My thesis is centered on looking at the history of a conjecture which could probably be considered a mathematical philosophy question. It took nearly 30 years for it to be answered. At the heart of the question - is the natural ordering system we have always give us the best result? By natural ordering, I mean the basic way of counting - how we learn to organize and number - 1 cookie, 2 cookies, and so on. I guess when I say "result" I am being a bit vague - I don't want to get into the nitty gritty here - I think I might lose everyone if I actually explained it. Probably better think of it - suppose you have a very long list of grocery items and are looking to see if "carrot" is on the list. What is the best way to go searching for it? Start at the first item on the list and check them off? Maybe start at the bottom of the list and work your way up? What about start in the middle, consider the first half and check the middle of that, and so on and so on? Any one of these methods could be considered an ordering system - which item comes first, second, third in each method?
What is interesting is that in some situations (which is a really good thing for scientists or well certain scientists) that we have found orderings that give great results (under certain conditions). One group of functions has great behavior if we don't count by 1's but by powers of 2. In the case of functions that relate to this conjecture, we find that the functions as a group don't behave as nicely as we want them to do, but we can do no better than this "ugly" nature if we try to change the ordering.
So you now you are asking me - well why did you name this entry "Crazy proof"? The group of mathematicians who produced the proof submitted an article - the article is approximately 6 pages. The proof of what is the major find, from which you can prove the conjecture in less than 3 lines, is about 2.5 pages long (which by many people's standards is unbelievably short). I've spent almost 10 hours with my advisor working through the proof, plus another 10 or 15 trying to convince myself that things we spoke about were true and figuring out ways to spell all this out. So my full complete version of the proof is the total length of original article. Talk about taking some mathematical freedom when you get to submit journal articles. Yet I think the proof is unsatisfying - there doesn't seem to be any explanation of how the authors came up with their idea - it does not allow any wiggle room for using the ideas in similar contexts. It's quite possible the methods will lead to dead-ends if I try to use them in a new situation. Oh well.
In the meantime, actual writing - 25 pages (it may seem a bit low compared to before - I had to rewrite several pages and combined several proofs), total page count - 29 pages. I really only have about 2 sections left to work one - one that is more a historical account, the other my work. Oh yes - the introduction as well. It's pitiful really. I wish I had some ideas on how to rework that.
Lots of other craziness going on - the wedding detail stuff seems to be ramping up - at least a huge chunk of this work is out of the way. Catch you all later.
End of Week 6
I am exhausted. I think that covers everything. My brain hurts, my body aches, even my hair hurts. Maybe sometime in the future I can manage to catch a good night of sleep. By good I mean refreshing - where I wake up and say, hello day - let's do something!
Seeing as I should be getting to bed - make up class Saturday morning. Not so fun - but I rather it that time then at 5 at night during dinner. Anyway - thesis update: 23 pages of written math, total thesis page count 27.
Sorry, I don't even have the energy to finish this entry. I'll just leave it like this.
Seeing as I should be getting to bed - make up class Saturday morning. Not so fun - but I rather it that time then at 5 at night during dinner. Anyway - thesis update: 23 pages of written math, total thesis page count 27.
Sorry, I don't even have the energy to finish this entry. I'll just leave it like this.
Start of Week 5
I was really good about posting an entry there at the beginning of the semester. But now I have started to get all muddled with things. To be honest - sometimes I am amazed at the amount of random thoughts I have floating around in that gray matter. It is a wonder that I can even manage to string more than three words together while writing my thesis.
I will admit that I am getting bogged down by the details - for lots of things. As I have been told by many helpful camps - there really is not anything I can do about some situations. I can not get a hold of the forces of nature and bend space and time to get me the answers I need when I want them, which incidentally is right after I ask for them. Needless to say, I have been very cranky over the most annoyingly tiny things. I feel bad because I know that Andy has been taking the brunt of my "cranky attacks". Now let me clarify this a bit - I am not cranky about colors of flowers, table linens, silverware, or lighting. The actual practical aspects of the getting married - transportation, moving self and stuff to Texas, getting all the correct forms processed with the right agencies - all doing this in a very short time. Stupid math brain is having a battle of logistics - but there is not one single thing I can do about it. At least not now. Silly me, I can't have a problem like this and not be able to come up with some sort of solution that makes me happy. But I must say things are coming around rather well - wedding wise. So outside of stressing about silly things I have no control over - it is going great.
In the thesis arena - I have written about 12 solid pages of mathematics (even some full-fledged paragraphs too!). Current total pdf number of pages: 19. I am somewhat worried though. I spent the past 2 weeks or so on my own. Little to no adviser guidance. I feel like when we finally get to start meeting again - he will have ripped my 12 pages to half of that, or what is worse, try to make me expand on the little bit of information I have already written. But I guess I have to do it though - if it sounds reasonable. Flashback to when I wrote my honors math research at Dickinson. This work was 29 pages long - but a lion's share of the space was filled with happy triangle pictures. I guess I am on a good track. At Dickinson, it was like pulling teeth to get me to sit down and write that paper. I suppose it didn't help that I had a physics research project and paper to work on at the same time. I intend on spending the rest of February and most of March filling in the 3 chapters I have yet to even touch - and make little adjustments to the ones that I have started.
Teaching: oddly enough, going really well. I am surprised how well the students seem to be taking in the information that I am giving them. The class isn't anything near rigorous math - but every conceptual question I ask (that I would get no reply or blank stares from students when I ta-ed for the 141-142 calculus classes) the students seem to be able to answer without much prodding. More importantly, they respond with the correct ideas. So it is probably the best 50 minute class I have had. I would have more stories - except it is at 8 am and for some reason I breeze right through it and then have difficulty remembering the lecture afterwards.
Other news, Andy is coming for a the long weekend. Do I have off? No - no President's day for me. But it is nice that he gets off.
I think I deserve some cookies and milk. Catch you later.
I will admit that I am getting bogged down by the details - for lots of things. As I have been told by many helpful camps - there really is not anything I can do about some situations. I can not get a hold of the forces of nature and bend space and time to get me the answers I need when I want them, which incidentally is right after I ask for them. Needless to say, I have been very cranky over the most annoyingly tiny things. I feel bad because I know that Andy has been taking the brunt of my "cranky attacks". Now let me clarify this a bit - I am not cranky about colors of flowers, table linens, silverware, or lighting. The actual practical aspects of the getting married - transportation, moving self and stuff to Texas, getting all the correct forms processed with the right agencies - all doing this in a very short time. Stupid math brain is having a battle of logistics - but there is not one single thing I can do about it. At least not now. Silly me, I can't have a problem like this and not be able to come up with some sort of solution that makes me happy. But I must say things are coming around rather well - wedding wise. So outside of stressing about silly things I have no control over - it is going great.
In the thesis arena - I have written about 12 solid pages of mathematics (even some full-fledged paragraphs too!). Current total pdf number of pages: 19. I am somewhat worried though. I spent the past 2 weeks or so on my own. Little to no adviser guidance. I feel like when we finally get to start meeting again - he will have ripped my 12 pages to half of that, or what is worse, try to make me expand on the little bit of information I have already written. But I guess I have to do it though - if it sounds reasonable. Flashback to when I wrote my honors math research at Dickinson. This work was 29 pages long - but a lion's share of the space was filled with happy triangle pictures. I guess I am on a good track. At Dickinson, it was like pulling teeth to get me to sit down and write that paper. I suppose it didn't help that I had a physics research project and paper to work on at the same time. I intend on spending the rest of February and most of March filling in the 3 chapters I have yet to even touch - and make little adjustments to the ones that I have started.
Teaching: oddly enough, going really well. I am surprised how well the students seem to be taking in the information that I am giving them. The class isn't anything near rigorous math - but every conceptual question I ask (that I would get no reply or blank stares from students when I ta-ed for the 141-142 calculus classes) the students seem to be able to answer without much prodding. More importantly, they respond with the correct ideas. So it is probably the best 50 minute class I have had. I would have more stories - except it is at 8 am and for some reason I breeze right through it and then have difficulty remembering the lecture afterwards.
Other news, Andy is coming for a the long weekend. Do I have off? No - no President's day for me. But it is nice that he gets off.
I think I deserve some cookies and milk. Catch you later.
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