Probability theory

Author: Huang Geren
Publisher:
Publish Date: 2005-08-01
Features: Probability theory is an independent branch of mathematics. In natural phenomena and social phenomena, there are some phenomena that are inherently irregular, but through a large number of experiments and observations, they exhibit a strict, non-accidental regularity as a whole. These phenomena are called "random phenomena." Probability theory is the discipline that studies the regularity of these "random phenomena." One of the origins of probability theory is the problem of gambling. In the 15th and 16th centuries, Italian mathematicians Pacioli, Tartaglia, and Cardano discussed probability problems in their writings, such as "How should the stakes be distributed if a gambling game is prematurely ended?" In the past decade, the main characteristics of the development of probability theory have been its mutual penetration with physics (especially statistical physics) and other branches of mathematics. Probability theory has been integrated into physics, introducing abstract probability into statistical mechanics and material mechanics, and applying dynamical systems theory and ergodicity theory to the study of turbulence. Probability theory has also permeated other branches of mathematics, such as statistics, partial differential equations, functional analysis and Banach space geometry, differential geometry and analysis on manifolds, dynamical systems, and so on. Probability theory has broad applications. With the rapid development of science and technology, it plays an important role in national economy, industrial and agricultural production, modern physics, geophysics, automatic control and communication theory, biology, and medicine, among other fields. The future of probability theory is bright.