exam prep

\bullet MSLC (Math & Stix Learning Center)
\bullet Tim Carlson’s 366 notes for Spring ’09. Proof templates & practice problems. (I found this material very useful in creating my own version of the course.)

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  1. recent email:

    there’ll be an induction proof…
    along the lines of 10 | (11^k – 1) \forall k \in Z^+
    (ten divides “11-to-the-k, minus 1” for all positive integers k)…
    and a bunch of problems very much like those of the quiz
    we recently went over together [to wit: basic set-theory
    like the power-set (of, say, a *four* element set) and
    the cartesian product, unions, intersections, complements,
    and set-differences; a relation considered-as-set-of-ordered-pairs;
    some proofs (most importantly to me) that certain functions
    are (or or *not*) one-to-one and/or onto (note that these
    properties depend on the *domains* and *codomains* given
    [not just on the formulas)]… and a few
    never-covered-on-a-quiz-or-HW-yet problems
    devoted to compositions and inverses. you should
    be prepared to *find* (a formula for) the inverse of
    a function (given as a formula); you shouldn’t panic
    if an exponential or log is involved (these are of
    course inverses to each other; in the example
    in class i had “let f(x) = log_3(x+1); find f^{-1}”;
    the student then bangs about until they see
    (and write down) that f^{-1} (x) = (3^x) – 1;
    other than that, a few compositions
    (remember that f-circle-g means
    “first g, then f”, i.e. f-circle-g(x) = f(g(x)) etc.).
    that’s about it. tuesday or thursday night
    (your choice).




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