I would have taken the following courses by graduation (Please note that my university uses the quarter system):
Lower Division:
-Single Variable Calculus (2 quarters)
-Multivariable Calculus (2 quarters)
-Introduction to Abstract Mathematics (1 quarter)
-Introduction to Linear Algebra (1 quarter)
-Elementary Differential Equations (1 quarter)
Upper Division:
-Introduction to Abstract Algebra: Groups, Rings, and Fields (2 quarters)
-Linear Algebra (2 quarters)
-Probability and Stochastic Processes (3 quarters, which means year long sequence)
-Elementary Analysis (2 quarters)
-Complex Analysis (1 quarter)
-Combinatorics (1 quarter)
-Set theory: Axiomatic development; infinite sets; cardinal and ordinal numbers. (1 quarter)
-Mathematical Logic: First order logic through the Completeness Theorem for predicate logic (1 quarter)
Also, what graduate level courses would you recommend taking?
Is this a good foundation for a PhD in Probability Theory?
Re: Is this a good foundation for a PhD in Probability Theory?
Take as many analysis classes as you can. The logic and set theory classes aren't necessary.