Course webpage for Freshman Seminar 24i: Mathematical Problem Solving (Fall 2010)

If you find a mistake, omission, etc., please let me know by e-mail.

Your favorite problems or solutions
Here's a clearer picture of the background pattern...
September 1
Initial meeting:

September 13

September 20

September 27

October 4

  • The “quadrilateral inequality” encountered during the geometrical solution suggest a segue to the important technique of induction. Base case (Sn0), inductive hypothesis (Sk), inductive step (Sk implies Sk+1). Variation: “strong induction” (equivalently: apply induction to the statement
    Sn: “Sk is true for each k between n0 and n”
    rather than to Sn itself). Standard examples of induction problems: sums and and other recursions, once we've guessed the answer from the pattern of the first few examples (an important problem-solving technique in general, but beware of false trails such as
    32+42=52,   33+43+53=63,  but   34+44+54+64≠74);
    maximal number of slices of a pizza produced by n straight cuts.

    Here are some more induction problems

    [October 11: no meeting — University holiday (Columbus Day)]

    October 18 (abbreviated)