Hints to Assignment 2

Q1 Algorithm: Miller, Heeren, Hornsby, Math. Ideas. (Addison-Wesley). Sect.4.3 (p.182), see handout.

Q2

• Typo in Assignment (fixed in the online version): Cross out the incomplete sentence after the formula.


• An example of Collatz iterates:    k₁=6,    k₂=6/2=3,    k₃=3*3+1=10,    k₄=10/2=5,    k₅=5*3+1=16,    k₆=16/2=8,    k₇=8/2=4,    k₈=4/2=2,    k₉=2/2=1.


• (A famous conjecture, still unproven, asserts that ultimately the iterates of the Collatz map reduce to the periodic sequence {1,4,2,1,4,2,..} for any given positive value of k. Thus the loop in the program will always terminate.)

Q3 (Ex.2.2.6 on p.47)

See Rules on top of p.44.