Can you prove under pressure?

I found out today whether I could or not!
Yes, I have survived my final exam. Passed. I don't know the exact grade, because as soon as my professor found out that he didn't have to give me an actual grade, he decided not to go to all that trouble. My college at home just pays attention to whether I've passed or not, and today, I passed.

I spent two and a half nervous hours in the study room again today, running through the proofs of the most important theorems because I had been told he'd ask about them, learned the "skeleton proofs", if you will - (just the structure and the rules or theorems you mention as reasons in a proof, not messing around with the actual nitty-gritty steps, because honestly, who has time for double or triple indices inside a linearly independent set during a half hour exam anyway?) until I had at least seven of them memorized. I studied three chapers - the three we covered in the class. Well, okay, two and a half. We didn't do much of the last chapter.  You tell me the name of the theorem, I could tell you how it goes and how to prove it. You tell me one condition about an Endomorphism, I could tell you the six things it was equivalent to. I felt good.

Anyways, I started taking deep breaths about a half hour before the exam started - I had already started to shake. I don't emotionally get that nervous for things like presentations or exams, but as calm as a lake on a day with no breeze as might be inside my head, my outside is the opposite. I can't write my name without the handwriting becoming squiggly and nervous in itself. My breathing is shallow unless I absolutely concentrate on it. And my voice quavers, too. But I stood in front of the professor's office, head bursting with Cayley-Hamilton, Jordansche-Normalform, Hauptraumzerlegung, Annulators and Eigenvektoren, and managed to knock and go inside.

Just as I knew it would, the half hour exam flew by. It was not quite what I expected. First of all, he only asked about the first of the three chapters we covered in the class. ONLY THE FIRST ONE. What the hell did I learn all the rest for??? That being said, there were also no questions about any of the major theorems, whose proofs I had learned forwards and backwards. Instead, there were tiny proof questions, having to come up with an Endomorphism that isn't diagonalizable on the spot, stuff like that. I wasn't the best at that. Those things are, of course, easy if you already had an example for just that in your head. Once I had an example, since my tools of calculation in linear algebra are quite sharp, I could immediately check if it were an example for that or not, but coming up with the example itself was tricky. I had a few lucky guesses. :)

Overall, there was not a single definition or theorem question that I messed up, but not a proof that I didn't stutter about a bit before I managed to get it. However, given how I had prepared myself, I did pretty well. And, as I thought while pacing outside the professor's door while he decided my grade, there's no way I could have failed. I knew too much for that. And I was right. He opened the door thirty seconds later to tell me just that. He told me that some of my answers could've been just a bit better, but overall it was very good. Then he shook my hand and I left.

And now I'm DONE.

Not bad for an academic year abroad.

:)