### 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.)

#### 1 Comment

1. vlorbik

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