This is the first half of a year-long first graduate course in probability theory. Topics will include independence, laws of large numbers, weak convergence and the central limit theorem, conditional expectation and martingales.
Basic knowledge of measure theory (such as from MATH 6110 or 6210) will be assumed, but we will review the relevant material (from a probabilist's point of view) at the beginning of the course. Students who are unsure about this are welcome to consult with me. An undergraduate course in probability might be useful but is not strictly necessary.
The textbook is R. Durrett, Probability: Theory and Examples, 4th edition. The 4th edition is to be published in coming months, and in the meantime a PDF is available. Other suggested texts will be placed on reserve.