Probability theory is the part of mathematics that studies random situations. Probability theory usually studies random events, random variables, stochastic processes, and non-deterministic events (events that do not follow a simple pattern).
Tossing a coin, winning the lottery, or rolling a die are random events. However, random events have certain patterns, which can be studied and predicted, using probability theory.
Scientists can use probability theory to obtain information about things that would be too complex to deal with, like statistical mechanics. Also, scientists discovered (in the 20th century) that atoms, and everything that we know, obeys something called quantum mechanics, which uses lots of probability theory.
The theory of probability was created by Gerolamo Cardano, a medical doctor and gambler who tried to calculate his luck. Years later, Pierre de Fermat and Blaise Pascal helped develop Cardano's theory.
Today, probability theory is used in statistics, which is useful to all kinds of areas: like medicine, economy, Science, Mathematics...
- Pierre Simon de Laplace (1812). Analytical Theory of Probability.
- The first major treatise blending calculus with probability theory, originally in French: Théorie Analytique des Probabilités.
- Andrei Nikolajevich Kolmogorov (1950). Foundations of the Theory of Probability.
- The modern measure-theoretic foundation of probability theory; the original German version (Grundbegriffe der Wahrscheinlichkeitrechnung) appeared in 1933.
- Patrick Billingsley (1979). Probability and Measure. New York, Toronto, London: John Wiley and Sons.
- Henk Tijms (2004). Understanding Probability. Cambridge Univ. Press.
- A lively introduction to probability theory for the beginner.
- Gut, Allan (2005). Probability: A Graduate Course. Springer-Verlag. ISBN 0-387-22833-0.
- ↑ Probability theory, Encyclopaedia Britannica
- ↑ 2.0 2.1 2.2 2.3 Chow, Y. S., & Teicher, H. (2003). Probability theory: independence, interchangeability, martingales. Springer Science & Business Media.
- ↑ 3.0 3.1 3.2 3.3 Feller, W. (2008). An introduction to probability theory and its applications (Vol. 2). John Wiley & Sons.
- ↑ 4.0 4.1 4.2 4.3 Durrett, R. (2019). Probability: theory and examples (Vol. 49). Cambridge University Press.
- ↑ 5.0 5.1 5.2 5.3 Jaynes, E. T. (2003). Probability theory: The logic of science. Cambridge University Press.
- ↑ 6.0 6.1 6.2 6.3 Chung, K. L., & Zhong, K. (2001). A course in probability theory. Academic Press.
- ↑ Tolman, R. C. (1979). The principles of statistical mechanics. Courier Corporation.
- ↑ Ruelle, D. (1999). Statistical mechanics: Rigorous results. World Scientific.
- ↑ Thompson, C. J. (2015). Mathematical statistical mechanics. Princeton University Press.
- ↑ Flügge, S. (2012). Practical quantum mechanics. Springer Science & Business Media.
- ↑ Griffiths, D. J., & Schroeter, D. F. (2018). Introduction to quantum mechanics. Cambridge University Press.
- ↑ Baym, G. (2018). Lectures on quantum mechanics. CRC Press.