MATH 312-01, Mathematical Statistics, Spring 2010

Abstract

The seeds of statistics—which is often considered a mathematical science quite distinct from mathematics itself—were sown in the 17th century, with the development of probability theory by Blaise Pascal and Pierre de Fermat. Probability theory itself arose due to interest in games of chance. In contrast to probability theorists (who propose probability models and then study those models with somewhat less regard for the random realizations generated by those models), statisticians are interested in the random realizations themselves (called data), and what those random realizations suggest about the parameters that govern the (perhaps unknown) underlying probability models. A critical development in the history of statistics was the method of least squares, which was probably first described by Carl Friedrich Gauss in 1794. Early applications of statistical thinking revolved around the needs of states to base public policy on demographic, economic, and public health data. The scope of the discipline of statistics broadened in the early 19th century to include the collection and analysis of data in general. Today, statistics is widely employed in government, business, and the natural and social sciences. Computers are transforming the field at a breathtaking pace. Statistics is widely considered an exciting, dynamic, and intrinsically interdisciplinary science. The work of statisticians powers search engines like Google, has proven critical to the exploration of the human genome, and is used by hedge fund managers to detect arbitrage opportunities (risk-free trading strategies that yield profit with positive probability) that are profitable only on average (called statistical arbitrage). The New York Times recently declared that statisticians will enjoy one of the highest-paying, highly-coveted careers over the next decade. I hope you’ll enjoy learning a little bit about statistics this semester with me!