lara versus the rutgers math qual, day 1

here's what i was up against and how i think i did... remember each problem's out of 10 points and 80 points over 2 days guarantees a pass, and lower scores *could* pass, but there's a freakin lot of smart 1st year students taking the test early to screw up our curve, so 80's a good goal... check it: (click on either page for a larger view)

part 1 -- 3 required questions



question 1: this one majorly bugged me for over an hour while i worked on other problems instead... then it dawned on me... if not full credit, pretty darn close

question 2: this one i started immediately, got sidetracked and came back to... colleen and i got the same answer (2 * pi / sqrt(a^2-1)), which makes me think i'll get all if not most credit on this one too

question 3: positive i did a darn good job on it immediately after starting the test... all if not most credit on it

part 2 -- choose 3 questions out of 6 possible



questions 4 and 6 i didn't even try to look at
question 7 i started to work with figuring one of them must be true and one false, but failing to come up with a counterexample to either i left it alone

question 5: clearly eisenstein's criterion on f(x+1)... however, i left
"claim: p divides sum from j = i to p-1 of (j choose i) for all 0 <= i <= p-1" with "i don't have time to finish the proof but it should follow from....."... maybe half credit on that... at least non-zero credit because i didn't tell lies, i just didn't fill in all the details

question 9: as soon as i remembered what it meant for a group to act transitively, this problem is a 5 minute easy problem... the answer is 4

question 8: i started this within 15 minutes of opening the test but it wasn't until the last 5 minutes of the 3 hour test that i realized how to fill in the missing chink in my proof... thinking 9 or 10 points :-)

saying that they're mean and only give me 8 points on each of the ones i think i aced, that's still MINIMUM mid 40s,... probably somewhere in the 50s today... which means i can do worse tomorrow, just get a couple right and *probably* still pass... good news indeed

no congratulations, because if tomorrow is a really sucky group of problems i'll be super annoyed and not want to hear any of it...

however: in conclusion, i think i did well today, so that much is good... don't talk to me until tomorrow.

i'm off to the guys' house to play pool with colleen :-)

later dudes