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days until the end of spring semester.days until Snakes on a Plane.
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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.
Friday, February 20, 2004
13:45I generally don't link to Joanne Jacobs...
Much like at isomorphisms, the commenters revel in the ignorance of the reporter on the story, but here they reveal their own ignorance.
factoring polynomials  a fairly important operation in collegelevel math and in the mathematical sciences, but it only works well when there is a wholenumber answer.Actually, not quite. You can factor when there is a rational solution to a quadratic equation. The applications of factoring also go beyond solving quadratics: It's also important for working with rational expressions, a subject covered in Algebra I (which is hardly "collegelevel" mathematics).
Or it is possible to derive the quadratic formula by trying to apply this method to arbitrary coefficients, through several pages of algebra.Um, no, it's not possible to derive the quadratic formula using this method (finding factors p and q of ac that sum to b is not possible without specific values for a, b and c). The quadratic formula is derived by completing the square. I did this in Advanced Algebra yesterday. It's short enough that I didn't bother to write the derivation in my class notes, but to get from ax^{2}+bx+c=0 to the quadratic formula takes 6 steps.
why she's getting praised for a method that's so difficultDifficult? It's by far the simplest and easiest to teach method for factoring ax^{2}+bx+c that I've found. The quadratic formula, incidentally, is of limited use for simplifying rational expressions.
Lizzie seems to me to be FOILing backwardsUm, factoring is taking a product and writing it as a product of two factors (thus the name). So of course it's going to look as if she's FOILing backwards. The problem is figuring out how to get from the product to the factors. It's much harder than it seems.