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