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Probability Through Problems - Problem Books in Mathematics | Advanced Math Study Guide for Students & Educators | Perfect for Classroom Learning & Self-Study
Probability Through Problems - Problem Books in Mathematics | Advanced Math Study Guide for Students & Educators | Perfect for Classroom Learning & Self-Study

Probability Through Problems - Problem Books in Mathematics | Advanced Math Study Guide for Students & Educators | Perfect for Classroom Learning & Self-Study

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Product Description

This book of problems has been designed to accompany an undergraduate course in probability. It will also be useful for students with interest in probability who wish to study on their own. The only prerequisite is basic algebra and calculus. This includes some elementary experience in set theory, sequences and series, functions of one variable, and their derivatives. Familiarity with integrals would be a bonus. A brief survey of terminology and notation in set theory and calculus is provided. Each chapter is divided into three parts: Problems, Hints, and Solutions. To make the book reasonably self-contained, all problem sections include expository material. Definitions and statements of important results are interlaced with relevant problems. The latter have been selected to motivate abstract definitions by concrete examples and to lead in manageable steps toward general results, as well as to provide exercises based on the issues and techniques introduced in each chapter. The hint sections are an important part of the book, designed to guide the reader in an informal manner. This makes Probability Through Prob­ lems particularly useful for self-study and can also be of help in tutorials. Those who seek mathematical precision will find it in the worked solutions provided. However, students are strongly advised to consult the hints prior to looking at the solutions, and, first of all, to try to solve each problem on their own.

Customer Reviews

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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 Experiments2. Classical Probability Spaces3. Fields4. Finitely Additive Probability5. Sigma Fields6. Countably Additive Probability7. Conditional Probability and Independence8. Random Variables and Their Distributions9. Expectations and Variance10. Conditional Expectation11. Characteristic Functions12. Limit Theorems