Illinois Tech Interview Questions
It took about 46 minutes.

[Functional Analysis]
What is a Banach space?
If ∫f_ndx converges to zero, then can we say that f_n converges to zero?
What is the dominated convergence theorem?

[Probability Theory]
Describe convergence of random variables.
What is convergence in distribution?
Does convergence in distribution imply convergence in probability?
Does almost sure convergence imply convergence in probability?

[Linear Algebra]
Define the rank of a matrix.
Define the linear independence of vectors.
Describe the Gaussian elimination.

[ODE Theory]
Solve y'=5y, y(0)=1.
Solve y'=5y+x, y(0)=1.

[Complex Analysis]
Evaluate the integral of e^z on the unit circle.

[Discrehe Mathematics]
What is the maximal number of edges in the graph of n vertices?

[Group Theory]
{0,1,2,3,4} forms a group with addition x+y := x+y(mod 5).
What is the inverse of 2?

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After those questions, I got time to ask questions to the professor.