i passed the basic!

yay!

first day of school

hey all -- it was my first day of school. i TA-ed for the first time this morning, and it went really well. i had a lot of fun, and i'm hoping i can be a useful TA. i had one TA session of my own, complex analysis, which was good, and then our real analysis professor gave us a lecture. he seems very knowledgeable, gives good lectures, and is funny. so all is well! except i may be getting sick, but i took a great nap and drank a lot of orange juice. what else is new... i've been working on analysis homework, going for runs, and playing guitar... it's strange; the groceries i bought 2 weeks ago feel like they're never going to run out. i mean, i'm sure they will, but man they have lasted a long time! thanks for reading!

santa barbara

Santa Barbara

boot camp day 19 (last day!)

last day of boot camp! went to the grocery store. treated myself to some vanilla ice cream. it's pretty much the first sweet thing i've had in my apartment since i moved in, and boy is it good. anyway, i am still up to my ears in old basic exams so i won't write much. in fact, i may not post for the next few days, because i've basically run out of interesting things to say, unless you want to hear about essentially non-interesting fundamental subjects of mathematics. in that case, let me know! at this point i could go on for hours... anyway, thanks for reading and i'll see you in a few days!

boot camp day 18

my new favorite things: the inverted fountain, and my daily lunch-time espresso (see below). also, pujols. thanks for reading!

boot camp day 17

counting down the days til the test... studying... typing up notes... working problems... eating potatoes... watching cardinals games... playing guitar. i think everyone gets the idea! thanks for reading!

labor day

today i have just been typing up notes, working on problems, re-reading old notes etc. i try periodically to get out of the apartment, so i went for a walk, and later i was outside playing guitar. there were a bunch of law students bbq-ing and a guy came over and told me i ought to join and play my guitar over there and have a beer, so i did join and have a beer and talk to a few people and play my guitar a little bit. there are lots of law students--there are 320 in an incoming class. the guy who invited me over actually worked for cbs entertainment tonight and was the boyfriend of a law student there, and his brother was also there; his brother worked for some animation studio. actual LA people! eventually i just felt like i was standing around without much to say so i came back to my apartment and i am back to work... but it was nice to branch out, even if it was just a baby step... anyway, carpenter pitched a complete game one-hitter, which was fun to watch. i guess tomorrow it's back to boot camp. the test is in 9 days or so... i'm ready to get it over with! thanks for reading!

sunday 4

nice day of guitar playing and math studying. i made a big batch of spaghetti with onions, spinach and tomato sauce. tonight i think kevin o will head over here and we will eat some ice cream sandwiches. no class tomorrow, which is nice! anyway, thanks for reading!

saturday 4

those damn ants made their way into my raisin bran that i just bought yesterday! that made me super pissed off this morning; i went to trader joe's and bought some orange-oil based air freshener thing to help combat but ants, but apparently the ants are just a problem i am going to have to get used to, is the impression i get as i talk to people. anyway, i just watched the cardinals game (they won by another hero home run courtesy of pujols) with another guy in the program and talked about some of the math problems etc. i don't know what i will do tonight; probably i should do math since i haven't done that much for the last couple of days. anyway, for now i am hungry so i will go think of something to eat. i may try to think of something to do music-wise tonight, too. anyway, a simple night in is the plan. at some point i need to call up the st. louis boys who currently reside in LA... but it's a long weekend, so i've got time . . . anyway, thanks for reading!

friday 4

i really love potatoes these days. 50 cents for a meal, basically! anyway... so last night i did end up hanging out; for a while i was not feeling it; i was very tired and people were drinking and therefore talking extremely loudly. but then i settled in a bit, had a beer myself, and eventually went over to siddharth's place to hear him play his incredibly cool instrument which is called a veena, also spelled vina. he's been playing old-timey music on it, which sounds extremely joyful and awesome. i then got my guitar and we played for a bit, which was a lot of fun. i have tentative plans for tonight to play music with him and another guy in the program named lee, who plays guitar/bass/keyboards. currently, i am waiting for my potato to finish cooking, watching the cardinals game, and getting ready to type up some math notes. today i went to the TA session, which was good, and then went to the music library and ralph's. ralph's was good, but i rode my bike and so had to balance groceries on the handlebars as i rode home, which was difficult and annoying. luckily i didn't break the eggs! anyway, time to get to work! thanks for reading.

boot camp day 16

hello hello -- today was a pretty good day but i am exhausted by now. classes are fine; in analysis he is just covering leftover material, and in algebra he is covering who knows what so i just work on problems during class. actually, today there was a cardinals game and it was the free game of the day so i could watch it on video; there were two instances where pujols had a chance to be a hero, so i watched those at-bats. he didn't hit either time, but that's all right. after classes i went to the TA session and it was extremely helpful; we covered a few topics that are decently important but which i really didn't understand. i think i really understand the implicit function theorem now. it's hard because there is one thing that is really not quite intuitive, but makes sense if you force your brain to think about the right things. i came home and ate, and feel like taking a nap, but there is a group of people hanging out in an apartment and i think i will stop by and see what's up there before giving up and falling asleep. anyway, thanks for reading!

boot camp day 15

i wonder if one of the queen ants of weyburn died, or something; i haven't found any ants in my kitchen for the last couple of days. no complaints here! another piece of good news, i received my espresso maker in the mail today (with the glass carafe broken but oh well, that's an easy workaround). things have been pretty good -- i've been going to bed early and waking up early and being fairly productive; in algebra he's no longer even working from the syllabus so i just work on old problems, which is a better way to spend 2 hours anyway, i think. anyway, i just ate a can of black beans with cheese and tomato and onions and that was pretty good and hearty; i'm sure i will be eating that again within the week. i am about to start a load of laundry, then it's cardinals game and math for the rest of the evening. it's a little bit difficult to remember what day it is. also, i wake up in the middle of the night thinking about math problems. i'll be glad when this test is over. anyway, thanks for reading!

here's a superb picture courtesy of my mom:

boot camp day 14

another day at boot camp and i am tired! watching the cardinals game and trying to hold off on a nap so i can go to bed early. classes were good today; in linear algebra the professor thought he had covered all the material so he was covering analysis stuff, but then i reminded him that he actually had not done traces at all, so he did that. analysis was fine; we worked a bunch of exercises. the professor for that class also has pretty much finished all the material, but i am going to search through the syllabus and old exams and try to find things that he has not covered. after classes i went to the TA's office and worked on a couple of problems for a while, which was good. for now i'm going to sit back and drink some tea and watch the game and try to unwind a bit before doing some work and going to bed early. it's nice to be busy. thanks for reading!

boot camp day 13

today was a little rough -- analysis was for some reason the most slow paced lecture possible and it was very difficult to stay interested. in algebra, all of the left-side seats were taken except for the back row left-side seat, so i sat there; as a result, i couldn't hear the professor or see the board; all i got was an earful of construction noise. i ended up just working on old problems, which in turn frustrated me. so, now i'm trying to relax by listening to boubacar traore while i do some work. i find it helpful and necessary to remind myself frequently that it's not worth it or helpful to stress out about this stuff. anyway, thanks for reading!

sunday 3

today i went to venice beach with kevin o-- he was kind enough to pick me up and drop me back off. that place is like another planet! it seems like it must be easy to go completely crazy as a species when you no longer have to think hard about basic survival. anyway, i think i am going to go seek out some ice cream, which i have been craving for about a week; tonight my plans include math and sleeping. thanks for reading!

here are a few pictures. the first one is kevin's sweet bike, and the second one is kevin's impressive odometer, which you should know hasn't even been functional for the last 8 years.

saturday 3

not much news today! i bought some chapstick from cvs, much needed, as well as some windex; the windex will hopefully help deal with the ants; the ants are ridiculous. if i leave a speck of food on my counter at night, then in the morning there will be 20 ants gathered around it and a line of ants on their way to join. i think that i can help wipe away the scent with the windex... currently i am listening to cardinals and trying to catch up a little bit on typing up notes; i'm taking a break from working problems for the day, the idea being that it's also worth it to review all the material and know the proofs of the theorems. (sometimes on the exam they just ask you straight up to prove one of the big theorems.) oh, one thing maybe worth mentioning; i had a terrible dream last night! i had a dream that some guy was following me around, and he had a gun, and he was threatening to kill me. but he wasn't planning on killing me right away; instead, he was planning on following me around and providing a constant threat of death. it was terrible; parts of the dream were just me trying to think of ways to sneakily get away from him, but it was impossible... i woke up in the middle of the night and was feeling very disconcerted and started walking around my apartment wondering why i felt that way until i remembered the dream. so that was weird. anyway, i also learned last night that a couple of people from high school are living in LA; i hung out with kevin o'neill a bit last night, who is in the air force going to grad school at the rand institute, and i also learned that tim heafner is going to law school at loyola marymount. both water polo guys... anyway, thanks for reading!

friday 3

this may be a stupid comment, but living in a huge city can be a lot like living in a small town. it's great--i walk to and from school; i walk to the grocery store; and, well, there's really nowhere else to go! (that's supposed to be a joke) anyway, today has been so far a standard friday -- i went to campus for the TA session, worked some problems, went to the music library, then went to the grocery store. i'm finding that i am able to figure out a lot of the basic exam questions now, even if upon first glance they look like questions i don't know how to answer.

well, tonight i will probably just listen to the cardinals game, make a batch of spaghetti, and do some studying and music playing. i've been told that there are good prices on decent beers at trader joe's, so for now i am off to investigate! thanks for reading!

recipes 1 - potato

i have made this two times now, and enjoy it:

cut up a potato into the shape of fries --
then soak the uncooked fries in water with
some salt in it for about 10-15 minutes.
at some point, turn on the oven to about
400 degrees.

then take out the uncooked fries and let them
dry; put them on some paper towels, e.g.
then put a bit of oil on them, either vegetable
oil or olive oil, and then put on salt and
pepper and whatever spices you think would be
good.

then put it all in the oven for about 15 minutes;
take them out when they look done.

(nota bene: the chef recommends
piles of ketchup on the side!)

boot camp day 12

well, it's the end of another week of boot camp. today, people hung out and had a bbq outside of the weyburn apartments... i joined, and it felt very typical as we discussed several good logic puzzles. later i talked to some people for a while that i had not met before. for the sake of writing something down, i'll describe one of the logic puzzles i was introduced to:

there are 10 prisoners in a prison and the guards decide to play a sadistic game. the guards describe their game to the prisoners: "each of you will be blindfolded, and then given a hat, either white or black, to wear. we will then line you up one in front of the other; then everyone will remove the blindfold, so that every one of you can see all prisoners (and their hats) that are in front of you but none that are back behind you. then, starting at the back of the line, we will ask each of you in order what color hat you are wearing: if you say the correct answer, you survive; if you answer incorrectly we will shoot you in the head. we continue this with each of you until we reach the front of the line. then our game is over. fortunately, you're not completely out of luck, as before we apply the blindfolds and hand out hats, you will have the opportunity to strategize as a group." the question is: if possible, come up with a strategy that maximizes the number of surviving prisoners. in particular, what is the maximum number of prisoners that can be sure to survive, given the right strategy?

thanks for reading!

boot camp day 11

today so far has been up and down. i fluctuate between feeling really confident and good about the upcoming test and feeling like i don't know anything and am going to fail. mostly how i feel depends on how a particular problem or lecture is going... but anyway, i've been working during lunch and after class with a kid in the program, trying to knock out as many problems as we can, and that's been good. in analysis, more series stuff, and then we started riemann integration.

in linear algebra, the bulk of the class was spent solving old basic exam problems, which was good. at the beginning, though, he talked a bit about the cayley hamilton theorem, which says that a matrix satisfies its own characteristic polynomial. his way to approach this problem was as follows (my discussion here is a rough sketch of what's happening): it is fairly trivial to show that this result holds for a matrix with n distinct eigenvalues (where n is the dimension of the vector space). but then, you can show that the set of matrices with n distinct eigenvalues is dense in the set of all n by n matrices. then, by using continuity of the determinant function (which is just a polynomial) you can argue that the result extends to arbitrary matrices. here's how he went about showing that the set of matrices with n distinct eigenvalues is dense (this is the cool part): given a matrix A, we can take its characteristic polynomial P, which is a polynomial depending on the entries of A. there is also something called the "discriminant" function, say D, which is a function of polynomials (D=D(P)) and is itself a polynomial in the coefficients of P. this function has the property that D(P)=0 if and only if P does -not- have n distinct eigenvalues. now, since there ARE matrices with n distinct eigenvalues, we know that the discriminant function D is not identically 0. on the other hand, it is a general property of a polynomial that if it is 0 on some open set, then it is identically 0. so, if we look at the set of all polynomials P such that D(P)=0, that is, the set of all polynomials with fewer than n distinct eigenvalues, then this set cannot have any interior! (for D is a polynomial; so if this set had an interior, D would be 0 on an open set, and therefore identically 0, which we know it is not, by the existence of matrices with n distinct eigenvalues) thus, since {P such that P(D)=0} has no interior, its complement is dense in the space. its complement is exactly those matrices with n distinct eigenvalues. anyway, he also proved that the discriminant D(P) exists and is a polynomial in the coefficients of P.

i think i will eat tuna and spinach salad for dinner and listen to the cardinals game now. thanks for reading!

boot camp day 10

well, i consider it a good day when i come home all covered in chalk; i'll spare you the details of classes, but i did work at lunch time and after classes and went and worked with the TA for a couple of hours. maybe my math stamina had something to do with the cup of coffee i bought at lunchtime; anyway, i'm hoping i can keep on working tonight but i am pretty hungry so i am going to make some dinner! so today i guess it's no news is good news. thanks for reading anyway!

boot camp day 9

well, class-wise bootcamp today was not necessarily great. we started doing series in analysis, which is good material, but i didn't feel like we necessarily covered much ground. although we did sketch out the proof of a pretty cool result, which is that if a series is conditionally convergent but not absolutely convergent, you can rearrange its terms to get it to sum to anything you want, or you can even get it to diverge. the idea is that if your series converges but not absolutely, then you can take its positive terms and negative terms separately, form two new sums from them, and both of these sums will diverge. so you can pick some 'target' L, and then sum from the positive terms until you get past L; then sum from the negative terms til you get below L. you'll always overshoot/undershoot L eventually because of the divergence of the two new separate series. but since the whole series converges, the terms of the series are approaching 0, so the terms of the two new series you have formed are approaching 0, so although you can continue to overshoot then undershoot L, you will be overshooting and undershooting by less and less. there's a slightly different argument to get it to diverge, but basically you sum positive until you're >1, then you sum negative until you're <-1, then sum positive til >2, etc. etc. and linear algebra was interesting but i think pretty off-topic as far as preparing us for the basic exam goes; we talked about expressing change of basis in terms of conjugation by a non-singular matrix, as well as the difference between diagonalizing a typical generic (diagonalizable) matrix and diagonalizing orthogonal matrices... this led to a discussion of basically classifying general orthogonal matrices... which led to a discussion of the orthogonal matrices as a topological group... for example, he proved that the subgroup of orthogonal matrices with determinant one is a connected group. anyway, then he went on to discuss exponentiation of matrices. it was interesting material, but i'll have to look over it to really get anything out of it, i think.

i also learned my TA assignments for the fall; i am TA for 2 sections of differential calculus (the typical 1st semester calculus stuff). so i do TA sessions tuesday and thursday at 10 in the morning, and it also says i'm responsible for 1 office hour, 1 hour of tutoring, and helping out with grading quizzes, tests, finals, etc. so, hopefully that will all work out; i was hoping for something standard like calculus, so i am happy with my assignment. anyway, no cardinals game today... but i am feeling like maybe i didn't get quite enough sleep last night, so maybe i'll replace the game with a nap before i get to work for the evening... anyway, thanks for reading!

sunday 2

hello -- today i went to the grocery store and got lots of good stuff for not too much money, which was nice. now i'm listening to the cardinals game and doing some work; later on i may give siddharth and rob a call and play some music. that's it! nice sunday. thanks for reading!

saturday 2

today i woke up extremely early to see adrienne off, then went back to sleep and woke up around 10. i did some work, thinking about problems and typing stuff up, and then i got picked up by aunt jenny and ryan; we went to hermosa beach. it was really nice! i went swimming for a while, got tumbled in some waves and drank some salt water... tried out the boogie board once or twice... stood and let the waves hit my feet and stared at the ocean for a while, which was nice... played some frisbee with ryan, etc. etc. afterwards, we went to a bar that jenny and ryan like and drank a couple beers; i played a bunch of ping pong with ryan; the table was set up outside, and it was really nice. after the bar, they drove me back home and here i am! currently i am eating dinner, listening to cardinals, and deciding what i'd like to do for the rest of the evening. anyway, thanks for reading!

friday 2

let's see... what's been going on since i posted last? last night, siddharth, a guy in the program, came over and we played music for a couple of hours and also listened to some stuff. he plays exotic flute type stuff, and his interests are in indian and irish music. i posted a couple of clips here. i woke up this morning and there was an outburst of ants invading my recycling; i guess ants can smell tuna even if you wash the cans... anyway, i took care it... i'll leave it at that. i dragged myself to the TA session, which was at first only mildly helpful, so i left after a bit. i went over to the music library and got some more albums, which look promising. on the way back, i stopped by the math building with the intention of asking a professor a question, but he wasn't there and i saw the TA session was still in session, so i walked back in. they were working on a problem i had tried a while back... anyway, i ended up spending a couple of hours there working on several problems and it was extremely helpful! so now i'm back home, and very hungry (all i had today was a tuna sandwich and an orange! by the way, grapefruit juice from concentrate is the bomb.) so i will now make some spaghetti and asparagus. later on, i may give rob (a guy in the program, mentioned yesterday, who plays lots of instruments) a call and see if he wants to play music... it will be a low key evening for sure... anyway, thanks for reading!

boot camp day 8

hello hello -- well, last night i fell asleep to the cardinals game; i was extremely tired for some reason. when i woke up, i brushed my teeth and packed a lunch but then just decided to go back to bed. so i woke up very early this morning, around 7, and did a little bit of work this morning. classes went well; in analysis, we did lagrange multipliers, and then we did exercises; there was one problem that i was able to solve because of the work i did yesterday after class! so that worked out well. in linear algebra, the professor gave a really good lecture i thought! he's normally pretty good, but it can be a bit confusing because he goes very fast; today he went at a good pace and delivered the material in a good order; we learned about the diagonalization of normal operators. after classes, i went to the graduate lounge and thought about a problem for a little bit with daniel, the guy i worked with yesterday; then i played ping pong with a guy named rob for about an hour and a half; it was good ping pong, and i stole some knowledge from him. he gave me a good example to develop an idea about random variables and how to start to understand the idea of independence, which he thinks is the fundamental idea that makes probability important. he also told me about haar measure on compact topological groups, and he also described to me a proof of the fundamental theorem of algebra that uses the fundamental group, which was very cool. we came home because we got word of a gathering of people in magnolia court, which is one of the weyburn terrace courts. so we all sat around and drank a couple of beers; a guy named quinn had his guitar out there so i mostly entertained myself by playing guitar. i eventually decided to diverge from the group; they were going to possibly eat then catch a bus to the beach. i didn't quite feel up to going; i think i am very tired. (plus i may go tomorrow?) i am more in the mood to relax and listen to a cardinals game... maybe next week. anyway, thanks for reading! by the by, i recently gathered a bunch of tracks i had made recently and compiled them into an album: 'list' by general beauregard, which you can download here if you're interested.

cucamonga collective

okay, well i will admit that so far the cucamonga collective has been more or less unimpressive. they have just played a bunch of standards and taken uncomfortable solos... but, i was surprised to hear them play a pat metheny tune! also, more people have shown up than before. so good for them!

boot camp day 7

today, so far, has been good -- i've been forcing myself to wake up early, and today i -really- didn't want to, but i eventually got myself out of bed and moving. classes were pretty good -- in analysis we saw actually a pretty good presentation of the inverse function theorem and how you can use it to prove the implicit function theorem. in linear algebra we talked about hermitian operators and their diagonalization; this is the complex analogue of the diagonalization of real symmetric square matrices...

anyway, after class i went down to my office (actually, i'm not sure if it's my office yet; it at least will be come fall) and met up with daniel, also a first-year grad student, and worked on a problem from the second analysis assignment; it took more than an hour but we finally figured it out! we discussed some general life concerns for a while, e.g. feeling like a slow-poke in terms of coming to understand mathematics, feeling intimidated by other students, professors, etc. etc., and then parted ways. i am now sitting in the 'powell rotunda' on the 2nd floor of the college library, waiting for the 'cucamonga collective' to start playing some jazz... free show, i figured i should come support some local jazz... (as you can see below, they clearly don't need my help.) i will try to stay for the whole hour but i am really hungry! so we'll see. anyway, thanks for reading! by the way, they just opened with 'wave' by jobim

boot camp day 6

i had a hard time turning my brain on today; shower and coffee weren't doing the trick, but a little bit of guitar helped. i guess i eventually woke up. classes were okay; more calculus stuff in analysis, and in linear algebra we went over a bunch of old exam questions, which was actually pretty helpful, although it is frustrating when the professor rushes through the solutions. i had a good moment in linear algebra where he presented a problem that i had actually looked at once before but couldn't figure out. he gave us 5-10 minutes to think about it and i actually figured it out! (at least, the first part.) after classes i went to ralph's -- i have fun at the grocery store trying to maximize my ralphs card savings... anyway, same story tonight... math, cardinals game, etc. etc. etc. i'm hungry! so i guess i'll eat. thanks for reading!

boot camp day 5

classes were good today; in analysis we started doing all the calculus stuff, differentiation and mean value theorem, multivariable calculus and taylor's theorem etc. in linear algebra we started talking about diagonalization of n by n matrices. there's a cool proof that a real symmetric n by n matrix (equivalently, any self-adjoint linear operator on a vector space over the reals) has a real eigenvalue. (actually, in class we proved something stronger, but i liked this first part of the proof best.) i am going to try to catch up on some linear algebra stuff tonight by typing up notes, and i'm going to read some of the calculus stuff on my own because i thought the presentation was a little rushed and a bit unclear in class...

i'm currently doing laundry since i'm running out of socks. i'm also making some french fries! potatoes are currently soaking... that plus a spinach salad should make for a decent dinner. i am really running low on food though; i'm just going to have to make a legitimate trip to the store someday soon. cardinals are in town tonight; if i felt like it, i bet i could find a TV to watch it on but i will probably just listen. anyway, all is well! thanks for reading! by the way, if you're interested in how the proof i mentioned works, i'd be glad to discuss it. originally i posted up a proof, but there were formatting mistakes because of typing in html, and so i did a proof in latex but then i made a few mistakes, and didn't save the file, etc. etc. etc.; so i decided to forget it!

sunday 1

well, again today i'm trying to make math my focus. i finally just solved a problem that i wasn't able to figure out for a couple of days. the 'trick' i ended up using is a trick that i have thought of before in a similar context; in the end, the proof isn't very long! it's just a bit confusing because you have to do something sneaky, which is find some delta, and then cover your space with balls of radius delta/2 for everything to work out. but anyway, last night i entertained myself by making a big 25 minute mix of a bunch of good piano solos played one immediately after the other, with minimal audio editing things done in between to make it flow reasonably well... if i do enough math today to be satisfied i will probably try to make another such mix this evening. cardinals are playing right now, and losing by 1, but now a rain delay is starting... anyway, cardinals are coming to LA tomorrow to play the dodgers! no rain delays here, i would assume. in fact the weather has been perfect every day i've been here... anyway, plans for the rest of the day, other than math and music... well, all i know is that spaghetti dinner seems reasonably possible. well, that's all for now! thanks for reading! (oh by the way, if you're going to read the proof below, then there's one place where i put X where i should have put \chi, but it's pretty obvious what i meant and you might not even notice it...)

saturday 1

today has been pretty good. mostly i've just been typing up notes and thinking about math in general. i think i'll probably work a bit more and listen to the cardinals game, and then try to do some music tonight. i got some music from the library yesterday and there is one track that i keep listening to over and over again, so i wanted to post up a clip. here is what i consider to be a really nice section of "monk's dream" from the album "memoirs" featuring paul bley (piano), charlie harden (bass), and paul motian (drums). all three of these players are really really loose when they play so as a trio it's pretty nice. anyway, thanks for reading and enjoy the clip!

boot camp day 4/friday 1

well, i didn't post yesterday because after boot camp a group of us were hanging out -- we originally planned to go get a drink somewhere, but instead we went to ralph's and picked up a bunch of beer and came back to one of the courtyards in weyburn terrace... it was fun; someone in the program had a bunch of instruments, including banjo, violin, mandolin, and someone else had some irish whistle-flute type of things, and they played and i played some banjo and it was fun. i did not get any useful contact information though... oh well. afterwards, a group went and got dinner and subsequently went to bar. after a while it was feeling late and i felt exhausted, but i think it was only about 11 when i decided to leave. i kept waking up around 7 this morning but i forced myself to sleep in, instead, wanting to take advantage of the opportunity.

anyway today i am planning on going to the music library, going to the grocery store, maybe doing laundry, working on some math, and hopefully coming up with something to post music-wise, since i haven't posted yet this week. anyway, thanks for reading!

boot camp day 3

this morning i had the classic 'everything goes wrong' type of dream... the type of thing where i was on a bus going to the airport, but it went to the wrong place, so i had to find my way to the airport, and i went to the ticket counter, but they couldn't find me on the computer, so i went to check my phone to see the email with the record locator, but my phone had been reset and i couldn't access anything... so then i had to answer some security questions on a screen to gain access to my ticket information, but of course the questions were incredibly cryptic, like riddles, or they were just symbols that i had to interpret, etc. etc. etc.

boot camp went well today. in analysis, we got through the arzela ascoli theorem. in linear algebra, we got through dual spaces. during lunch, i joined a big group of first year students and walked over and sat outside at the union and ate lunch, which was just fine and dandy.

after classes were over, i went and saw a talk by Jean-Michel Morel about the "retinex algorithm." the topic had to do with how we perceive images... probably everyone has seen this famous optical illusion. the point is that there are two parts of the image that are exactly the same color, but because our brains are smart and can filter out shading, we perceive the two parts of the image as being two different colors. so, people have tried to come up with algorithms that take an image and filter out the shading, so that the resulting image is closer to what we actually see... e.g., if you perform the retinex algorithm to that image, the part that looks darker actually _is_ darker and the part that looks lighter actually _is_ lighter. basically, there are 3 different models of how this works, and when you use these models to create algorithms to reconstruct an image with the shading removed, you basically end up having to solve the same partial differential equation (PDE) in each case... it's not exactly the same, but it's close. anyway, a lot of the talk was over my head, but i did learn some things, like the idea of the discrete laplacian being an operator used for 'edge detection' (even though i don't know how this works! but i would love to, if anyone could tell me) and how you can basically get rid of gradients below/above certain levels to yield an image with different levels of contrast. anyway, it was neat and i'm glad i went. here is a link he provided during the talk to see some of this stuff in action.

after that talk, i met with my faculty advisor to plan classes for the year... in the fall i'm going to take complex analysis I, real analysis I, and applied PDE I. (plus the class that's supposed to teach you how to be a TA.) technically, i am taking classes that an applied math PhD student should be taking! but that's okay... i'll do the geometry/topology sequence next year (schedule-wise, it's not possible for me to take it now)... also, in the winter and spring, terry tao is giving a topics in real analysis course which i am thinking i will take if the topics aren't too above my head. we also charted out a good potential bike route to the beach that involves bike paths and avoids deadly streets...

anyway, cardinals game is on, and i am thinking i would like to get some work done now even though i feel that a nap may be more likely in my near future... maybe a music blog post, but that might have to wait til friday... anyway, thanks for reading!

boot camp day 2

today, material wise we covered more ground than we did yesterday, which was good. in linear algebra, we proved a fact which the professor then used to prove a whole bunch of simple but fundamental results about finite-dimensionality of vector spaces. the fact is: given any collection of vectors v_1,...,v_k that span your entire vector space, then any collection of vectors w_1,...,w_n with n>k must be linearly dependent. he gave us two proofs, one was brute force computation style and one was slick. i'll write down the slick one below... after classes i came home, made a bunch of spaghetti, ate it, and then took a great nap to the cardinals game, which we lost. (but it's okay, since the cubs lost too.) but for now i'm going to stop writing, so i can maybe get some work done tonight! okay, thanks for reading! the proof is below...

the proof is by contradiction. so first you assume that w_1,...,w_n are linearly independent. then each w_i is nonzero. (proof: without loss of generality, assume w_1=0. then 1*w_1+0w_2+...+0w_n is a nontrivial linear combination of the w_i that equals 0, which implies linear dependence.) since v_1,...,v_k generate the space, you can write w_1 as a linear combination of these vectors. since w_1 is not 0, not all coefficients in this linear combination are 0. take the vector v_i corresponding to the last non-zero coefficient, and remove it from your list v_1,...,v_k, replacing it instead with w_1. the resulting set of vectors w_1,v_1,...,v_{i-1},v_{i+1},...,v_k still generates your entire space. (this is true because you can write v_i as a linear combination of w_1 and v_1,...,v_{i-1}, so that in any representation of a vector using v_i, you can use w_1,v_1,...,v_{i-1} instead of v_i. to see why you can write v_i as a linear combination of these other vectors, note that we have w_1=a_1v_1+...+a_iv_i, where a_i is nonzero. then you can solve this equation for v_i.)

now, you continue this process with w_2,w_3,... each time you remove one of the vectors v_j and add some w_i, and your resulting set of vectors generates the entire space. nick pointed out below that's there's another comment that needs to be made to guarantee that this actually works, i.e. that each time you're actually removing some v_j. to see this, consider the case with w_2. you write w_2 as a linear combination of w_1,v_1,...,v_{i-1},v_{i+1},...,v_k. now, one of the coefficients of the v_j had better be nonzero, since otherwise you would have w_2 as a scalar multiple of w_1, which contradictions linear independent. then you can actually remove the v_j corresponding to the last nonzero coefficient, as you need to. with w_3, you know you have a nonzero coefficient corresponding to one of the v_j because you can't write w_3 as a linear combination of w_1 and w_2 because of linear independence, and so on.

so, if you iterate this process k times, you get rid of all of the v_j! then you have w_1,...,w_k generating the entire space. in particular, you can write the vectors w_{k+1},...,w_n as linear combinations of w_1,...,w_k, which implies that the set w_1,...,w_n is linearly dependent, which is a contradiction, and you're done.

boot camp day 1

well, it went well! there was a really long orientation that got really irritating because for about the last 35 minutes i really had to pee, and the graduate advisor was talking and talking and talking. there were a couple of annoying things that i noticed in particular: one is that in an attempt to "conclude" and make a point, people end up repeating the exact same thing they just said. ("don't leave your books somewhere where people can steal them. really, if you leave them on your desk, or just on a table somewhere for a minute, someone can steal them. it happens all the time. so, really, don't leave your books somewhere people can steal them...because if you leave them around, like on your desk..." etc. etc.) the second thing i noticed was hinted at in the first, which is that people will often times give an excessive amount of examples to illustrate what is a simple point to begin with. i was really about to lose it, and the orientation "ended" several times, before another point was brought up, or something was reiterated... etc. i guess inefficient presentation of simple, detail-oriented material is just very very frustrating when 2 cups of coffee and a tall glass of orange juice are swelling in your bladder. i was squirming!

class-wise, the boot camp was actually a lot less rigorous than i thought it might be. it's probably because the stuff we were doing was pretty elementary, but the professors really glossed over a -lot- of details. which is fine, because it will give me something productive to do in the evenings (i.e. fill in the details!). the lecturers are both relaxed and friendly -- i just hope they really get me ready for the test!

i did meet some people in the program. nice, normal people! which was a relief. i came home and made the mistake of trying to fill out tax forms! i also began looking into establishing california residency... dear lord... i'm more or less in a horrible mood now, but i think mostly i'm just tired. tonight i'll probably look over/transcribe some notes from today, work on some problems, possibly try to do something for the music blog... anyway, it will be an early night for me. okay, thanks for reading!

coke or pepsi?

today was and remains fairly uneventful... i woke up very early, and for some reason felt compelled to catch up on failblog... i posted a track to the old music blog that i am actually pretty happy with, and i listened to the cardinals game (we won)... called home, took a couple of walks, etc. etc.

one thing i did that was kind of fun was watch the entire series of tim heidecker stand-up youtube videos. it's a bit reminiscent of andy kaufman in that tim more or less pretends to be a horrible comedian, and his entire 'set' could be looked at as a prank on the audience. in the series of 8 videos, you see him basically present the same scraps of terrible material again and again, with slightly different delivery each time (plus some new material emerges). the dates of the videos span over the course of a year or so. in the first videos, people don't really get it, but by the end he actually has the crowd laughing quite a bit. i myself was laughing from the beginning, mostly because i've watched enough tim and eric etc. to get his humor and see what's going on in his act; i was wondering if more people begin to laugh near the end of the series because he actually does tweak the presentation an get more comfortable in the stand-up setting, or if his popularity just rose over the course of that year, so that by the end of the series more people are familiar with his humor, so that more people 'get it'. anyway, i think the videos are quite funny and encourage anyone with some time to kill to watch them.

boot camp starts tomorrow, bright and early. as for tonight, i see spinach salad in my future. okay, thanks for reading!

vonnegut

hello to anyone reading! i decided to start this blog to keep track of the details of my new life in LA. it's been a few days since i've been on my own in my apartment here in westwood. i've been getting acquainted with the area, and campus, etc. i've spent a lot of my time reading Kurt Vonnegut books i got from the UCLA library, listening to new music (from the UCLA music library), listening to cardinals games, and wondering how i'm going to eat all the food in my fridge before it goes bad! i also took a walk around the botanical gardens on campus, and later bought a bike pump... anyway, i just finished 'Bluebeard,' which was very good, and from which i stole the quote at the top of this blog, as i felt it was appropriate. my 'real life', i.e. the reason i am in LA of all places, begins on Monday when i start my math 'boot camp.' it should be a blast, or at least a good way to pass the time! anyway, i read a good passage today from Bluebeard and thought i would share it. it concerns the ingredients necessary for a successful revolution:

"...most people cannot open their minds to new ideas unless a mind-opening team with a peculiar membership goes to work on them. Otherwise, life will go on exactly as before, no matter how painful, unrealistic, unjust, ludicrous, or downright dumb that life may be.

"The team must consist of three sorts of specialists... Otherwise, the revolution, whether in politics or the arts or the sciences or whatever, is sure to fail.

"The rarest of these specialties... is an authentic genius--a person capable of having seemingly good ideas not in general circulation. 'A genius working alone... is invariably ignored as a lunatic.'

"The second sort of specialist is a lot easier to find: a highly intelligent citizen in good standing in his or her community, who understands and admires the fresh ideas of the genius, and who testifies that the genius is far from mad. 'A person working like that alone... can only yearn out loud for changes, but fail to say what their shapes should be.'

"The third sort of specialist is a person who can explain anything, no matter how complicated, to the satisfaction of most people, no matter how stupid or pig-headed they may be. 'He will say almost anything in order to be interesting and exciting... Working alone, depending solely on his own shallow ideas, he would be regarded as being as full of shit as a Christmas turkey.'"

--Kurt Vonnegut, "Bluebeard"

okay, thanks for reading!