Projects
days until the end of spring semester.days until Snakes on a Plane.
Boxes unpacked
Math article project
Finished mathematical core of article. Next: Write analytical core of article.
Dummit and Foote, Abstract Algebra
Finished section 1.6 (86 to go)
Silverman and Tate, Rational Points on Elliptic Curves
FInished 2.5 (31 to go)
Conway, Functions of One Complex Variable I
Finished section 7.5 (27 to go)
Munkres, Topology
Finished section 21 (60 to go)
Royden, Real Analysis
Finished section 2.4 (97 to go)
Nonfiction book project
Todo list uptodate
Fiction book project
1443 out of 100,000 projected words written.
Top 100 novels of all time
Reading Ulysses
IMDB top 250 films
Tengoku to jigoku next in queue.
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Vito Prosciutto: Teaching community college math on the road to a PhD.
Wednesday, October 20, 2004
20:23Math GRE prep: precalculus
 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  Which of the following best describes the graph of the equation x^{2}+y^{2}=2x+4y+5=0 in the xy plane?
Laziness. I looked at this, saw that I was going to have something that simplified to (xu)^{2}+(yv)^{2}=r^{2} and didn't bother to check that r^{2} was positive.  One of the foci of the hyperbola y^{2}=(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  Which one of the following polynomials p(x) has the property that sqrt3sqrt2 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.  When the polynomial p(x) is divided by x1 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 x^{2}1.
Embarrassingly, I wasn't even sure where to start on this one.  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  The hyperbolic sine function, denoted sinh is defined by the equation sinh x=(e^{x}e^{x})/2. Find a formula for sinh^{1} x
It didn't occur to me to, once I had an equation with an e^{2x} term, an e^{x} term and a term without e to rewrite as a quadratic using u=e^{x}.  The hyperbolic cosine function... hyperbolic tangent... find a formula for tanh^{1}x
Having missed the previous one, there was no hope for progress here.
 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  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.
For the searchers who show up here, I'll continue doing any problems from the comments until (at least) December 10th 2004.