The Life of a Mathematician

I had my oral exam today, and I passed. So I now have a master's degree. It will be nice to be able to put that on job applications. They didn't ask me anything about Numerical Analysis, or Partial Differential Equations. Not too surprising, I guess. Those were pretty much applied classes and I picked theory people to be on the committee. I was glad that they did ask about Representation Theory. That was a fun class (in retrospect) and I enjoyed reviewing the material.

Most of the test focused on the three courses that I took full year sequences in; namely, Real Analysis, Topology, and Modern Algebra. Most of the topology questions were on point-set topology, because Dr. Stowe didn't realize that we did a lot of algebraic topology second semester. As a result, he asked me about fundamental groups but not about homology groups, since he was just asking stuff off the top of his head once he realized that algebraic topology had been covered. The most involved proof they asked me to do was in point-set topology; namely, to explain why any infinite sequence of points in a compact metric space must have a cluster point. It's not a complicated proof, given some preliminary stuff that we had already talked about, but given the fact that I didn't actually look at this proof while studying, it was rather involved to come up with extemporaneously. Then he asked me the difference between a cluster point and a limit point, which was ironic because the whole time we were talking about cluster points, I was trying to think how the two concepts were different, and hadn't figured it out. After thinking about just that for a few moments, I realized that I was reading a condition into the definition of cluster point that wasn't there. Hmm, I just realized that I failed to answer one question that he asked in that regard. I answered a related question, and then he said something like, "That's close enough; let's move on." Huh. I still don't know the answer. What he actually asked was whether something like the Bolzano-Weirstrauss Theorem applies to an arbitrary compact metric space. He asked it in such a way that implied the answer is no. I'll have to think about that one.

When we got to Modern Algebra, Dr. Hill pointed out that all four questions I skipped on the written exam were about Field Theory, and then proceeded to ask all Field Theory questions. That part of the exam didn't go so well. At least she didn't ask about Galois Theory.

After it was all over, the outside committee member, who was from the business department, commented that the only thing she understood the entire time was the term "function of x".