Elementary Probability for Applications is an undergraduate introductory text covering the basic concepts of combinatorial and conditional probability, Markov chains, continuous distributions, and limit theorems. The book is intended for undergraduate students encountering probability for the first time; as such, it assumes almost no prerequisites beyond some basic calculus.
The overall philosophy of the book is to teach probability via examples. I completely agree with this approach, especially for the level of undergraduate education that this book is written for. Formal mathematics is really kept at a minimum. There are no theorems or official definitions; instead, the author defines the concepts as he goes along, always keeping in mind, however, to follow (or precede) each concept with an appropriate example or a teaser to promote active thinking. The text contains numerous examples which are all presented in great detail, to the extent of writing out the thinking which should occur in the student’s head. The majority of the examples are accompanied with either a table or a figure that further highlights the concept or is simply there for further clarification. The author presents well known examples, such as the birthday problem, numerous versions of card games and others, which should easily capture the reader’s interest.
The chapter on Markov chains is really a gem in itself. It should provide students with an ace in the sleeve when going further in their studies in mathematics. Two chapters, on Markov chains and continuous distribution, follow the same style of writing and discussion. This really makes a difference when it comes to topics like these, as full and correct understanding is vital for more advanced study.
Exercises are provided at the end of each chapter and are segmented like the chapter. The exercises do not deviate from the text, i.e., if one read and understood the chapter one should have no problems successfully solving the exercises.
The book is an easy read for someone who would like to catch up with the forgotten probability class and a positive challenge to a newcomer but never a troublesome endeavor. I would strongly recommend this book to any undergraduate student planning to take or currently taking a probability class. This is one of the best elementary book I have come across.
Ita Cirovic Donev holds a Masters degree in statistics from Rice University. Her main research areas are in mathematical finance; more precisely, statistical methods for credit and market risk. Apart from the academic work she does statistical consulting work for financial institutions in the area of risk management.
1. Basic concepts; 2. Combinatorial probability; 3. Conditional probability; 4. Markov chains; 5. Continuous distributions; 6. Limit theorems; 7. Option pricing.