Up yer date, buddy
I've been working hard on my thesis this spring break. Broadly speaking, there's two parts to my thesis: an algorithm (which I've had done for months), and a formal proof the algorithm is correct.
Months ago, my advisor saw me struggling with the proof, so basically wrote up the framework for me. At first I thought he'd given me pretty much the whole proof, but it soon dawned on me he'd given me maybe 10% of what I needed. He seemed to have the whole proof in his head, and seemed to want to give me just enough to get started so I could fill the rest in myself. Frustratingly, the way he was doing the proof made little sense to me--some parts were backwards, some parts seemed superfluous, some overwrought, etc. However, feeling I had no other direction, I took his and tried to do something with it. I was never able to.
So, last weekend I sat down and asked myself a question that seems obvious in retrospect--"What makes you believe your algorithms are correct?" I didn't care about the formality of my answer, or if it was "a real proof," I just started writing what came to mind. Suddenly, things started coming together. Patterns started emerging so fast it was difficult to note them all! It started becoming apparent that things in the old proof that seemed superfluous really were, and things that seemed backwards really were. The things I was ending up with were quite different from what I had before, but I actually understood them, and they felt "right" to me.
Currently, I think I have everything I need to sketch the whole thing out. 'Course, I thought that yesterday, too, and then started sketching but stumbled. I think I've figured out the problem, though, and should be able to pick up stride again. My hope is to get the full proof sketch laid out by this weekend, and then get it "inked and colored" (so to speak) in the intervening days before Thursday (there's no meeting this week due to spring break and my advisor's being out of town). I only have a few days after Thursday to get a draft of the thesis to my committee, so I'll be running close to that deadline!
If the worst should happen and either I fall on my face again or my advisor rejects my proof, I don't know what I'll do. I could try submitting my thesis to the committee sans proof, although I'm almost certain they'd reject it. I could keep plugging away until December (end of the fall semester), but, damn; I don't think I could handle it emotionally. This is pretty much my last shot. If this doesn't do it, and my committee doesn't accept a proofless thesis, I'll have to cut my losses and do something else entirely. Maybe a project.
Anyway, here's hoping my proof idea works out and it doesn't come to that!
Months ago, my advisor saw me struggling with the proof, so basically wrote up the framework for me. At first I thought he'd given me pretty much the whole proof, but it soon dawned on me he'd given me maybe 10% of what I needed. He seemed to have the whole proof in his head, and seemed to want to give me just enough to get started so I could fill the rest in myself. Frustratingly, the way he was doing the proof made little sense to me--some parts were backwards, some parts seemed superfluous, some overwrought, etc. However, feeling I had no other direction, I took his and tried to do something with it. I was never able to.
So, last weekend I sat down and asked myself a question that seems obvious in retrospect--"What makes you believe your algorithms are correct?" I didn't care about the formality of my answer, or if it was "a real proof," I just started writing what came to mind. Suddenly, things started coming together. Patterns started emerging so fast it was difficult to note them all! It started becoming apparent that things in the old proof that seemed superfluous really were, and things that seemed backwards really were. The things I was ending up with were quite different from what I had before, but I actually understood them, and they felt "right" to me.
Currently, I think I have everything I need to sketch the whole thing out. 'Course, I thought that yesterday, too, and then started sketching but stumbled. I think I've figured out the problem, though, and should be able to pick up stride again. My hope is to get the full proof sketch laid out by this weekend, and then get it "inked and colored" (so to speak) in the intervening days before Thursday (there's no meeting this week due to spring break and my advisor's being out of town). I only have a few days after Thursday to get a draft of the thesis to my committee, so I'll be running close to that deadline!
If the worst should happen and either I fall on my face again or my advisor rejects my proof, I don't know what I'll do. I could try submitting my thesis to the committee sans proof, although I'm almost certain they'd reject it. I could keep plugging away until December (end of the fall semester), but, damn; I don't think I could handle it emotionally. This is pretty much my last shot. If this doesn't do it, and my committee doesn't accept a proofless thesis, I'll have to cut my losses and do something else entirely. Maybe a project.
Anyway, here's hoping my proof idea works out and it doesn't come to that!