Title of the course: A rigorous introduction to further probability theory
Instructor: Arif Mardin
Institution: –
Dates: 31 August – 4 September 2020
Prerequisites: In order to follow this course, the contents of “A rigorous introduction to basic probability theory” are necessary and sufficient. Students who do not possess such a background are not advised to take this course.
Level: First or second year undergraduate students of mathematics.
Abstract: This course may be regarded as a natural continuation of the preceding course, entitled ”A rigorous introduction to basic probability theory”. Only discrete probabilities will be considered here. We shall start by studying the moments of random variables, some basic inequalities such as Bienayme-Tchebycheff and Markov’s. We shall then deal with the weak and strong laws of large numbers, and the central limit theorem. In the rest of the course we shall study the simple random walk on one, two and three dimensional regular lattices, and prove the celebrated theorem of Polya.
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