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.