Customer Reviews

Probability Through Problems

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Doing problems is the best way to study mathematics. The question to most authors is that: How to select problems that are nice to the students. This book did quite well. As I see, the authors gave the exact right pace to offer the students an exicting course, and give the students a thorough understanding.

If you want to master this subject in a month, or even in a shorter time, this book may be the right choice.

This book uses a format I've never seen in a math textbook before: Each chapter consists of a couple of paragraphs to define a new concept, followed by several dozen problems to explore the concept in depth. The problems are followed by hints, and then solutions. This fresh approach teaches otherwise dry subject matter in an unusually lively (and memorable) way.

Note that this book teaches probability in a mathematically rigorous way, possibly too rigorous for a first course in probability. You'll have to work your way through several chapters of abstruse concepts (e.g. sigma fields) before you see any of the more fun, applied probability problems. A basic understanding of set theory and analysis are prerequisite.

The chapters are:

1. Modeling Random Experiments
2. Classical Probability Spaces
3. Fields
4. Finitely Additive Probability
5. Sigma Fields
6. Countably Additive Probability
7. Conditional Probability and Independence
8. Random Variables and Their Distributions
9. Expectations and Variance
10. Conditional Expectation
11. Characteristic Functions
12. Limit Theorems