just found a tortoise born in 1832 and still alive and i laughed coz i couldn't believe it
jonathan the tortoise google him. sounds like his instagram handle eh?

while being productive, see previous post, i also found catfish that looks like a cow!!!

it's real even though looks photoshop.

here's the article ok.

so i prayed for no math dreams last night and i really didn't... i had something scarier.
SHARK DREAMS. omg don't even know why. my bro, mom and i were swimming in a pool full of sharks. idk why we didn't get out. the fear was so real. some sharks my size, some sharks like.. 3 times bigger than me like a megalodon. damn scary. i woke up like.... nightmare. super scary omg.

gimme math dreams thanks. **LOL**.
2 papers tmr!!!!! and i never touch the second one. at all lololol gna read it tmr before the paper. hahahah. i also haven't rly do much japanese lolol but can't wait. tdy's paper quite hard but seemed quite hard for everybody so that's good HAHA

*lol* should be doing smth more productive but so cute right

and by productive i mean google megalodon and other interesting shark stuff *LOL*

gna do some readings (reading math btw these are my readings HAHA read tutorials etc) but anw.

sigh i have been having a lot of math dreams recently because of finals. like my mind won't stop it with the math??? i keep having a lot of math dreams its hard to explain just that the concepts are in my dream like...conditional probability etc it's very hard to explain.

eg. what i perceive the concepts i feel it in my dreams!!!

stop math dreams stop i wake up and my mind's a little tired. 1 paper down today. not too bad, could possibly get full marks. COULD. POSSIBLY. maybe not *Lol*.

Quotient groups (Work in progress post)

since I'm doing some prep for algebra, let me explain a little about quotient group and the quotient map. i encountered this in MA1100, and MA2101, but tbh i never really fully understood it. until algebra. super fun, super cool. so hopefully, i can do a good enough job of explaining it simply, such that those who like me didn't get it in MA1100 and MA2101 would not be so lost.

ok let's use this diagram to explain.

So, we start with $f:G\rightarrow H$, as shown by the top arrow. $f$ maps items from $G$ to $H$.

$f$ is surjective, could be injective or not. 

$q_{a}:G\rightarrow G/A$, maps items from $G$ to its equivalence class in $G/A$

$f_{1}: G/A \rightarrow H$ maps the equivalence classes in $G/A$ to $H$. in this case, the equivalence classes in $G/A$ are the elements. equivalence classes aka cosets. 

example (which i invented hehe, suppose all tans stays in the west, lees in the east, ngs in the south)

$G = \left \{ Tan Mark, Tan John, Lee Matthew, Ng Luke \right \}$

$H = \left \{ stay in the West, stay in the East, stay in the South \right \}$

$q_{a} = \left \{ surname Tan, surname Lee, surname Ng \right \}$

so under this map, $f:G\rightarrow H$, $f(Tan Mark)=stay in the West$, $f(Tan John)=stay in the West$, $f(Lee Matthew)=stays in the East$, $f(Ng Luke)=stays in the south$

then $q_{a}:G\rightarrow G/A$ maps each ppl to their surnames, i.e $q_{a}(Tan Mark) = surname Tan$, $q_{a}(Ng Luke) = surname Ng$ etc . this group is definitely surjective, because each element has to belong to some class, they all have a surname, so definitely surjective. 

then $f_{1}: G/A \rightarrow H$ maps surnames to where they stay for eg. wah damn tiring to type all i v tired

but it's that simple, nothing tricky about it. as prof says, "the quotient map doesn't tell u much, plus, we're not even doing much to get it. it just falls out if you stay at it hard enough. "

well there's a little more group axioms in the quotient group itself too. and isomorphism. screw it, i lazy explain now *LOL* i'm so not a dedicated math blogger *LOL*

cramps suck :(

suppose to study with joel but i'm not up for it. 

anw my bro came into my room as was like.. i want jogger pants so i threw him my pyjama pants *LOL* he put it on and went out for lunch HAHAH i rmb i told yuqi i want jogger pants too like 1 /2 years back and he bought me pyjamas HAHA its the same one i threw at my bro *lol* 

errrr... i think i messed up

i rly should blog about this. because i can laugh at this next time. but right now very emo. but a little funny in retrospect, so i think it'll be hilarious very much later.

kind of embarrassing also. no, actually very. erm.
i had some exchange interview, its like a pre-interview interview. and... i cried at the interview. er yeah. very awkward. ok because the interviewee started with some qns, then it seemed like to every single ans i gave he was shooting me down like.. quite bad. and also.. rly made me feel like my thoughts don't matter, like idk how to think?! and i also like.. huh? but i did that what... in response to his criticism. anw then the lady asked what am i gonna do with a math degree and.... i just started to cry. because my ans is I'm not sure, and i just knew that was the wrong ans and my heart sank soooooo low. but thats the truth and i'm not gonna lie. i also don't think there's anything wrong with and "idk" ans, i mean... i'm in the uni to figure that out. and i have done stuff to go in a particular direction, so i'm not useless. but idk just after that trigger i was quite emotional, like when they ask me qns tears just roll down idk for the whole interview like 1 hour plus????? crazy. then my eye v swollen. but damn stupid also dk why i cry SIGH

but i think what they said... i rly needed it. i'm confident in a fair amount of areas, but i'm not confident in saying what i wna be/do. they said that i should be sure of what i wna do NOW, because that might change in the future, we don't know. but i don't have to be sure how to get there.

sigh i still think damn stupid why i cry wahlau damn sian whole day damn emo

also have to edit my ps......

paris attacks v scary.
don't think i should blog stupid stuff.
lets be a little bit emo about the lives lost.
noo u shouldn't kill other ppl.

Aww thursday

saw something super aww first thing in the morn, on the bus. there was a bunch of kindergarten kids, and whenever buses pulled up as the bus stop, a teacher would accompany one of the students to board the bus, and hand the bus driver a card. seemed like a handmade card, and then the teacher would snap a photo of kid and driver. how cute. then they'd get off and rejoin their group. then as the bus pulled away, all the kids would start waving at the driver. how awwww.

another aww thursday... erm idk its nic's bday? haha idk what else is aww about today.
OH i did not too bad for a test! pretty well very happy yayyayayyayaya

bought cupcakes for nic and we studied and not too productive :(
but went for dinner with nic and tom as well. not too bad.

chris staples is quite nice. i am liking him more.

also funny, hahahah nic sherm and i have same dp *LOL* cute

thought of things to post. but not in the mood to extract serious thoughts. 

usually when i'm doing calculations (i.e. applied math, eg. stats/calculus computations) i will always wonder.. whats the point of all this??? coz i rly don't like calculations (but I'm good at it ok) and its so ironic *LOL* coz i'm doing pure math and i like the theory stuff and theorems and algebra 

so i had this convo with isa.

isa: i used to talk to this guy.. but his "grandma" was very bad... i mean, my "grandma's" not perfect, but his "grandma" had a lot of errors and flaws....

the whole time i was like... wth is going on?????? what grandma. *lol* turned out she meant grammar *LOL* i hear wrongly haha but damn funny