Probability With Martingales, D. Williams

This volume presents extensive research devoted to a broad spectrum of mathematics with emphasis on interdisciplinary aspects of Optimization and Probability. Chapters also emphasize applications to Data Science, a timely field with a high impact in our modern society.

This textbook offers an approachable introduction to measure-theoretic probability, illustrating core concepts with examples from statistics and engineering. The author presents complex concepts in a succinct manner, making otherwise intimidating material approachable to undergraduates who are not necessarily studying mathematics as their major. Throughout, readers will learn how probability serves as the language in a variety of exciting fields. Specific applications covered include the coupon collector’s problem, Monte Carlo integration in finance, data compression in information theory, and more.

The present book contains 11 articles accepted and published in the second edition of the Special Issue “Analytical Methods and Convergence in Probability with Applications” of the MDPI journal Mathematics, which cover a wide range of topics from the theory of distributions and analytical methods in probability to limit theorems, convergence rate estimates, and statistical estimation.