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• 12 Suppose $e^A = A$, prove that $A$ is diagonalizable
• 9 Is there always an intermediate field between non-prime field extension?
• 6 A number related to the roots of a quartic polynomial is a root of a cubic polynomial
• 6 Show the projective space $RP^2$ minus a point is homotopy equivalent to the unit circle $S^1$
• 6 If $A, B$ are positive definite and $\|A+B\| = \|A\|+\|B\|$, they have a common eigenvector
• 5 Show an ideal is a finitely generated projective module via a split exact sequence
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