### exam prep

MSLC (Math & Stix Learning Center)

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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son of daadd

MSLC (Math & Stix Learning Center)

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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December 3, 2010 at 4:33 am

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).