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APPLIED PROBABILITY

	Overview
	Statistics, Summaries, events, probability, random variables, expectation, Markov chains; Limit theorems including modes of convergence, law of large numbers, central limit theorem; representative examples of modern applications from the sciences and engineering, including branching processes and information theory.

	Learning Outcomes
	On successful completion of the module, students should be able to: describe and discuss the foundations and key results of modern probability and information theory in an integrated format describe contemporary applications of probability pursue independent research in these topics

Assessment

	Autumn Supplementals/Resits
	Are supplemental/resit registrations permitted? No

	Pre-Requisites
	Registered PhD student; Advanced Calculus; Basic Linear Algebra; some knowledge of real analysis and basic probability

	Co-Requisites
	None

	Additional Reading
	P. Billingsley, “Probability and Measure'', third edition. Wiley (1995). [Wiley series in probability and mathematical statistics] J. S. Rosenthal, “A first look at rigorous probability theory'', second edition. World Scientific (2006). Y. Suhov and M. Kelbert, “Probability and Statistics by Example'', Volume 1, Basic Probability and Statistics Cambridge University Press (2005) T. M. Cover and J. A. Thomas, “Elements of Information Theory'', second edition. Wiley (2006).

Additional Reading

P. Billingsley,

“Probability and Measure'', third edition. Wiley (1995).

[Wiley series in probability and mathematical statistics]

J. S. Rosenthal,

“A first look at rigorous probability theory'',

second edition. World Scientific (2006).

Y. Suhov and M. Kelbert,

“Probability and Statistics by Example'', Volume 1, Basic Probability and Statistics Cambridge University Press (2005)

T. M. Cover and J. A. Thomas,

“Elements of Information Theory'',

second edition. Wiley (2006).

	Timetable
	This timetable is not currently available, please contact the Hamilton Institute Department.