Sunday, August 29, 2004
haha... eating kong bak from Westlake now... haha yummy... haha better play more badminton and tennis this coming week... haha speaking of tennis... haha hmmm today din get into the sun much... haha... excessive cloud cover... haha anyway mom shooed these 2 guys off from the court cos she booked court 4... but i wuz like... aiyah... since court 5 and 6 no one use... no difference wat... but she wanted 4 so.. let her do the dirty job of shooing pple away... haha... practised forehand today.. trying to generate more spin... which means i hafta lift the ball up a bit more... kinda difficult to get the timing right... especially for the follow thru... oh well... in the end wuz quite ok la... think my string and racket helps to generate a lot of spin which is good so my balls dun fly outta court... but then again... cos of the spin... alot will hit the top of the tape.. haha shall practise that next week again... haha
anyway the rest of the day quite duh la... boring... oh ya... watched volleyball and diving last night till 3 plus in the morning.. haha china came back from a 0-2 deficit against russia to claim the gold in volleyball 3-2... haha and diving... wahhh hu jia this 21 year old did a magnificent perfect dive... 10s all the way to ensure that the gold wuz his... haha superb!! haha
oh visited christine too... she looks thinner but nevertheless looks ok la.. haha hope ya recover soon xtine... hahaha... no proofs today cos tmr got tkm tutorial... need to keep my braincells for tmr... haha nitez for now!! hee
BURP!
i guess eating kong bak cannot be considered healthy right.. oh and i confess i just ate KFC too... burp...
{11:09 PM}
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Saturday, August 28, 2004
... wat a week... so many things happening con currently... haha not all of which are good of course... including something at home... haha oh well... that shld be resolved rather efficiently... albeit with a loss of a certain amt of cash... haha hmmm dunno y mum wuz so uptight abt it... anywayz... xtine's in hospital now... kidney infection i believe... hope she gets well soon... shall vist her with gerri and francis tmr... evening... which ought to be a fun day considering i did work today... haha the words nicholas and work dun seen to like each other very much... haha
hmmm anyway, as part of nicholas' collection of nice proofs, i shall relate an interesting thing that happened on friday during 4263 lecture... haha INTRO TO ANALYTIC NUMBER THEORY... basically the class wuz and still is small... say 14-16 pple only... so the lecturer CHH sed that he wanted to get to know us better during the tutorial... so he called some of us up to present questions from the tutorial... he had in his hand... a class list with our pictures on it... so he wuz busy trying to fit names to faces... haha... then... came qn4... he asked the class "who would like to present qn 4?"... no reply... he asked a few students sitting near him if they would like to try and they all sed they din noe how to do it.... then came the interesting bit... he sighed... and sed "aiyah... then i haf to use my SECRET WEAPON!!"... and then... "KJ, can u pls present qn 4 on the board." hahaha i wuz momentarily stunned... haha but i already knew the sheer intelligence this guy possessed man... but i really din noe how famous he wuz in the entire dept... this guy really has talent man... GENIUS seems to be an understatement... haha AND... he actually went up to the board without and answer and did the whole question on the spot!! my god!! i nearly wanted to kowtow to him there and then!! it wuz sooooo cool!! he really does have the "seh" and the poise of a genius!!... haha
anyway here is wat he proved:
Suppose p is prime, then (p-1)!+1 is a p power if and only if p=2, 3 or 5.
Proof. We need to use the following lemma which can be easily proved: If (n-1)² (n^k-1), then n-1 k. Let us first assume that (p-1)!+1 = p^k for some positive integer k, which is (p-1)! = p^k -1. Now let use assume that p prime and p ≥ 7. Now we already know that (p-1) (p-1)!, but in order to use the other lemma we need another factor of (p-1). Consider this: since p>2 and p is prime, then p-1 must be even. That means that (p-1)/2 is an integer and since p>5, then (p-1)/2 >2. Thus, since (p-1)/2 and 2 are 2 values in the factorial of (p-1). That is, (p-1)! = (p-1)(p-2)...((p-1)/2)...(3)(2)(1). which means that (p-1)((p-1)/2)(2) (p^k - 1) so according to the lemma above, p-1 k which implies that p-1 ≤k and p-2 ≤k-1. Thus we arrive at the following: p^k-1>p^k-p^(k-1)=p^(k-1) (p-1)≥p^(p-2) (p-1)≥(p-2)^(p-2) (p-1)≥(p-2)!(p-1)=(p-1)! which is a contradiction to our original assumption. The converse is easy to check and that completes out proof.
And there u have it... haha one of another nice nice proofs... haha hmmm speaking of which i wuz browsing thru the prospectus of the university of london, imperial college... thinking of going there for my graduate studies to get my MSc from there... then i realised that if i want to do algebra for my paper, i shld actually apply to Queen Mary... apparently it has a maths dept that specialises in algebra!!! haha how cool is that... but then again.. i need a really good second uppers degree in order to get in and succeed... haha i really hope i do well this sem... ok ok time to go do something abt that... haha promise to write more tmr... haha ciao...
FIRE!!
finally back on track... a bit slow... but tau huey is a good reward for keeping up with it...
{9:00 PM}
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Wednesday, August 25, 2004
haha waaahhh din believe it when the 2 days after i pleaded with caleb to return the rain to SUNNY singapore was filled with dark clouds and rain storms... haha... excellent but wrong timing la dude... the nite the nite my frend... haha i want the rain to be at nite... haha...
anyway just came back from an excellent badminton game... well... sort of excellent... haha... wuz quite OFF today but still nice game la... haha it feels good to win... hahahaha...
hmmm graph theory today... nothing really interesting... haha let me try and recall something academic to write here today...
hmmm can't think of anything... anyway... want to win some cash real quick? haha... 1 million dollars to be exact? haha well all u haf to do is solve a mathematical problem... haha 7 actually each worth a wooping 1 MILLION DOLLARS... so if u have the brains and the time... just try and solve these 7 problems and u'll be 7 MILLION DOLLARS richer!! haha... here ya go... http://www.claymath.org/millennium/
hee hee... remember to give me a nominal sum if u do... haha just joking... anyway... haven't really been doing much recently... been chatting less and less too... i wonder y... i wonder where all my time has disappeared to... been slacking and not doing work...
arrrgghh... dun feel like typing liao... will type more tmr... haha ciao!!
Boom!!
arrrgggh forgot to set alarm for 2 consec days!! so off my plan... nvm start tmr...
{8:45 PM}
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Monday, August 23, 2004
freaking hot weather!!! TIAN YU!!! give me back my rain!! haha dun just keep it for urself in France!! haha ok i'm on the verge of going nuts... haha anyway today i think yang yue took us for set theory... and i must say he's damn good!! haha anyway got a very nice proof which i shall write here...
Cantor's Theorem: The cardinality of the power set of any set X is strictly greater than the cardinality of X.
Proof. First we show that card(X) less than or equals to card(P(X)). To do this, we need only prove that there exists an injection from X onto P(X). Let f:X->P(X) where f(x) = {x}. Clearly f is well defined and injective. Therefore card(X) less than or equals to card(P(X)). In order to show that card(X) cannot be equal to card(P(X)), we show that there cannot exist a surjection bewteen these 2 sets. We suppose, for the sake of contradiction, that g is one such function. To proceed, we need to show that there is an element in P(X) that does not lie in the image set of g on X (ie. we will show that there is a subset of X that does not lie in the range of g. We now define a set A which is a subset of X as follows: A={x ε X : x NOT ε g(x)}. Now, since g is surjective, A must lie in the range of g (ie there exisit an element a ε X such that f(a)= A. However, a ε A=f(a) => a ε f(a) but a ε f(a) => a NOT ε f(a) which is a contradiction. Similiarly if a NOT ε A=f(a) => a NOT ε f(a) but a NOT ε f(a) => a ε f(a) which is also a contradiction. Therefore for any set X, card(X) is strictly less than card(P(X)).
phew... i din think i would be able to provide the proof... haha finally understand it... hmm this seems like a good idea... haha writing down proofs that took me a while to understand... haha really drills it in... haha this one in particular is sooooo elegant!! haha... hmmm anywayz i think more proofs on analytic number theory shld be coming soon... haha really confused with that topic... hee... anyway... think i had enuff for tonight... frends coming up... haha... okie... time to rest... hee hee ciao!
overheated!!
had breakfast with gerri at ghim moh today...
{9:08 PM}
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Saturday, August 21, 2004
hmmm just finished watching another marathon match up in women's doubles badminton... haha quite an engaging match... china wuz going for another olympic cleansweep of the ladies doubles titles... tried to replicated their collection of the bronze silver and gold medals... but... in the end... korea stopped them... to the bronze that it... haha
oh well... must be a really bad year for china this year lor.. haha first the divers then lost their top seeds in badminton... then gymnastics failure... then now lost theire cleansweep victory... waaaah it's a bad year in general... oh well... wonder if beijing 2008 will be better...
anyway... i realised that i haven't been studying lately... been getting thru based solely on the fact that i attend lectures and listen... haha but think not enuff la hor... haha esp for complex 2... hmmm ok ok next week... shall start studying... haha (yeah rite)... hmmm anyway hopefully it wun rain tmr... i need to play tennis and i need the sun... haha badminton this coming wed... prob with sifeng as well... haha cool... haven't played with him for so long liao and he's leaving for the land of maple syrup soon... haha
oh oh li jiawei playing this unseeded korean tonight... hope she does well... haha but i have a bad feeling today... better not watch the match... haha might jinx it... haha oh well... 1 week into olympics liao... and i just picked up a copy of SciPhi magazine and re-read my article on the olympics which i wrote abt a month ago... haha... i realised that this year's olympics din really affect me as much as i tot it would... haha in fact, the coverage din really seem overwhelming... coupled by the fact that mediacorp wuz the sole broadcaster here in singapore... even the cable channels dun show any olympic events... haha oh well i suppose it's good also... give me more time to do other stuff... haha
hmmm here i make it a note that i am supposed to write sort of an aide memoire for functions... haha bought the tys liao... so shld really begin to do it... supposed to finish it b4 the end of aug... so i guess i'll start tmr la... hmmm shld really finish it b4 my tutorials come it... finished 3 tutorials... 3201 3233 and 4263... that leaves me with 3205 3209 and 4247... haha ok... another day of work tmr... hmmm shld start reading the texts also la... since i already purchased them... haha and in the wise words of leyton hewitt... "C'MON!!" hahaha
hmmm class outing later tonight at swensen's... wonder who will be there... haha need to go out and get myself a nice dry-fit top... the reebok one i'm wearing now soaks up perspiration like a sponge... i wuz dripping sweat all over the court the last game... haha wonder y i generate so much perspiration... haha anywayz... there goes my budget again.. haha i'm really damn bad at finance management... haha...
gonna watch another match...
OUT!
sama sama
{3:53 PM}
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Thursday, August 19, 2004
hmmm very sian now... gonna skip set theory lecture later at 4... haf only finished 2 out of 7 tutorials for next week... better start on the rest esp analysis on metric spaces... arrrgghh...
the confusion has begun... complex analysis is abt to kill me again... even though TWK is teaching i still have a bad feeling abt it... can't remember anything abt it... all the Cauchy Goursat Theorem, the Cauchy Residue Theorem, Cauchy Integral Formula, singlarities, pole etc etc... arrrggghh... wat have i gotten myself into?!?! number theory doesn't seem to be much easier as well... luckily i bought the reference text today... hopefully will be able to catch more material tmr...
rings wuz pretty ok today la... except there were quite a few mistakes in TKM's notes... haha but i can really understand... and relate... afterall i too prepared notes that had lots of errors in them... haha... well algebra seems to be going along just fine... which affirms that my decision to remain in pure maths and in particular, abstract algebra, was a right one... well i guess i shld also start thinking abt wat to do for my honours project... shld i approach TKM now? or maybe lang mong lung?? hmmm the pple who end up doing algebra for their honours or masters research seem to be the creme de la creme... rest end up doing either analysis or OR... decisions decision... shld speak to TKM after the first mid term... hopefully i will do well enuff to convince him that i am a suitable candidate to be his student... haha
hmmm oh speaking of which... he mentioned today that when he wuz in Cambridge, the tutor-undergrad ratio wuz 1:2... that's soooo cool... if only they could have it in NUS as well... i sure dun mind paying more... haha after all MOE's paying for my education... haha... well if i do well this sem... i think i will try for ISM in group theory next sem... hopefully also with TKM... that way i will be able to get more out of the lessons since i think my interest lies in abstract algebra... haha...
terence sez he prob be applying to Imperial to do graduate studies... so i'll prob apply there too... arrrghh.. but i need 2 recommendations... 1 from TKM and another from some other prof who i haf to get to know soon... haha deciding between CHH and KKM... TWK would have been a good choice if only i had not skipped his tutorials in sem 3 and did badly for complex analysis... oh well... shall leave that till later to decide... for now... need push myself ahead of the lectures... lagging behind liao...
oh oh... condolences to ronald... he din exactly play a good match against boonsak yesterday but well i can understand the immense pressure he was probably under... good job of reaching the quarterfinals anywayz... hope 2008 will see him making it to the finals... haha... oh and congrats to mia for reaching the finals too... haha hmmm henin-hardenne seems to be back from time off the courts too... maybe this olympics will be like her jumpstart to claiming the us open grand slam next... hee... oh ya... got this really nice poster of her... from adidas... cool...
ok ok time to do a bit of reading up for set theory since i will not be going for his lecture... haha ciao!!
IA IA!!
yes yes still going for the gold...
{2:57 PM}
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Tuesday, August 17, 2004
wow... been a long time since i updated.. haha but nothing much recently though... crappy show on ch u now... local productions are really quite bad... well.. not all... the comedies on ch u are actually damn funnie.. haha but dramas... haha singaporean media has a long way to go...
hmmm arrrggh... cutting the crappy sob sob conversations between some guy and girl out by listening to MY SANCTUARY by YUKIE NISHIMURA... haha excellent jazz piano piece.. haha... oh oh speaking of which... i am reminded again that ronald susilo is now in the quarter finals of the olympics... haha playing against boonsak from thailand... i think ronald stands a good chance... but it will be tough from here on... after boonsak he will play... probably peter gade... whcih in my opinion will be 10 times harder to defeat than lin dan... haha
arrrghh.. upsets of the week!! the mighty kim dong moon and ra kyung min have fallen... not to their arch rivals zhang jun gao ling but to a pair that has never beaten them b4... and the shocking think is they lost in straight sets... wat is the world coming to? that means that europe has booked a place in the finals already, with the only remaining asian pair coming in the form of zhang and gao... the defending champions... haha...
hmmm anyway korea shld be happee in some sense la... kim dong moon and ha tae kwon are in the semis and so are lee dong soo and yoo yung sung... haha and kim yong hyun and yim bang eun look set to upset the indo pair to get in to the semis as well.. haha if that were tha case... the only representative not from korea will be (HOPEFULLY!!) cai yun and fu haifeng (feng yun) from china... haha amazingly.. this is also the almost exact opposite scenario from women's doubles... where 3 are from china and 1 from korea... haha this olympics is really weird...
but but but... happee to say ronald has made it thru again... though some pple still find it discouraging that no native singaporean has won anything... well... i've had enuff of trying to convince pple to shed their inhibitions of accepting foreign talent who have assimilated into singaporean society... frankly... i think this mentatlity is kinda disturbing... it's sort of a defence mechanism kind of like how singaporeans were worried foreign talent in singapore were stealing job oppourtunities from the locals... well... in my opinon... i think these foreign talents who contribute to society to a greater extent than losuy singaporean who just mope and whine about their lost jobs... complain abt the influx of foreigners... all while sitting on their tuckus expecting a job to be delivered on a silver platter... these "foreigners" some of whom hold PR here in singapore or even citizenship... are by far more deserving of their status than the likes of useless singaporeans who grow fat with arrogance... sitting around demanding the government assure them of their birthright... well... i spit on these pple... PUI! haha
ok... now after having sufficiently expressed myself... haha i think it's time for me to get back to analytical number theory... haha why in the world did euler and mobius come up with such functions... hahaha... or rather how did they? hahaha
ok ok till next time...
OUT!
still on track...
{8:17 PM}
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Friday, August 13, 2004
great show!! laughed till i wuz in stitches... reached there a bit late... cos of many factors of which teh most hilarious one wuz mel mel's attempt at parallel parking... haha can't remember how many attempts it took but Francis had to go out and guide her from outside the car... haha...
reached the theatre just after the start of the show... din really miss much and the atmosphere wuz great!! the show wuz soooo politically incorrect which also added greatly to the humor... haha it wuz really like watching the avergae life of a singaporean all while drinking tea and having a cha siew bao... haha
i can't even express how much i really enjoyed the show... haha i've booked tickets to treat gerri and weiquan to watch tmr with me again... haha been a long long time since i had such a good laugh... haha... can't wait for tmr... moring lecture with KKM... lunch with terence and jiaen... DIM SUM DOLLIES!!! birthday dinner with jiahui... how much better can it possibly get? hahaha
oh ya i forgot... today is FRIDAY the 13th... haha dun think anything bad has happened to me... haha... in fact i usually consider 13 my lucky number... haha remember getting marksman when i wuz firing in the lane (is it called the lane... in a chamber?? can't remember...) number 13 when i wuz in army... haha lot's of other things as well... too tired to recall.. maybe tmr.. haha
okie going to sleep soon... haha...
Cease Fire
yay yay!! 4th day HLP!!
{11:59 AM}
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Thursday, August 12, 2004
tired... nothing much... TKM is still the same but good... tried to make pple drop the module as usual.. wonder how effective it will be... hope we will have a smaller class size so no need tutorial... hmmm set theory lecturer wuz pretty good also... teaches like masson which i like... teaches wat masson taught... which i like even more... haha hmmm guess my involvement in the french double degree programme has finally come to some use... haha... set theory seems quite easy for now... hee...
i wonder y they always let visiting profs teach that module... like some unwanted child... but i actually think the subject material is quite interesting... victor going US to do it... as a graduate level module... which IMHO shld be the case considering that set theory is still developing and many things are not solved yet... anyway... nice problem... which as of now (according to prof stephan) has not been solved... is the set {x x is an even natural number greater than or equals to 6} = {x x is the sum of 2 odd prime numbers?}... always seems easier to try and find a counterexample to disprove... but is there one in the first place... haha
interesting... i guess this semester... the modules i will have some trouble with are 4247 and 3209... not really interested in the topics so i dunno if i can keep my motivation up there... hee...
anyway tmr is FRIDAY!! supposed to be a good day cos the weekends are here but i got class on saturday... so much for that... BUT... i will be watching the fabled revenge of the dim sum dollies... haha shld be in for a good time with mel mel and francis... haha
ok... kinda still early but dun really feel there's much to write...
last shot out!
today kinda din really sleep and din really wake up... haha so how... nvm count it as 3 days into HLP haha!!
{8:45 PM}
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Wednesday, August 11, 2004
haha koh KM is sooo hilarious... in his own unique way... no wonder he got the faculty teaching award soo many times liao.. haha that's it... not dropping 3233 for anything liao... haha stoopid as it may sound... i actually understand the lectures so much more cos i pre-read all the lecture notes... haha wonder y i never did it earlier... stooopid me... ok... CAP 5 here i come... :) i will getddit!!
heard abt yang yue... and his lectures... seems interesting... but too bad exam timetable clashes with set theory... hmmm of which.. i dun even noe who the lecturer is... frank stephan.. or smthing liddat... who is adapting feng qi's notes.. haha hmmm see how la tmr... haha i got tough competition in that module also... so come on nic...
but for now... enjoyment and relief from the stresses of studies and personal problems... haha BADMINTON!! with francis spencer and RV weiquan... haha... and the it's a night slumber at lin jia's house which, not being such a spoilt blanket, may turn out to be either really fun or totally disasterous for me... we'll see what happens... but at least today i dun need to think much abt stuff... dun need to worry abt other pple... abt my sanity... haha funnie how sometimes the only thing keeping me going is a thought and a song stuck in my head... haha the power of music... :)
oh gosh... no time for that now... gonna be late if i dun take taxi... francis... u'd better be early... haha... another 8 bucks down the drain...
BURST fire!!
second day without failing the HLP
{3:25 PM}
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Tuesday, August 10, 2004
hmmm so much for the first day being bad... i thought it went quite well actually... haha QTS was surprisingly good... haha oh ya must remember his quote for posterity... "Any lemma with a name attached to it is important. Any lemma with 2 names attached to it is doubly important" haha... namely Cauchy-Schwarz Inequality...
TWK followed after that... mr... err... err... ummm...err...err... cracks me up everytime i hear it... but well he did me a favour by revising complex analysis I b4 actually proceeding... *phew* i better start reading Churchill b4 i die big time for this module...
4 hour break with with enuff time for a 1 hour lunch cum chat session with terence hoinam kelvin and yongxing... hmmm... can't exactly remember the topic.. but i suppose that's the point... haha
after that 4263... intro to analytic number theory... din catch the intro where he wuz trying to explain some prime number theorem thinggie... wuz staring at an equation on the board with a big O on it... tot it wuz a function... until he divided by x and the interior lost one too... haha wonder wat it is... hmmm... oh sat beside LKJ today... waaahh could sense the aura of intelligence... frightening... should ask him more questions... haha... or as QTS sed during 1104 tutorial... shld MAKE USE of the pple arnd me... haha
hmmm realised that i'm been teaching at CTSS the way NUS lecturers teach... hmmm bad... not enuff practise... not enuff hands on... haha no wonder... haha talk too much as well... haha next time then... maybe i shld try observing TKM... afterall he is IMHO one of the best if not THE BEST lecturer in math dept... haha
hmm soooo tired after today's lessons and trying to figure out how to make this blog look nicer...haha gave up... live another day to fight another battle... i shld sleep soon... my healthy living plan requires that i wake up at 6 tmr morning... arrgghh... dunno how much i can take... haha see how.. got a bet with terence.. haha 17 weeks only... and i get a treat... (darn i've been duped!!) haha...
anyway carry on with the salvo... out!
1 day without breaking the HLP... yay!
{10:50 PM}
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HLP means healthy living plan? confirm will break it one..=P
Monday, August 09, 2004
well... not supposed to start today... but i gotta see how this looks first... hmmm this is supposed to make more reflect and think more... haha wonder if it works... never written a diary much less a blog... so here's my first shot at it...
FIRE!
{10:49 PM}
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