Archive for December, 2010
(i couldn’t put this in a comment for this “log laws” post at f(t); too long.) it’s the old principles-versus-procedures problem. students hate general principles. i’ve had tutees pay me hundreds to supervise their homework who very clearly “tune out” whenever i try to explain what’s going in in a general way. it’s worst when [...]
here’s a long thread (at KTM) about barry garelick’s “EducationNews.org” post it isn’t the culture, stupid (with throbbing googol ad). my take? “we” can’t even *consider* getting teachers competent in math for *everyone*… and yet are committed to create (some emperor’s-clothes version of) the illusion of “equal opportunity”. so teachers committed to the “math has [...]
5. Let and again; compute a. and b. . Obviously { (0,0), (0,5), (3,0), (3, 5), (6,0), (6, 5) } and = { (0,0), (0,3), (0,6), (5,0), (5,3), (5,6) }; what’s more, almost all my students knew it on the day (typically in the form and ). it bothers me not at all that they [...]
4. Let again; compute (the power set of ). OK. First of all, that’s a “Weierstrass pay” not a script-P; typesetting is always harder than it looks. There’s a “caligraphy” font available I think. But why should I have to know or care? One curly-P looks an awful lot like another and for all I [...]
3. Let be the Universal Set (for this problem) and let , , and . Compute the given sets. (Remark: we will have shown that set difference is not associative). Again (sorry for the child’s play). A poor workman blames his tools; this doesn’t make him wrong. Obviously X – Y is (the set) {1, [...]
Very close… embarrassingly close… to the questions of the recent quiz. The “A” students obviously get pretty bored seeing the same thing over and over. And I’ll freely admit that I’ve been more or less ruined as an instructor for these (reasonably well-prepared) students by (what seems like) a lifetime of “remediating” the losers of [...]
10. Prove by induction that for all positive integers , one has . Proof: Let P(n) denote the proposition . Base Case For n = 1, we have 3|4^1 – 1; P(1) is true. Induction Step Assume for some that P(k) is true: . Then for some integer a; rewrite this as . We then [...]
8. Consider the function given by (for all positive integers ). a. Is f one-to-one? (Prove your answer.) b. Is f onto? (Prove your answer.) 9. Now consider given by (for all integers ). a. Is g one-to-one? (Prove your answer.) b. Is g onto? (Prove your answer.) 1a. The function given by f(n) = [...]
1. Let A, B, and C denote subsets of some Universal Set. Use an “element” argument to prove the set equation: . (“Let …”). 2. Let A, B, and C denote subsets of some Universal Set. Use an “algebraic” argument to prove the set equation . Do not begin your proof with the equation to [...]
1. Compute the sum: . 2. Prove by induction: . (“For every integer n greater than or equal to 1, six divides “.) 3. Prove that whenever a mod 6 = 3 and b mod 6 = 2, it is also true that ab mod 6 = 0. (Remark: this shows that the “Zero Product [...]
Owen “Vlorbik” Thomas
Open A Vein (homepage)
Math 151 posts
e-mail: vlorbik@gmail.comW'press login.
More mathy stuff by me:
Lectures Without Words (drawings mostly)
Vlorbik On Math Ed ('07—'09)
Community College Calculus (S '09)
Math 148: Precalculus (W '09)
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Listserv posts: amte (11/98—8/00)... math-teach (6/05—11/06)
