I.Contents:
1.Law of large numbers,
2.Central limit theorem,
3.Discrete time martingales.
II.Course prerequisite:
1. Measure theory, (REAL ANALYSIS, Course number: 221 U2870 )
2. Undergraduate probability theory. (INTRODUCTION TO PROBABILITY THEORY, Course number: 201 31700)
III.Reference material ( textbook(s) ):
1. Probability Theory. By S. R. S. Varadhan. Courant Lecture Notes in Math. 7. CIMS, AMS, 2001.
2. Probability: Theory and Examples. By R. Durrett. Brooks/Cole—Thomson Learning, 3rd edition, 2005.
IV.Grading scheme:
1. Recitation (Wednesday 10:20—11:10) and homework: 60%,
2. Final exam: 40%.
V.Others:
Wednesday 10:20—12:10 and Friday 11:20—12:10,
Room 103, Old Math. Building.