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Vito Prosciutto: Teaching community college math on the road to a PhD.

Friday, October 22, 2004

17:19
Princeton Review: Cracking the GRE Math Test 

Aha, I finally figured out the difficulty with the derivative of an inverse function that was offered in the Princeton review book. I had thought that the book had offered:
(f-1)'(y0)=1/f'(y0)
But in fact, it was
(f-1)'(y0)=1/f'(x0)
Aha, and given that y0=f(x0) (or more, to the point x0=f-1(y0), then we really have
(f-1)'(y0)=1/f'(f-1(y0))
which explains why the derivative of arcsin x is actually 1/sqrt(1-x2)

Wednesday, October 20, 2004

20:23
Math GRE prep: precalculus 

Whoa, that was demoralizing. At the end of chapter 1, I scored 14/25. Where did I go wrong?
  1. Let f be a function such that f(n+1)=1-[f(n)]2 for all nonnegative integers n. Which of the following correctly expresses f(n+2) in terms of f(n)?
    Stupid algebra error. I forgot to keep careful track of exponents
  2. Which of the following best describes the graph of the equation x2+y2=2x+4y+5=0 in the x-y plane?
    Laziness. I looked at this, saw that I was going to have something that simplified to (x-u)2+(y-v)2=r2 and didn't bother to check that r2 was positive.
  3. One of the foci of the hyperbola y2=(x/a)2+1 is the point (0,sqrt(2)). Find a.
    I need to make sure that I memorize all the little details about conic sections, asymptotes and foci
  4. Which one of the following polynomials p(x) has the property that sqrt3-sqrt2 is a root of the equation p(x)=0?
    Tried to be too clever. I figured that it had to be fourth degree and tried to find the product of the roots rather than doing a substitution to turn the product into a quadratic. This is a recurring theme on some of these questions.
  5. When the polynomial p(x) is divided by x-1 it leaves a remainder of 1, and when p(x) is divided by x+1 it leaves a remainder of -1. Find the remainder when p(x) is divided by x2-1.
    Embarrassingly, I wasn't even sure where to start on this one.
  6. Given that p(x) is a real polynomial of degree <= 4 such that one can find five distinct solutions to the equation p(x)=4, what is the value of p(5).
    Another one I didn't know where to start
  7. The hyperbolic sine function, denoted sinh is defined by the equation sinh x=(ex-e-x)/2. Find a formula for sinh-1 x
    It didn't occur to me to, once I had an equation with an e2x term, an ex term and a term without e to rewrite as a quadratic using u=ex.
  8. The hyperbolic cosine function... hyperbolic tangent... find a formula for tanh-1x Having missed the previous one, there was no hope for progress here.
  9. Which one of the following is in the domain of the function f(x)=log(sin x)? You may use the fact that 11111 is just slightly greater than 353,64xπ
    A 11 B 111 C 1111 D 11,111 E None of these
    Perhaps stupid arithmetic, perhaps worse
  10. Determine the exact value of the sum Arctan 1 + Arctan 2 + Arctan 3
    I got killed by not remembering the tan a+b formula. I spent a little bit of time deriving it algebraicly before starting this post, so now I can get it if I need it.
So why post all this here, other than public self-flagellation? I'd like some more practice problems. Feel free to post them in the comments and I'll offer up solutions in future posts. Apologies for those who came here looking for teaching stuff. Not a lot of that likely in the near future.

For the searchers who show up here, I'll continue doing any problems from the comments until (at least) December 10th 2004.

Thursday, October 14, 2004

19:51
For those who are wondering 

I'm not dead, in fact, I'm actually quite a bit happier nowadays. That to me, is the clearest sign that teaching high school was probably not the correct path for me. Pretty much as soon as I got over the initial shock of losing my job, I was much happier. My wife has commented about how nice it is to have me back.

I've been working on finishing up a book on mathematical typesetting that I'd started some time ago that I'll probably self-publish. The market is small, but will likely purchase the book in sufficient quantities to net me a couple hundred dollars a month for a few years.

I'm looking at grad school options and will get applications in to six(!) schools in the next couple of months. The options are:

That last one is a bit of a long-shot: They rejected me as an undergrad. Actually, I'm expecting to get rejected by everyone but the CalStates on this go-round, but with a pure math MS and a demonstration of superior grad student abilities, I should be able to make a more creditable application next year. The CalState programs also have the advantage of leaving open the possibility of working full time while working on grad school which would be nice for the household finances.

I'll also look at taking the actuarial exam in the spring. I'll have to look for some sort of test prep as there's some stat stuff in the sample actuary exam that I don't really know (but I could easily learn in a few weeks).

Monday I re-take the general GRE (my most recent GRE score dates from the last century and is probably no longer valid), then in December, I take the Math GRE (I have the Princeton Review GRE book and have been using that to get an overview of what I need to know and review some skills. I've portioned it out so that I'll be done with the book two days before the exam and can then work through the two practice exams one day apiece before the actual test).

I've put in one application for a community college job and next week I'll be really pushing for adjunct work, but none of that is likely to make a difference between now and January, so I may do some office temp work or sell balloons or something to bring in some money in what's left of the year.

Friday, October 01, 2004

12:30
Valedictory 

That I'm writing this from home at 12.30 should be sufficient to reveal the outcome of the meeting this morning.

I'll miss the 8 kids in 6th period who actually cared about the class and whose parents told me last night that they supported me.

I'll miss the new kid who sat in the front row 3rd hour and always wanted to talk baseball. It's too bad that I didn't get a chance to try and get one of his playoff tickets from him. And I'll always laugh at his story about going to a funeral with "lots of gorgeous blue-eyed blonde-haired chicks" that he couldn't hit on because it was, well, a funeral.

And the football player in fourth hour who had a "smart day" yesterday and suddenly realized that he did get what was going on. Not just understanding what I had said, but being able to put it together to form new knowledge.

And even the loudmouth girl in fifth hour who was always a pain but also was smarter than she wanted to admit (except when it came time to take a test).

Where to now? There's a full-time position at a community college open in the spring. I'll call up about the adjunct positions at some of the other community colleges. And I'll go to monster and see if I can't find something a bit more immediate, perhaps back to IT...

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