Can Probability I be used as a substitute for Classical Probability as an ACO core course?
It can, but Probability I is a much harder course. It requires Real Analysis I as a prerequisite. Those who have not had Real Analysis I or an equivalent would be well advised to stick to Advanced Classical Probability. Furthermore, Probability I does not cover condititional expectations or martingales, needed for the ACO exam. You would need to study those topics on your own. How is the new course “Theory of linear inequalities” related to Optimization I? This course replaced Optimization I as a required course for ACO students. Students who entered in Summer 2007 or earlier may use Optimization I; all others must take Theory of Linear Inequalities. Who must take Advanced Combinatorial Optimization, and who can take Optimization II? What will the corresponding problem on the comprehensive examination be like? Students who enter in Summer 2008 or later must take Advanced Combinatorial Optimization. All other students may take either course. For the Fall 2008 and Spring 2009 sittings of