Introduction To Probability Theory: A First Course On The Measure-theoretic Approach

This book provides a rigorous introduction to probability theory using measure theory and functional analysis, geared toward undergraduate students in mathematics and physics. It covers random events, random variables, probability measures, expectation values, distributions, characteristic functions, independence, convergence, and limit theorems. The second part explores more advanced methods like conditional expectations, martingales, and Markov chains.

Format: Hardback
Length: 292 pages
Publication date: 21 April 2022
Publisher: World Scientific Publishing Co Pte Ltd

This comprehensive book offers a thorough introduction to probability theory, employing modern and rigorous techniques from measure theory and functional analysis. Designed primarily for undergraduate students studying mathematics and physics, it also serves as a valuable resource for students from other disciplines such as economics, finance, and engineering. Whether used as a companion to a related lecture or as a standalone learning tool, this book is an invaluable resource for anyone seeking to gain a deeper understanding of probability theory.

The first part of the book provides a foundational introduction to probability theory. It begins by exploring the concepts of random events and random variables, probability measures, expectation values, distributions, characteristic functions, independence of random variables, and various types of convergence and limit theorems. These topics are presented in two chapters, with the first chapter focusing on combinatorial aspects of probability theory and the second chapter introducing the modern probability language.

The second part of the book delves into more advanced methods, such as conditional expectations, martingales, and Markov chains. These concepts build upon the foundations established in the first part and are designed to provide students with a deeper understanding of probability theory. By the end of this section, readers will have acquired the tools necessary to apply probability theory to a wide range of real-world problems.

Overall, this book is an excellent resource for students seeking to excel in probability theory and related fields. Its comprehensive coverage, rigorous approach, and clear explanations make it accessible to a wide range of learners, and its applications in mathematics, physics, and other disciplines make it an invaluable tool for future professionals.

ISBN-13: 9789811246746