This is a tentative list of topics to be discussed in Maths 635. Adjustments will be made to accommodate the needs of the students:

• Introduction to basic probabilistic ideas
• Conditional probability and independence
• Bernoulli trials and the binomial distribution
• Normal approximation and the central limit theorem
• Weak and strong laws of large numbers
• The Poisson distribution and its relation to the Binomial distribution
• Random variables and their distributions
• Expected values, variance and standard deviation
• Discrete and continuous distributions
• Exponential distributions
• Poisson processes
• Random walks