Understanding Probability

At first, I thought I was unhappy with this book. There are several unusual things about it, like its small size, cartoon illustrations, historical anecdotes and sometimes quirky example problems. The early chapters were straightforward and simply written to the point of being boring. Sure enough though, as I worked my way through it, I kept flipping back to those chapters I'd deigned too simple and only skimmed. By the end, my familiarity with linear algebra was coming in handy, and calculus was almost essential. It was not too simple after all; rather, it simply communicated the fundamental principles of probability in a refreshingly fun and clear way. The difficulty ramps up toward the end, but the early chapters lay a solid foundation for the later chapters. Tijms takes his time on important topics like Bayesian and Markovian methods, but only touches on less useful methods, as a good textbook should. The small size ended up being another big plus--this textbook was easier to carry around than most. I would highly recommend this to undergraduates with any interest in probability and statistics, and to graduate students and professionals who aren't statisticians but who do need to use or at least understand probability and statistics in their work.

Great book. Divided into two parts, with the latter part being more formal. The first part is "intuitive" and "light on math" only if you count being asked to derive the birthday problem's approximation formula as "light on math". Aside from misleading promises about the approachability of the first part (for instance, the author claims it could be tackled with only a high school mathematics background.... not likely), somebody who is willing to put in the effort will find an awesome introduction to an extremely counter-intuitive subject.

Gave it as a gift... but looked okay.

I enjoyed the book very much, the author approach probabilities theory from a gambling angle and other personal situations with a clear mathematical foundation.

Clear, in depth and with many examples.

All good as expected

I used this as the textbook in an undergraduate course on probability. I enjoyed it a lot. It has many delightful examples drawn from court cases, gambling, and other real situations. The author's love and enthusiasm for the subject shows on every page. However, my students found the book incomprehensible. When I polled my class of 65 students after 8 weeks, I was shocked to discover that all 65 of them preferred to have no textbook at all than to have this one. The first half is intended to build one's intuition but is crammed with counter-intuitive examples and clever, elegant arguments that novices cannot appreciate. Formalism is delayed until the second half. If I had to do it over again, I would start with the second half, which is logical and self-contained, and finish with some of the cleverness in the first half. But I will never teach beginners from this book again.

This is a peerless introductory textbook. It starts very gently and relying on intuition and only later introduces rigor in a manageable way. There are lots of exercises and examples: this is a book to be followed with pencil and lots of paper. On the back side I wished that some of the examples were more thoroughly explained. In particular there are a handful cases where the author just states an "obvious" probability model and then goes on solving it without further explanations and leaving the students hanging on without a clue on why the model was specified that way. I also think there are more than enough examples using casino and card games. I wished to see more examples related to the natural sciences and engineering, where you usually do not have the advantage of knowing the sample space of the problem! These comments notwithstanding, a great book that is also a joy to read. Perfect for both the classroom and for self-study!

Dr. Tijms two level approach makes this book unique. It is highly recommended for anyone want to understand probability concepts.

This book makes you think deeply, if you are beginner in probability.

Great for fundamentals

You are being introduced to a lot of rather complicated problems where you can apply probability theory, but it is very unclear how and when in book they are linked to the more theoretical part of deriving the results. In general the book fails to give the reader an intuition for probability theory. For example, the link from the binomial distribution to the Poisson distribution is being derived on a few lines. If the book wants you to understand probability these very important relations between distributions should be explained in much more depth, in my view.