2007-05-07
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1. Turn in your homework

2. Hand back projects -- say a few words:
    a. many got bad "grades" because they were very incomplete. 
    b. Next draft due Friday, May 18 (Friday after next).
    c. Every proof should be:
       1) clear and comprehensible
       2) have at least one illustrative example, to convince
          somebody it's true without the proof.  E.g., convince
          both the logicians and the scientists in each case.
    d. Reference format -- I don't care much, as long as 
       it's crystal clear how I can find the source you are
       referencing. 
    e. Every paper should have some nontrivial number theoretic
       arguments, and they shouldn't be just copied from the
       Math 480 textbook.

3. Basics of continued fractions:
   a. Defn of simple cont fraction
   b. Defn of partial convergents
   c. Defn of pn, qn and that they are the partial convergents
   d. Relations that pn, qn satisfy
   e. pn / qn in lowest terms
   f. every rational number is a continued fraction
   g. convergents bounce

4. Next time: continued fractions of real numbers like e, pi, golden
   ratio, etc.