Done
My last final--Combinatorics and Graph Theory, is done.
I was pretty confident going into it, and am also fairly confident having come out the other end. The only anxiety I had about it is that exams in subjects like that do tend to be very difficult to predict. I think it was also a little harder than I expected, though again it's hard to say.
Still, there were really only two problems that I got hung up on at for at all long. One involved finding a recurrence relation for something. Through mere observation, I found one that worked fairly quickly. And it didn't take me long to understand conceptually why it worked either. I just had a really hard time explaining my reasoning for some reason. So I fear that I might lose a few points on that one due inexactness in my explanation.
The other problem was a counting problem that seemed hard for a while until I had a "duh" moment and realized that it could be broken into two fairly obvious independent subproblems whose results I could just multiply together.
I also got hung up far too long on the very first problem, until I realized that it could be solved with a simple generating function (aka "getting out my canoe paddle and stirring").
Other than that, I'm confident that I got everything right, and if I lose any other points it'll be just a few from careless errors like writing a 2 instead of a 3 and crap like that.
I was pretty confident going into it, and am also fairly confident having come out the other end. The only anxiety I had about it is that exams in subjects like that do tend to be very difficult to predict. I think it was also a little harder than I expected, though again it's hard to say.
Still, there were really only two problems that I got hung up on at for at all long. One involved finding a recurrence relation for something. Through mere observation, I found one that worked fairly quickly. And it didn't take me long to understand conceptually why it worked either. I just had a really hard time explaining my reasoning for some reason. So I fear that I might lose a few points on that one due inexactness in my explanation.
The other problem was a counting problem that seemed hard for a while until I had a "duh" moment and realized that it could be broken into two fairly obvious independent subproblems whose results I could just multiply together.
I also got hung up far too long on the very first problem, until I realized that it could be solved with a simple generating function (aka "getting out my canoe paddle and stirring").
Other than that, I'm confident that I got everything right, and if I lose any other points it'll be just a few from careless errors like writing a 2 instead of a 3 and crap like that.