Customer Reviews

Probability Theory: A Concise Course (Dover Books on Mathematics)

5 star:		(7)
4 star:		(1)
3 star:		(1)
2 star:		(0)
1 star:		(1)

 

 

It is amazing that a 148 page book can cover so much with such clarity. Even more amazing is the way it covers all basics, going from combinatorial problems to limit theorems in the first half, with a measure of relevant examples and a good selection of problems. It makes an equally excellent choice of "additional topics": Markov chains and processes, information theory, game theory, branching processes, and optimal control.

This book is not for everyone, as it does require a small degree of mathematical sophistication. But it will prove most useful for a very large audience. For serious beginning mathematics and science students it will provide the quickest way to learn the subject. For lecturers devising an introductory probability course it will make an excellent textbook. And, most importantly, for mathematicians and scientists of all kinds it will serve as an indispensable concise reference book.

This is not meant as an introductory text--rather, it's a very handy reference for major concepts needed in probability and stochastic calculus. It was one of the few places where I could find a proof of the DeMoivre-Laplace theorem.

The examples are also very good--they touch upon basic problems in the field without being overly trivial.

There are quite a number of books offering a quick introduction to the fundamentals of probability. And there is a demand, as these tools have many practical uses: Testing data, sampling, insurance topics, quality checking, finance, investment, and finance, to mention only a few. Rozanov's book, of just a little over 100 pages, helps the novice turning practical problems into numbers. What it does well is letting the beginning student acquire a sense of what the rules are, events, combination of events using the mathematical notions of union and intersection; show how they yield computations with probability, distributions; dependence and independence, repeated experiments; and use of conditional probability. It concludes with limit theorems, Markov chains and Markov processes.
There are other nice books that go beyond Rozanov; for example Heathcote's PROBABILITY, also in the Dover series.
Review by Palle Jorgensen, August 2008.

This a really nice book to begin probability with; then it opens up to deeper parts of the theory, especially branching process and Markov chains within its very thin format; it obviously cannot compete with Feller's monumental work which is a natural follow-up to this one but you can't tackle with Feller from scratch either...So, have look at this one and then try Feller (and avoid getting lost in it...)

Nice cute book. I really liked the exposition of chebychev inequality, which is in many other books proved though markov's inequality in a rather inelegant way. Some typos and not too clear exercises. Still highly recommended, specially in view of it's price.

The problem with this book is that there is no way you can understand the later chapters based on the earlier chapters. This is a more like the survey of the important topics in probability and stochastic processes. There are appendices on information theory, game theory, and branching processes. The book includes basic concepts of probability, random variables, and Markov chains. Feller has a better introductory book on probability.

It is really unbelievable that so much about probability theory could be placed in such a small book in such a clear and inspiring manner. I think this book should be in the library of anyone who is interested in the probability theory and mathematical statistics. Have it!!! you will really enjoy reading.

It is a good book for self study, especially for beginners. It gives a quick as well as depth into certain level of introductory probability theory. So I recommend for any one interested on this field....

I love this book but can see why some people don't.
It doesn't hold your hand, and it doesn't spend much time on
intuition. But if you have a sense of what "mathematical
elegance" is, then you will probably love this book. It gets
right to the point, unlike lots of probability theory books,
and is based on standard modern probability theory. Lot of
worked and unworked exercises help with intuition. I did
find a few typos but for the price it is excellent. Another
minor flaw is that definitions and theorems are not marked as
such, so occasionally you have to read carefully to see which
it is. Not recommended for those with little math background,
or who want a book that will "explain probability theory".

This book is translated from Russian and it might be more understandable if they left it in the original language. This book is the required text for a university probability class I am taking. I can not imagine any text being worse. Almost everyone in the class has bought the Schuam's outline title Probabilty by Lipschutz and Lipson. We are using it to try to decode this text. The exercises in the book are vague and often completely void of even the slightest hint of how to solve them. What is much worse is that there are many very basic and important facts completely left out (A good example is the conditional probability multiplication theorem for dependent events which is only noted in an exercise). I also should note with some reserve, for I know all mathematics texts are problematic in this area, that the notation used is often very difficult to follow (Example: Sumation notation without a simple case explanation beforehand). There is just enough left out of this book to get you confused and frustrated. The only good thing I can say about this book is that is it not very expensive but I strongly believe you can find a better text even at this price.