Title of the course: A rigorous introduction to basic probability theory
Instructor: Arif Mardin
Institution: –
Dates: 24-28 August 2020
Prerequisites: Familiarity with sets, elementary operations on them, as well as some basic properties of combinatorics are what is needed to follow this course.
Level: Undergraduate
Abstract: The aim of this course is to present the calculus of discrete probability through the basic axioms of probability theory as formulated by A.N.Kolmogorov. Fundamental notions such as probability space, sigma-algebra of events, random variables, independence, Borel-Cantelli lemmas, different forms of convergence of random variables, weak and strong laws of large numbers, the central limit theorem will be studied.
Textbook or/and course webpage:
(i) Uluğ Çapar: “Olasılık Teorisinin Gelişimi II-VI”, Matematik Dünyası, sayı 101-105; 2014-2015;
(ii) J. R. Rosenthal: “A First Look at Rigorous Probability Theory”, 2nd edn., World-Scientific, 2006;
(iii) A.N.Shiryaev: “Probability”, 2nd edn., Springer Verlag, 1996; Chapter I, pages: 1-130.
Language: EN