Measure Theory Interblog

Goldbach Conjecture:

Every even integer greater than 2 can be written as the sum of 2 primes.

Jeff’s Theorem:

Every even integer n can be written as the sum of n/2 primes.

Proof:

Let p1 = p2 = p3 = … = p(n/2) = 2

I am done tutoring for the year. In my last tutoring session (for calculus):

“Ok, so when you do … what’s that called again?”

“Um, differentiation”

People I tutor ask me this. And I tell them that usually when I go shopping for groceries and I’m trying to figure out how much tax I’m going to have to pay, I use Lagrange Multipliers and Double Integrals.

But, actually, you can use math to avoid problems like this.

I notice that (especially around exam time) the number of times a person’s mechanical pencil breaks during a tutoring session is usually proportional to their stress level. A few years ago I tutored a guy and a girl together and their pencils broke a combined 15 times during the hour. Which was a lot. Until last night. One girl’s pencil broke upwards of 25 times. There was a 20 second block where it broke three times alone.

Sometimes when I’m tutoring and someone keeps making mistakes (especially small, stupid mistakes that they usually know better), I tell them that they’re probably just having a bad day. This is the exchange that took place:

Me: You’re probably just having a bad day

Student: You say that EVERY weekend!!

My one student has their own names for each of the topics we’ve covered in Calculus. She calls partial fractions “the thing with the A’s and B’s.” We were going through a practice exam and came to a partial fractions question. She didn’t recognize what she needed to use for it. So, I wrote down: (8x - 30)/x(x-3) = A/x + B/(x-3).  And she said, “OH!! Is this the thing with the A’s and B’s?” (meaning “Is this partial fractions?”), which would have been a more profound statement if I hadn’t already written down an equation involving A’s and B’s.

So, I’m tutoring someone in triginometry. And they need to find sin(45). At first, they wanted to use the sine curve, but then I said that it would be too hard to read off of it and theyd need to use one of the special triangles. So, this is an image I made in Microsoft Paint to depict what they drew:

Usually, even if there’s a few mistakes in what they write, I try and work with it and say “Well, _____ is a little off, but that’s ok, you can just….” and I go on to explain how they can still use what they put. This time, however, I just said “Well….um….what you put is actually wrong……on many, many levels.”

When I tutor close to exam time (i.e. now), I try to get the students to actually solve the problems themselves (as opposed to having them watch me like they always do). Something I’ve noticed, if they write down a step, I usually say “yep…” to acknowledge that they’re on the right track. However, sometimes I’ll say “ok…” This completely throws them off. They think I’m saying “ok…” instead of “yep…” so that they continue, realize the error, and correct it. While it turns out that this is actually usually true, it’s funny seeing them trying to find what is wrong when there’s nothing to be found. Also, occasionally, I just say “ok…” instead of “yep…” when they do the right step. But they think I’m trying to say that they made a mistake. Hilarity ensues.

Me: “And so, we sub in 1 function and then 0 to get e to the negative 1 minus e to the 0 which is one over e minus 1″

Student: “How did you get the e to the zero. I get e to the negative zero.”

Yeah, she said negative zero.

Holy crap.

You know that scene in Jurassic Park where there’s a velocirapt that comes across some poor mammal. And the velociraptor tears it to shreds and then devours it.

The velociraptor represents the exam I just wrote. And I’m the poor mammal.

And, in another example of my body making things go from bad to weird, my stomach decided it was going to make noises throughout the exam reminicent of the mating call of a wild antelope.

One down, three to go.