detailed explanation of its interface and examples of its use for Gibbs sampling for Bayesian estimation.
No previous experience using R is required. An appendix introduces R, and complete R code is included for almost all computational examples and problems (along with comments and explanations). Noteworthy features of the book are its intuitive approach, presenting ideas with examples from biostatistics, reliability, and other fields; its large number of figures; and its extraordinarily large number of problems (about a third of the pages), ranging from simple drill to presentation of additional topics. Hints and answers are provided for many of the problems. These features make the book ideal for students of statistics at the senior undergraduate and at the beginning graduate levels. ... Read more

Product Description
This is a masterly introduction to the modern and rigorous theory of probability. The author adopts the martingale theory as his main theme and moves at a lively pace through the subject's rigorous foundations. Measure theory is introduced and then immediately exploited by being applied to real probability theory. Classical results, such as Kolmogorov's Strong Law of Large Numbers and Three-Series Theorem are proved by martingale techniques.A proof of the Central Limit Theorem is also given.The author's style is entertaining and inimitable with pedagogy to the fore. Exercises play a vital role; there is a full quota of interesting and challenging problems, some with hints. ... Read more

Customer Reviews (16)

Interesting book, but needs supplementary material
I used this book as a companion through two courses, one in measure theory (including Lebesgue integration theory) and the second in advanced probability (ending just before stochastic integrations). The book is well written, but somewhat whimsical. Certain topics (such as integration) are covered somewhat superficially. For example, what Willams calls the 'standard machine' for integration (indicator functions to simple functions and then monotone convergence, etc.) is a very powerful idea but hastily described. Doob's theorems are well covered, and stopping times are also treated well. Unfortunately, many proofs are covered very hastily; call me stupid, but I need to refer to Billingsley or other text material in order to understand them.

But my favourite part of the book is the Brobdingnag sheep problem example. In most other books, examples of applications of martingale theory come from the hackneyed financial modelling world; this problem is not only an interesting riddle, but also lays the germs of stochastic optimal control, which to me (as an engineer) is probably of far more interest.

In summary, well worth the buy, but make sure that it is not the only thing you depend on. However, I found plenty of good supplementary material on the web, so that should not be a problem.

I bought the book after reading it
I have taught probabilityto undergraduates (in the US) from Sheldon Ross' A First Course in Probability, which I recommend to any student. I have also read Feller (superb) and Billingsley (superb) for myself, so you may imagine that I am not new to these topics. Learning from Ross is like learning calculus, learning from Billingsley is like learning mathematical analysis. One must progress from one to the other.

On the other hand, even after learning the subject, one is always looking for something concise, consistently engaging, that gives a good view of the subject, allows you to make new connections, and gives you new ideas. Williams' book is all of that. It is not a book to have on a first exposure to the subject, maybe not for a second exposure either -- that will very much depend on what kind of student you are, and what you want to learn, and how you want to learn it. Only some very special students will go unaided through Williams' book on a first reading. But if you have some experience with the subject already (or with measure theory), and you want to broaden your horizons, then this book will allow you to do that. Williams' enthusiasm shines through every page, which is a plus. At this stage in my understanding of the subject, I actually appreciate that the book doesn't go into every detail, but shows more than enough to be a good guide. I didn't give it 5 stars because, to my taste, it should contain more exercises.

Having said all of that (about the book not being suitable for a first reading), I will take it all back, if you have the "correct" intructor teaching you the material: someone who will fill in some gaps when you need it, give you extra exercises, and in general give you that confidence that you need to feel that you are doing the right thing, and not just lost in the woods.

Enjoy!

Not an introductory text
Williams is of course a distinguished probabilist but not a particularly good writer despite his sofistication.
His goal is to write original, entertaining, rigorous, and sofisticated mathematics which is simply not possible. Instead of developing subject with rigor it needs, he often makes puzzling remarks like "philosophers are pompous where we are precise, they are thought to think deeply" (?) or "don't tell me about those things" (?) and forward references and he does that in all of his books. Sometimes it is clear why, sometimes it is not. On occassion it is not clear what is the topic about, even in the proofs. For example Skorohod's representation on page 34 is never stated, Williams engaged himself into proof of it without ever stating the theorem. He probably assumed we already know what it is about. The rigor suffers from that and it basically confuses inexperienced reader. One needs to figure out in which order to read the sections. For example Chapter 0 in this book is just a waste of time, god only knows why it is there. Chapter 15 is pretty much a gibberish and fairly irrelevant waste of space. I suggest any reader to skip over it since it is hard to read given the absence of careful presentation and yet it is really no gain whatsoever. In general while trying to present examples Williams is simply not capable of doing that with reasonable clarity.

Out of the three parts of the book, the first part is elementary, the second part is the best and at graduate level, the third part is just a sketch as far as textbook value goes.

I would say if you want to be entertaining and insightful in mathematics then make vivid, clear, and efficient examples not vivid remarks. This is not a novel writing. I personally do not care one iota for somebody's "wits" and "humour" but I do care about clarity of concepts. Read Kolmogorov, Sierpinsky, Kuratowsky ... all great math writers without any unnecessary "humour."

For all these reasons I would not recommend this text as introductory, certainly not on undergraduate level. It is interesting to read if you already had an introductory text in probability. It is definitely a good book to read if you are refreshing your knowledge on rigorous basic/discrete probability, some of the proofs are rather elegant, for example truly nice and simple proof of Strong Law of LN (with stronger assumption), a brief Martingale proof of 0-1 law, or a nice constructive Martingale proof od Radon-Nikodym. On the good side Williams does not suffer withdrawal symptoms in the proofs which is good. His proofs are careful, concise, and clear, without missing details ... well, by the most part. For the "counterexamples" take a look at overly sketchy proof of Jensen's Inequality - certanly not accessible to most American undergraduates, or hard to read mess Williams made of Law of Iterated Logarithm. Or "Levy's Inversion Formula" - how hard was to write a nice presentable proof? I am sure Williams was capable of that but he has chosen to make it clumsy. He does exhibit more withdrawal symptoms in his remarks and examples which are often puzzling and not clear enough. It looks to me like a old professor who fails to connect his knowledge with his presentation.

I've seen better and worse books, if one needs introductory graduate level textbook then I would suggest still unbeatable Kai Lai Chung classic, I am yet to see a better written probability textbook. I feel Williams' book was a real nice idea (at least the second part of the book) that could have been made better but got distracted with author giving himself a bit too much "literary" freedom. It is still a nice book to have though and Williams is still a person to learn from. Unfortunately he is not a great textbook writter.

excellent probability text
This is an excellently written text on probability theory that emphasizes the martingale approach. The treatment is softer than Neveu's "Discrete Parameter Martingales". Williams intends this book for third year undergraduates with good mathematical training as well as for graduate students.
It provides all the classic results including the Strong Law of Large Numbers and the Three-Series Theorem using martingale techniques for the proofs. It includes many exercises that the author encourages the reader to go through. The author recommends the texts of Billingsley, Chow and Teicher, Chung, Kingman and Taylor, Laha and Rohatgi and Neveu's 1965 probability theory book for a more thorough treatment of the theory.

Measure theory is at the heart of probability and Williams does not avoid it. Rather he embraces it and views probability as both a source of application for measure theory and a subject that enriches it. He covers the necessary measure theoretic groundwork.

However, advanced courses in probability that require measure theory are usually easier to grasp if the student has had a previous mathematics course in measure theory. In the United States, this usually doesn't occur until the fourth year and measure theory is mostly taken by undergraduate mathematics majors. Sometimes it is taken by first year graduate students concurrent with or prior to a course in advanced probability. For these reasons I would advise most instructors to consider it mainly for a graduate course in probability for math or statistics majors.

In the Preface, the author is quick to point out that probability is a subtle subject and honing one's intuition can be very important. He refers to Aldous' 1989 book as a source to help that process. I was disappointed that he didn't mention the two volumes on probability by Feller. Feller's books, particularly volume 2 with his treatment of the waiting time paradox, Benford's law and other puzzling problems in probability is a most stimulating source for appreciating the subtleties of probability, for honing one's intuition and for craving to learn more. It is a shame that Williams didn't mention it there. At some point Williams does refer to Feller's work but he only references volume 1.

A Pedagogical Masterpiece
A Pedagogical Masterpiece
I used this book for self-study after struggling with Billingsley and Chung for months. Williams has a deep love for probability and it comes out rather beautifully in his writing. He gives the various topics just enough attention to maintain the brisk tempo necessary for a first course in measure theoretic probability and his proofs and exposition are on average much clearer than the aforementioned authors'. He has a knack of anticipating the average readers' stumbling blocks and states clearly which results are the fundamental ones and which aren't so important.

Read this book as a companion to Billingsley, Chung, or any other. Read it to lead up to Karatzas and Shreve, Rogers and Williams, or Protter. Or read it simply for inspiration. ... Read more

Product Description
WILEY-INTERSCIENCE PAPERBACK SERIES

The Wiley-Interscience Paperback Series consists of selected books that have been made more accessible to consumers in an effort to increase global appeal and general circulation. With these new unabridged softcover volumes, Wiley hopes to extend the lives of these works by making them available to future generations of statisticians, mathematicians, and scientists.

"Many examples drawn from the author’s experience of engineering applications are used to illustrate the theoretical results, which are presented in a cookbook fashion...it provides an excellent practical guide to the analysis of product-life data."
–T.M.M. Farley
Special Programme of Research in Human Reproduction
World Health Organization
Geneva, Switzerland
Review in Biometrics, September 1983

Now a classic, Applied Life Data Analysis has been widely used by thousands of engineers and industrial statisticians to obtain information from life data on consumer, industrial, and military products. Organized to serve practitioners, this book starts with basic models and simple informative probability plots of life data. Then it progresses through advanced analytical methods, including maximum likelihood fitting of advanced models to life data. All data analysis methods are illustrated with numerous clients' applications from the author's consulting experience. ... Read more

Customer Reviews (5)

Applied Life Data Analysis
I don't own many dedicated volumes on this specific topic, but I have used several and this compares very well. The Weibull sections are explained vary well. There is enough information for a novice and yet will still be a good reference for someone with experience. Modern software tools have made the tedious tasks more automated, however this volume covers the theory and has reference material and good examples.

How to do Weibull analaysis - and how to understand it.
There was a sharp client need, my experience with weibull was a while ago, and my (excellent) software was still new to me.Wayne Nelson's book, _Applied Life Data Analysis_, was just right.He has the equations; he has the examples, PLUS the pitfalls and cautions that go with them.Using this book, I was able to understand an unexpected but mathematically valid result in life test data.I strongly recommend this book for those who need to understand what they are doing with life test analysis and prediction.

Nelson's first book
At the time this book was written Dr. Wayne Nelson was a research statistician for General Electric as well as a private consultant.Through his work at GE he became very familiar with the application of censored "life data" in practical reliability applications and this was one of the first well-presented applied books in reliability similar to other statistics books written on survival and reliability.Wayne never revised this book but he did go on to write books on accelerated testing and recurrent events and was a major contributor to the research in reliability both from the theoretical and practical sides.Wayne has said that one reason that he never revised it was that at a time when a revision might have been appropriate the book by Meeker and Escobar came out and that text was very close in content to what Wayne would have written.Although the book is outdated, it does rightfully belong in the Wiley Classic series and is affordable in its current paperback form.It is still a valuable resource and has historical significance.

An Excellent Coverage At All Levels
This book has an excellent coverage of the topic of survival analysis from the basics through to far more advanced techniques. As both a practitioner using practical survival analysis, and as a student I find this book particularly useful.

Of particualr use is the focus on real situations, which may differ from the simplest forms that are often used in other texts.

The Bible of reliability data analysis
This is Dr. Nelson's classic work on life data analysis, and should be on the bookshelf of anyone working in reliability and risk analysis. It covers the full specturm of reliability data analysis methods, and can be read at several levels - from a beginner who is trying to learn the language, to someone interested in developing their own software. Dr. Nelson once mentioned that he wasn't going to write an update to this classic as new developments were covered by Prof. Meeker's book. Although Meeker's book is excellent, this book remains an all-time favorite. I think part of this books popularity is it's writing style in addition to the way the topics are structured and covered. Well worth the price ! ... Read more

Product Description
The theory of probability is a powerful tool that helps electrical and computer engineers to explain, model, analyze, and design the technology they develop. The text begins at the advanced undergraduate level, assuming only a modest knowledge of probability, and progresses through more complex topics mastered at graduate level. The first five chapters cover the basics of probability and both discrete and continuous random variables. The later chapters have a more specialized coverage, including random vectors, Gaussian random vectors, random processes, Markov Chains, and convergence. Describing tools and results that are used extensively in the field, this is more than a textbook; it is also a reference for researchers working in communications, signal processing, and computer network traffic analysis. With over 300 worked examples, some 800 homework problems, and sections for exam preparation, this is an essential companion for advanced undergraduate and graduate students. Further resources for this title, including solutions (for instructors only), are available online at www.cambridge.org/9780521864701. ... Read more

Customer Reviews (4)

Quick delivery
I'm surprised that the delivery to New Zealand is very quick, even quicker then the projected date that has been made by Amazon in advance.

good book
I used this book for a EE Probability course, and the professor is a freak Korean guy....

an excellent book to begin probability
This is an excellent book on probability. What I liked about it is the fact that it is sprinkled with numeours examples. The language the author has used is also easy to understand but at the same time, formal. It really strikes the balance.

However, I think there should be more explanation of combinatorics in ch2. But if a person has had some prior knowledge of probability, they should refer to some other book for that portion.

well suited for a university course
Gubner provides an excellent text for undergrads or grads wanting a solid background in applying the ideas of probability and random processes. The emphasis is on applications in electrical engineering. The book presupposes a solid background in calculus and some circuit theory. Ideally, the student might be a third year undergrad or higher.

The main ideas in probability are developed. Getting to the Central Limit Theorem and the Gaussian (bell) curve. The probability distributions most useful to you might be the continuous ones.

Then, the text develops the ideas of random processes. When these can be assumed to be stationary, then it makes tractable vast areas of applications, as in the communications theory of the signal to noise ratio of a channel.

The book shines as a text for a university course because of the wealth of examples and problem sets. The difficult of the latter varies considerably, which is also another advantage to a lecturer facing students with a range of abilities. ... Read more

Product Description

This is the first book to comprehensively cover quantum probabilistic approaches to spectral analysis of graphs, an approach developed by the authors. The book functions as a concise introduction to quantum probability from an algebraic aspect. Here readers will learn several powerful methods and techniques of wide applicability, recently developed under the name of quantum probability. The exercises at the end of each chapter help to deepen understanding.

Product Description
The new edition of Anthony Hayter's book continues in the same student-oriented vein that has made previous editions successful. Because Tony Hayter teaches and conducts research at a premier engineering school, he is in touch with engineers daily and understands their vocabulary. This leads to a clear and more readable writing style that students understand and appreciate. Additionally, because of his intimacy with the professional community, Hayter includes many high-interest examples and datasets that keep students' attention throughout the term.PROBABILITY AND STATISTICS FOR ENGINEERS AND SCIENTISTS employs a flexible approach with regard to the use of computer tools. Because the book is not tied to a particular software package, instructors may choose the program that best suits their needs. However, the book does provide substantial computer output (using MINITAB and other programs) to give students the necessary practice in interpreting output. "Computer Note" sections offer tips for using various software packages to perform analysis of the datasets, which can be downloaded from the website. Through the use of extensive examples and datasets, the book illustrates the importance of statistical data collection and analysis for students in the fields of aerospace, biochemical, civil, electrical, environmental, industrial, mechanical, and textile engineering, as well as for students in physics, chemistry, computing, biology, management, and mathematics. ... Read more

Customer Reviews (14)

Good book
I purchased this book for my daughter who is studying to be a Chemical engineer.She tells me that the book is in the condition that she expected it to be in and it is serving its purpose.Good deal and shipped within a reasonable time.

A great textbook for probability
I have only started reading this text. What I have seen is that this book is very easy to understand, contains many examples, and has very reasonable problems. Additionally, answers to the odd numbered problems are provided;which is great as you can check your understanding. What is really neat, is the text has a practical case study that is developed as the chapters develop. A student solutions manual is also available to students which is a definite plus. All in all, a great textbook on the subject.

anonymous
This book is not designed for people who are starting to learn statistics or probability.Use this book ONLY if you have undergraduate degree in mathematics or engineering (just like the book says).You NEED to have calculus background in order to understand some portions of the book.There are a number of reasons why I don't personally like this book.
1) Examples cited jump around a lot.There really needs to be a central example library instead of searching through the whole book looking for the example.For example, it would say "Example 38" and talk about how to do a calculation for the chapter but in order to find the data on Example 38, you would have to search another chapter or another part of the book.Why make it so difficult to find the example? Make it easy to access.Don't make me waste my time searching through the whole book, looking for the data on Examples.
2) Index is very poorly designed, if not useless.You have to search for a topic in a number of ways to find anything. It is too limited.
3) Calculations are not fully spelled out.For example, Hayter makes too many assumptions.For example, you cannot skip around to cover different topics because if you do, you wouldn't understand how he obtained the answer.I don't understand why he didn't spell out everything or omits steps and gets right to the answer. To me, process is more important than the answer.
4) Talking about answers, Study Guide is also very useless in my opinion.It only gives you the answer and does not tell you how you get it.What's the use of having the study guide if it doesn't tell you how you got the answer? It was waste of money to buy the study guide.
I believe there are a lot of great books on probability and statistics. In my opinion, this is NOT one of them.

Hayter - Probability and Statistics for Engineers and Scientists
This is a good textbook for learning the basics of probability and statistics. It is written at the graduate level, and breaks into single and multivariable calculus without missing a beat. The calc tripped me up because it has been a while since I've seen it, and there is no refresher in the text.
It reads easily and uses a lot of real-world examples to illustrate concepts, which makes it easy to comprehend and apply.

Great Transaction
This was a great transaction and I would be happy to do buisness with this seller again in the future. ... Read more

Product Description

Customer Reviews (4)

A Really Good Book
Actually, I really like this book. I realised that it can be used as a text itself. It can used with advanced probability and math stats courses or in graduated courses. I highly recommend this book.

Great collection of problems, but with some problems
I am enjoying working through this book.Each section contains several worked examples, and problems, which supposedly correlate with the examples.In several situations, though, there is a simpler solution than following the example.Unfortunately, this is only one of several problems.For instance:
* Asks that you prove a statement, which is usually false (A'B u B'A = A' n B').Only one found so far.
* Some solutions don't exactly correspond with the questions (i.e . the numbers used in the solution are different from the question.)Easily recognized.
* Ambiguous wording of problems (what is the difference between a boat moving "along a bay" vs. "across the same bay"?) This could be due to poor translation.Very frustrating. (And really why I can't give this book five stars)
* Some complex problems have an answer, but no solution, so you aren't sure if the mistake is yours or the book's.
* Different notation.(Uses D and M rather than E and Var) Easily adapted to.

Despite these problems, I am finding working through these problems to be a very rewarding experience.Solving Buffon's needle problem was definitely the highlight of my day.

Challenging probability and statistics problems
Sveshnikov gives a very brief introduction to each topic, with definitions and formulae presented without proofs, followed by a couple of worked examples, and a couple pages of problems.Answers to all problems are in the back, making it ideal for self-study.
If you have not studied any statistics before, you might want to start with a book that gives more explanation, such as Bulmer, "Principles of Statistics."
This book makes use of calculus in many sections.For interesting probability problems with less advanced math, you might try Mosteller, "Fifty Challenging Problems in Probability."
If you take the time to work through a number of problems from each chapter, you can learn how to apply probability and statistics to a wide variety of problems. The equations I derived for the thesis I'm working on are the topic of chapter 6!

A most useful compilation
Instructors and students alike will find here a real treasure ofexercises in probability and statistics. A broad range of topics is covered. Solutions for typical examples are provided at the start of each section. Apart from the more than 1000 problems (the answers and solutions to all of which are provided at the back), the book contains problems both simple and challenging. I personally found some of the latter most fascinating. ... Read more

Product Description
This textbook is ideal for an undergraduate introduction to probability, with a calculus prerequisite. It is based on a course that the author has taught many times at Berkeley. The text's overall style is informal, but all results are stated precisely, and most are proved. Understanding is developed through intuitive explanations and examples. Graphs, diagrams, and geometrical ideals motivate results that might otherwise look likely purely formal manipulations. ... Read more

Customer Reviews (18)

no complaints
the book arrived timely and in great condition --little wear/tear on the outside and no writing/highlighting on the inside. examples in the the book effectively explain concepts, and there are several helpful appendicies along with an index in the back of the book.

So Hard!
This book is extremely difficult. I have solutions for this book. You will love it. If you're interested, email me at KenRobert2910@gmail.com

Text may be for beginners; the problems aren't.
I used this textbook in an undergraduate class, and went back to it to study for SOA/CAS Exam 1/P.The examples and explanations were run of the mill, but the problems... wow.

There was a wide range of problems, in scope and in level of difficulty.They ranged from medium to hard to impossible.Some of the more memorable ones were research-level problems that required you to do a little bit of independent research on the internet, and the hardest problems could easily take you all day to solve.The problems were easily the strongest part of the book and you will learn the necessary concepts by solving them - the examples and explanations are really just there as a guide.I can attest to this because I did them ALL, 709 of them in total - a feat that took me roughly two months and enabled me to pass Exam 1/P with flying colors.

Overall, I found the explanations and examples to be less than top-notch, but the problems will really test you.Just make sure to work in groups and ask for help, and stick to problems that are relevant to the course (or exam) - otherwise the book can chew you up and spit you out.

P.S. This text does not have a section on moment-generating functions, so you'll have to find another source for that topic.Wikipedia has a good article on the subject.

Save your money and time
Terrible book. The problems have nothing to do with the chapters. Every time I read this book for my Probability class, I couldn't help falling asleep. I recommend Ross's First Course in Probability. Stay away from this bane of students.

Try before you buy
If you are interested in this book, you might want to look at its Google books page (for which the tinyurl is pitman-prob1993).

Disclaimer: because this book was typeset with my professional typesetting system, a customized TeX, I can vouch for the quality of the math and text composition, with the stipulation that I was professionally involved with its production as a consultant. ... Read more

Product Description
This book teaches students to apply their basic knowledge of statistics to both routine and complex problems. They will quickly be able to identify what type of problem they are faced with and will have the skills to solve that problem correctly.

Most problems presented in core texts are repetitious and require students merely to do some computation, look something up in a table, or recall the proper Excel command. Even study guides and review manuals do not push the student beyond this introductory level. 101 Special Practice Problems in Probability and Statistics, fourth edition, challenges students to think at a higher than basic level, without involving a higher level of mathematics, while still teaching them to solve diverse groups of problems such as those they find on most exams. The book s approach will put an end to the frequently heard student lament, I did fine on the homework, but I was BLOWN AWAY by the exam!This new edition contains additional class-tested problems to further increase an emphasis on the use of Excel. A mini CD-ROM containing data sets for the appropriate problems, is included with each book. ... Read more

Product Description
A thrilling way to learn about probability, statistics, and math-by watching Sherlock Holmes help victims exploited by evil con men.

In Conned Again, Watson!, Colin Bruce re-creates the atmosphere of the original Sherlock Holmes stories to shed light on an enduring truth: Our reliance on common sense-and ignorance of mathematics-often gets us into trouble. In these cautionary tales of greedy gamblers, reckless businessmen, and ruthless con men, Sherlock Holmes uses his deep understanding of probability, statistics, decision theory, and game theory to solve crimes and protect the innocent. But it's not just the characters in these well-crafted stories that are deceived by statistics or fall prey to gambling fallacies. We all suffer from the results of poor decisions. In this illuminating collection, Bruce entertains while teaching us to avoid similar blunders. From "The Execution of Andrews" to "The Case of the Gambling Nobleman," there has never been a more exciting way to learn when to take a calculated risk-and how to spot a scam.Amazon.com Review
Some people who think they hate math are lucky to learn that they actually just can't abide its often dry, abstract presentation. Physicist Colin Bruce turns math teaching on its head by using conflict, drama, and familiar characters to bring probability and game theory to vivid life in Conned Again, Watson! Cautionary Tales of Logic, Math, and Probability. Using short stories crafted in the style of Sir Arthur Conan Doyle, he lets Sherlock Holmes guide Watson and his clients through elementary mathematical reasoning. This kind of thinking is growing more and more important as poll numbers, economic indicators, and scientific data find their way into the mainstream, and Bruce's gambit pays off handsomely for the reader. Delving into such arcana as normal distribution, Bayesian logic, and risk taking, the stories never dry up, even when presenting tables or graphs. Holmes's quick wit, Watson's patience, and their various friends' and clients' dubious decisions unite both to entertain and to illuminate tough but important problems. Even the cleverest numerophile will probably still find a nugget or two of hidden knowledge in the book, or at least a few new ways to explain statistical concepts to friends and students. The rest of us can relax, enjoy the tales, and come away a little bit tougher to con. --Rob Lightner ... Read more

Customer Reviews (15)

Holmes and Probability
Brilliant piece of work. Very good for stretching the 'little grey cells'.
Probability comes to life, and death,in the usual Holmes way.

You might want to re-think that last bet you made!
Talk about niche marketing! "Conned Again, Watson" is a pretty difficult book to categorize. Perhaps the sub-title does a fair job of letting a potential reader know what it's all about - "cautionary tales of logic, math and probability".

It's not a pastiche in the typical sense. What author Bruce does is simply use the characters of Watson and Holmes and some very light-hearted mysteries to probe typical ignorance and common misunderstandings about probabilities, statistics, game theory and so on. Bayesian conditional probabilities, the drunkard's walk, probability distributions, the cab driver fallacy, gambling fallacies and other topics of interest in decision theory are touched upon and explained in a fashion that even the most math-phobic reader could hardly fail to understand.

That said, I expect this is the kind of book that would appeal only to that specific niche market I referred to earlier - past readers of the Sherlock Holmes canon who also had an interest in popular mathematics. That interest needn't be deep or at a university level but "Conned Again, Watson" is unlikely to succeed on the basis of an interest in Sherlock Holmes alone.

Recommended.

Paul Weiss

Good infotainment on probability, logic and related fields
The book consists of 12 detective cases, solved by Sherlock Holmes, his brother Mycroft and Dr. Watson. The stories happen in 1900, but the historical setting shouldn't be taken too seriously because the author takes liberties with it (as he explains in the afterword). The cases are solved by using mathematical and logical reasoning in an informal way. Most of the cases involve some probabilistic concept or result. The potpourri of topics is well-chosen: all either carry some important practical lessons or are intellectually interesting; best cases have both.

It is true, as a reviewer noted, that most of the stories are predictable if you know the mathematics. That didn't prevent me from enjoying the text: I find the concepts illustrated quite fascinating, and the pleasure was in seeing how they were illustrated. It is also true, as another reviewer noted, that some results are repeated, with different applications. I found this theme-and-variations treatment good because one gets a fuller view of the implications and applications of the particular result. Besides, if one finds this repetition tedious, all one has to do is to read more cursorily or skip some paragraphs.

A reviewer pointed some errors in the book. It seems though that an error in chapter 4, The Case of the Ancient Mariner, has not been reported so far. To simplify matters, I'll talk only about the coin-tossing example presented. A coin is tossed 100 times. The coin produces 13 more tails than heads. From this, Watson and Holmes draw the conclusion that 63 tails have been thrown in the 100 coin tosses. This isn't so. It is easy to see - for parity reasons - that it isn't even possible to throw 13 more tails than heads in 100 coin tosses; but when the number of coin tosses is 99, the number of tails must be 56, and the number of heads must be 43. A reader familiar with highschool algebra can check this by solving the pair of equations y=x+13 and x+y=99 (or x+y=100 in the original formulation); here y is the number of tails, and x is the number of heads. Indeed, if the number of tails would be 63 (and thus, by implication, the number of heads 37), there would be 63-37=26 more tails than heads. This error is regrettable because it affects the rest of chapter 4.

I read most of the book on a holiday trip, and can testify that it is good, light and informal reading for a mathematically oriented reader. Due to its level of treatment, the book should also be accessible also to readers with little mathematical knowledge.

Enjoyable Holmesian Read
I `m suspicious of any novel purporting to be written in the `spirit of Sherlock Holmes' but Colin Bruce truly pulls one off here with his book "Conned Again Watson!" I picked it up initially thinking that a blend of Holmes and math would make for a good read but ended up reading it simply as a Holmes story.The book is obviously written for folks with an eye for math, logic, and stats and for those readers who have studies these subjectsthe math will be a bit lean but I'm not sure how you can weave complex math into a readable novel.I do like the concept, though, and it follows largely along the same lines of "Godel, Escher, and Bach."
I would certainly recommend the book to Holmes fans and probably not for math fans looking to learn anything new. For an easy and fun read , though, I think Bruce has succeeded.

Sherlock Holmes stories on logic, maths & probability
Twelve short Sherlock Holmes stories challanging logic, probability, statistic, game theory, more or less relevant to daily life. The authors approach of telling the story seen through Holmes and Watson is brilliant (incl. the dialogue between the two). Some stories are a bit simple and boring while others were quite amazing. Example Chapter 7 illustrates the error of assuming that a well-defined ordering retlation must also define a unique hierarchy. In higher mathematics it is quite possible to have x greater than y, y greater than z, and yet z greater than x! Last but not least, the afterword is extremely useful where the author sheds more light on each chapter. ... Read more

Product Description
This book grew from a one-semester course offered for many years to a mixed audience of graduate and undergraduate students who have not had the luxury of taking a course in measure theory.The core of the book covers the basic topics of independence, conditioning, martingales, convergence in distribution, and Fourier transforms.In addition there are numerous sections treating topics traditionally thought of as more advanced, such as coupling and the KMT strong approximation, option pricing via the equivalent martingale measure, and the isoperimetric inequality for Gaussian processes. The book is not just a presentation of mathematical theory, but is also a discussion of why that theory takes its current form.It will be a secure starting point for anyone who needs to invoke rigorous probabilistic arguments and understand what they mean. ... Read more

Customer Reviews (7)

interesting perspective
I spent long hours learning probability theory from Billingsley's book, which is worth every bit of effort I put in. Then, by chance I picked up this book from the library, and could not put it down. After finished the book, I wend ahead to buy a copy.

Contrary to an earlier reviewer, I appreciate very much the same symbol for probability and expectation, which allows a quite natural and united treatment of the two important concepts. It brings great clarity. Also, de Finetti's notation, once introduced, seems only natural.

The tempo of the book is at once deliberate and brisk. The author makes excellent judgment selecting the coverage. He also makes good decision on when to slow down and get dirty, and when to be brief and cover territory. The discussions in the book, combining simple explanation motivation and intuition, provides exciting road map for exploring in the first reading and for surveying in later readings.

Excellent book!

Excellent and idiosyncratic
There is no shortage of graduate-level probability textbooks. Theclassics (Ash, Billingsley, Breiman) have been partly replaced by (among others) Dudley, Shiryaev, and Durrett (the de facto gold standard). You can now Pollard's book to the list. It is written in a peculiar style, conversational yet rigorous. The author does not hide his preferences and feelings toward theorems, and I find this useful and illuminating, as it helps the reader sort the essential material from the ancillary. Most importantly, the choice of topics is truly unique. Clearly, the goal is to cover the basics very well, rather than offer an assortment of theorems. For example, the ergodic theorem (a mainstay of every textbook) is nowhere to be found. However, you can find advanced material that are becoming important tools for the applied probabilist (esp. the of the mathematical statistics variety) as well as advanced applications. Random examples: isoperimetric inequality, Dobb's theorem on consistency of posterior measures, coupling, multivariate normal distributions. Overall, I have read half of the book, and loved it. In my list of personal favorites, it ranks second behind William's booklet ("Probability with Martingales"). Like William's book, this is a quick, enjoyable, rigorous introduction to probabilistic tools. I am perfectly comfortable with a selection of topics, as long they are covered rigorously, they are motivated, and their relative importance is stressed. When this happens, the reader is well equipped to read a monography (e.g., Karatzas & Shreve) or a reference book (e.g., Kallenberg) for the in-depth study that subjects like ergodic theorem or brownian motion require.

Not recommended for beginners
This is an interesting book. It presents a rather complicated and difficult subject in a chatty un-math-book like way. I personally like that some of the time. I feel, however, that some things are just explained better when the presentation is more straightforward. The author jumps around a lot. I would really not recommend it for someone new to the subject. Get a more standard text. This book is better for someone who is already aquainted with the subject somewhat. Once you already know about the topics you can come back to this book and learn a lot more from it. But then again that is almost always true. What is the best book on probability? The fourth one you read. ;-D

fantastic but very difficult
i took probability theory with prof pollard using this book. at the time, i found the book to be very difficult and frustrating. i don't know if i would recommand it to the casual reader. however if you're really interested in probability theory and analysis in general, this is definitely the companion for you. indeed, after many a readings, i've found it to become an indispensable friend. it'll defnitely change the way you think about mathematics.

Worst book ever
This is the worst book you will find on measure theory and probability. The author does not provide any good explaination of any topic, and seem to be writing a comic book rather than a math book. Measure theory, which is covered in chapter-2 doesn't explain even the very basics and the actual content is put in an appendix. Furthermore, the author assumes that the reader is not interested in masure theory, so he resorts telling a lot of catch phrases. If you are writing a book, you should not hand wave and write jokes where mathematical arguments are needed.

Another annoying aspect of this book is that the author uses the P symbol for both probability and expectation. I found it very confusing (and contrary to author's claim that it "aids understanding," it only got me more frustrated.)

Probability and measure theory are simple concepts, if explained probability. For some reason, most books try to complicate things. I used to have great respect for Cambride University Press, but I don't know how this book got through their editorial process. ... Read more

Product Description
This text focuses on the utility of probability in solving real-world problems for students in a one-semester calculus-based probability course. Theory is developed to a practical degree and grounded in discussion of its practical uses in solving real-world problems. Numerous applications using up-to-date real data in engineering and the life, social, and physical sciences illustrate and motivate the many ways probability affects our lives. The text's accessible presentation carefully progresses from routine to more difficult problems to suit students of different backgrounds, and carefully explains how and where to apply methods. Students going on to more advanced courses in probability and statistics will gain a solid background in fundamental concepts and theory, while students who must apply probability to their courses engineering and the sciences will develop a working knowledge of the subject and appreciation of its practical power. ... Read more

Customer Reviews (3)

Good explanations, but needs corrections and additions.
3.5/5 stars

First off, this book does a very good job of explaining probability concepts.Examples are explained well enough and are presented in a step by step fashion so it's not particularly hard to follow along.You'll very rarely find huge paragraphs of text, which is great if you're an engineer but bad if you're a math major.I'm docking 1/2 star because this book sometimes doesn't give enough information about a concept and how it's useful/how can it be proved.

The real reason why this book deserves 1 full star lost though is the exercises.The solutions in the back of the book are *terrible*.Not only are the "answers" incorrect, but in some cases the question would have 4 parts, but the answer would only have 3 parts.It's as though no one even bothered to cross check the questions and answers before putting this to print?I'd forgive them if this was 1 or 2 scattered problems, but it really ended up being every other problem with a mistake, in every chapter.It's extremely frustrating to take time trying to find a mistake you made, only to realize it's the book that made the mistake.

So, in summary,this book is a good "intro" book...probably best suited for engineers.If you want a book that goes through long proofs of various formulas, look elsewhere.

Look out!
The book was totally highlighted hot pink inside. It also smelled damp when I took the textbook from the bubble wrap envelope. It smelled like it had mold buildup.

well written
This was part of a school project for me.
The book is well written and easy to follow.It has plenty of good examples and makes for a good self-study as well. ... Read more

Product Description
This introduction to some of the principal models in the theory of disordered systems leads the reader through the basics, to the very edge of contemporary research, with the minimum of technical fuss. Topics covered include random walk, percolation, self-avoiding walk, interacting particle systems, uniform spanning tree, random graphs, as well as the Ising, Potts, and random-cluster models for ferromagnetism, and the Lorentz model for motion in a random medium. Schramm-Löwner evolutions (SLE) arise in various contexts. The choice of topics is strongly motivated by modern applications and focuses on areas that merit further research. Special features include a simple account of Smirnov's proof of Cardy's formula for critical percolation, and a fairly full account of the theory of influence and sharp-thresholds. Accessible to a wide audience of mathematicians and physicists, this book can be used as a graduate course text. Each chapter ends with a range of exercises. ... Read more