Currently Reading The Picture of Dorian Gray (Modern Library Paperbacks) By Oscar Wilde see related

yo

The other day I was taking a shower and I squirted out some of my facial soap (the foaming kind, so I don't have to waste my time sudsing) and immediately put it in my hair.  What the hell? I guess it's because I usually wash my hair first and then my face, and that day I happened to reach for the facial soap first...

     I have good news since I last posted, and it would be utterly depressing if I didn't since it's been so long.  But before you can appreciate it, I have to explain the inner workings of getting a PhD at uky. There are various hoops, as there should be, the first of which is, of course, a credit hour requirement, which is really one of the easier requirements (since who doesn't like taking courses?).  Typically, grad students take 3 courses a semester, but I took 4 my first semester, as seen in previous posts.  This puts me 3 credit hours ahead of the game, and because of this, by the end of this coming fall semester I'll be jumping through my second hoop.  Which is getting my Master's in Math. What's required to get my Master's other that course requirements, is that I read and present some current math research done by somebody else. It's about an hour and a half long ordeal with my advisor, the grad. dept. supervisor, and some prof's that I will choose. 

     After I get my Master's, I have some more requirements before I can "qualify" for my PhD. The first is what the good news is about.  There are six prelim. sequences: Real(or Complex) Analysis; Numerical Analysis; Algebra; Discreet Mathematics; Partial Differential Equations(PDEs for short); and Topology.  Of those I have to choose 3 sequences by taking the 2 courses(although the real/complex analysis sequence is 3 courses: intro, reals, and complex) for each sequence and passing a prelim. exam(~3 hours of mathematical joy  ).  They offer the prelim. exams in Jan. and May/June.  Supposing one passes three of the exams, there are fun things in store. 

    It's my impression that the semester after you pass your last prelim exam, you start or continue(depending on your situation) original research in an area of your choice(with an advisor of your choice).  Meanwhile you have to take a foreign language course, with the language being either of "classical" interest or having been shown by you that there are related mathematical journals and active research being published in that language.  To me this seems to be done mostly for the sake of posterity, but I maybe wrong. Math certainly is an international endeavor, but from what I understand most people speak English and translations don't delay the process crucially. I could be wrong.  I'm not complaining, really, it might be fun to try and remember more of my German(does that capital G make it mean that I'm wanting remember a person? I sucks at grammar) that I forgot.  So, anyway, after that semester of prepatory research, there's a qualifying exam which is a 40 minute talk given to probably the same people as the master's talk.  You present what knowledge you have, give some preliminary results, and explain in a general way, as well as a concrete way, where you think this research will lead. If you pass, and this exam should not be the stressful one, you are "qualified".  This means you may continue with your research and prepare your dissertation. The dissertation is the last hoop, which must be published and presented to the department. The preparation of the dissertation can take up to four years, but it is usually done in two or three. It's not impossible to do it in one year, but you'd pretty much have to be crazy or you will be after that year.

    Are you still listening? On to the good news!   
    The first year I was here, I took 2 of the real/complex analysis courses and the algebra courses. Which meant that I took my first two prelims this past May/June. That gives about a month of study time after the spring semester is over. I had a strong analysis background from undergrad, so I mostly studied algebra.  As time passed I grew more and more anxious about the whole ordeal, and started having those shitty anxiety dreams where you are driving from delaware to kentucky and won't be able to get to the exam until 1 hour after it starts, but then you actually get there and 2 hours have already passed since it started.  Yeah, you could say I was freaking out a little bit.  I used to think that I didn't let stress get to me, that I was above it or something.  How delusional of me.  Maybe at CMU I was so stressed out, I didn't realize that there was anything else .  In any case, to make a long story short(too late), I took those to prelims and passed them both!  Which makes me two thirds of the way through the second hoop.

 I'll be starting the PDEs course sequence this fall. In fact, here's my fall semester 06:

• PDEs: It's funny because there are so few PDEs with explicit solutions, most of the course will be grinding into my silly head that math is hard, and even the stuff actually known is hard.  Hopefully, I'll survive.
• Real Analysis II: This class will be fun so long as we finish up the material left off of the end of Real Analysis I due to time.  We'll cover some more measure theory (integrals for grown-ups) and functional analysis(something I have no idea about).
• Mathematical Methods in Theoretical Physics: It's what I've been accidentally calling Theoretical Methods in Physics, which sounds like it should be another course entirely, offered in some Philosophy dept. It's pretty self-explanatory. The name reminds me of two courses I took my first semester at CMU: Matter and Interactions I and Interpretation and Argument, in that its exactness without brevity(like this post, except not exact).

   I guess I talked a lot about school today. Sorry 'bout that. I'll have to think of more interesting stuff next time. Later!

Currently Listening Lost and Gone Forever By Guster see related

   So I've almost finished my first week of graduate classes at UKY, and here's what I've learned: the real polynomial P(y)=||z+yw||², where z,w are complex vectors of with n-components, and ||  || is the standard Euclidean norm, isn't a complex polynomial if you let y be a complex variable...hm, who knew?...I didn't that's for certain, until the prof did the calculation on the board, and then I got it. It's good, because otherwise if it was still a complex polynomial, then the Schwarz Inequality would just be in the Schwarz Equality, which is just an unbelievable situation. I learned other stuff too....Like, if you have a Fourier Sine (Cosine) series for a function f, you can replace it with a Fourier exp(i m pi x) Series just by multiplication of the terms by -i/2 or i/2, depending on the sign of m.  That little tid bit came up in my Numerical Method for Differential Equations(Read: Partial Differential Equations).  Of course, it was an obvious fact once I got back to my office and scribbled some nonsense on some paper. 

Warning: the following is a long digression into my silly math:
   The steepest learning curve has definitely been that for my Numerical Methods knowledge, and I still have a long way to go. I will probably have to go to the prof's office to get acquainted with MatLab enough to make files that will 1) Create the list of points (x_i,t_n), where i=0,1,...,J and n=0,1,...,F, and x_0=t_0=0, x_J=1, and t_F=some positive number. And I'll just be making a uniform grid, so x_i=i*dx, where dx=1/J, and likewise t_n=n*dt, where dt=(t_F)/F. Now that I'm thinking about it, I could just as well define two functions in matlab, x(i)=i*dt, and t(n)=n*dt...That'd be smarter than saving a long ass list of ordered pairs...You see! These are the mistakes I make, I feel so inadequate, it's rediculous. But at the same time, I have moments of  überconfidence where I think I can take on this dragon of a task. Of course, if I had the right preparation (the fact that I don't is nobody's fault but my own, I love CMU), it wouldn't be a dragon so much as it would be a fun exercise...but that's for another reincarnation.
<end math>

   But in any case, I learned some other stuff...Like that 2^X=P(X) is more than just notational, it actually has some interesting information encoded in it, once you define the following:  1) what is meant by X^Y where X and Y are sets; 2) define the whole numbers in terms of sets; and finally of course 3) what is meant by the symbol P(X) where X is a set.

Warning: Again with the math.
   So let's do that: 1) Given sets X and Y, we define X^Y to be the set containing all of the functions from the set Y into the set X(if you don't recall what a function is, just ask). 2) Let us define the whole numbers in the following way: let 0=empty set, that is the unique set that contains no elements. Then given we have defined the whole number k-1, let k={0,1,..., k-1}. So 1=the set containing the empty set(which since it has an element should not be confused with the empty set itself). And finally, 2= the set containing the empty set as well as the set containing the empty set, i.e., 2={0,1}. 3) This is the easy one, P(X) is just the set of all subsets of the set X, including the empty set and X itself.
   <end math>

   I'm excited about this weekend, because it's a long weekend--which happens to be my favorite kind of weekend.  In other news, I finally have a 4-piece dining chair set. For a week or so I only had 2 chairs, because each of the boxes the 4-piece set came in contained a broken chair. I'm hoping that it's not a sign of the durability of the chairs in general, but who's heard of hope stopping a chair from breaking?  I've been reading strictly math books lately, which has been a kind of nice submersion, but sometimes I wonder if I'm just working for an unattainable goal of being better than I'll ever be. Of course, I won't know my limitations for a while, if I'm optimisitic.  Either way, I'll enjoy my learning while I can.

I should get back to re-copying my notes, and thinking about my homeworks...

Currently Listening All That We Let In By Indigo Girls see related

   Graduate School orientation is officially over, and next week course work begins.  Since moving into my new apartment a lot of things have happened.  The second day I was here, I set up my computer, but had a hell of a time with the pins that connect the monitor to the computer. This wasn't the first time I've had trouble with it, so I said, "Screw it, I'm getting a new monitor!" So I went to the Super Wal-mart and grabbed a 17" LCD screen, which is so much nicer than the one I had before.  I know, I know, that was a bit drastic, perhaps a better investment would have been in some pliers. But cest la me.

   So I plug in this monitor and whatnot, and push the power button. Nothing happens! I take it to CompUSA and find out the motherboard is broken, so I have to order a new one. I do, and it finally gets here yesterday. I decide I'm going to change the motherboard myself. Everything goes fine except I couldn't figure out at first how to take off the processor(and what I find out later a detachable heat disperser thingie). Finally I randomly push the clamps in the right direction and I pull the thing off. The processor, for those who don't know, has about 1.5 million little pins, each of which are to fit into corresponding holes. Unfortunately for me, the method for doing this is to detach the thing I didn't know was detachable. So I mess with it until I've sufficiently bent the shit out of some of the pins and (most problematically) break off one. This morning I found out from CompUSA this means I need to order a new processor($99 for one that'll work with my motherboard). I think I could do it right now that the big heat dispenser thing is off, but I dunno, I've blown a lot of money on it already...

   So that's my computer troubles, not to mention the fact that my pocket pc's screen appears to be garbage(why does this shit happen?). I've been pretty good about eating the food in the refridgerator instead of eating out. I think that's actually lost me 5 pounds, but that may just be water weight or whatever. The other graduate students are all really nice, though I haven't really had a connection with anybody, and I miss hugs. I'm sure that kind of stuff just takes time, and will be helped by course work. Speaking of course work...
I will be taking:

• Principles of Analysis: Your basic graduate introduction to real/complex analysis focusing on the reals, of course.
  • The text will be Gurtin's Principles of Mathematical Analysis, which although I never used it in undergraduate courses, it looks like its at the same level as Spivak. The professor for the course is said to be a really good teacher, so I'm looking forward to it...especially with my love of analysis.
• Modern Algebra I: Again, basic graduate introduction to algebra, covering groups, rings, and fields. Although presumably, Algebra II goes into fields more than Algebra I does.
• I'm not really sure about the texts, I think it'll be Dummit and Foote's Abstract Algebra; Lang's Algebra; and Hungerford's Algebra, but there will probably be a primary text.  The professor for this course comes highly recommended, in fact some people just take courses for his lectures(a sort of UK equivalent for Hrusa).
• Matrix Theory and Numerical Linear Algebra I: This course is pretty self-explanatory, but I'm kinda nervous since the last time I took a course in programming was freshman year, and it was the lowest level in java.  I will probably have to try harder to like the material in this course than the others since it's new and for me disinterest and fear are hard to distinguish sometimes.
• Since I have no experience in numerical analysis, I really have no idea what the texts will be like. They are Applied Numerical Linear Algebra by Demmel and Matrix Computations by Golub and van Loan. I also don't know the professor, so here's to the luck of the draw!
• Selected Topics in Analysis: This is the only non-500 level course I'll be taking this semester, instead it is 700-level.  It will be a lecture-based course on continuum mechanics and material's given a microstructure.  When I talked to the professor offering it, he encouraged me that while some people will know more than me at the onset, other's will know less.  So that puts me in the middle, considering it'll likely be a 4 person class.

   That makes 4 courses this semester, a heavy load by anybody's standard.  Since the guy who is sponsoring me for an RA is out of the country until tomorrow, I talked to his colleague(the instructor for the last course I mentioned). He told me that my research advisor will not expect me to do much research this semester since I simply don't know enough yet, so I should take advantage of my extra time to take another course.  This will help me finish my Master's earlier which I have an interest in doing for two reasons: 1) If I end up hating graduate school, at least I can leave with a degree sooner andI get a higher stipend once I earn my Master's.  The second reason is the more motivating one, since I don't think I'll hate grad school.

   As far as my mental health goes, I think I'm lonely, but that's normal.  To cope I've been, slightly unhealthily I'm sure, spending money and doing distracting activities like going to the movies and working on random math problems.  In particular, I bought the first season of Law and Order. I've nearly finished the 17 hours worth of show...the intro has started to wear on me. Man, have they come a long way as far as writing goes.  I mean, it's a situation where I can tell that the good ideas and themes are there and just waiting to be born out, but its like cheap imitation of the more recent shows.  I guess, whenever we improve, our old self looks like a cheap imitation of our new self. And I wouldn't say it's bad--it certainly hasn't stopped me from watching 2 episodes a day--but Jerry Orbach and Sam Watterson really helped make that show great. Also, except for the beautiful, and I mean beautiful, people in The Island, the movie was as contrived and faux meditative as most sci-fi summer blockbusters.  I did like Willy Wonka. Some people hated what they did with the Oompa Loompas, but they didn't bother me.  I loved the grandmother--you know which one.

   This morning I dealt with a water leaking from the floor above into my waterheater/AC closet, the maintenance guy came pretty quickly, and the problem is pretty much solved--they'll be painting and sealing on Monday.  Now it's time to get ready for a pool party. yay!