Plans for Chapter 1
                            Street Networks

Chapter objectives: Understand the basic terminology of graphs (edge, vertex,
valence, connected).  Learn about Euler circuits, what kinds of problems they
are used for, when they exist in a graph, and how to find them when they do
exist.

Day 1: (probably the second class day of the semester)
     Have students work on sheet M1a, and compare their results with the
     student(s) next to them.  Have a brief discussion on the questions at
     the bottom of the page.

     Show all of tape #2, Street Smarts.  (You may want to stop the tape and
     point out that in practice, added edges should be duplicates of existing
     edges if you're going to use the number of added edges as some measure
     of the goodness or badness of an Eulerization.  The tape botches this
     somewhat.)  If time allows, discuss problem 13 in class.  (If not, you
     may wish to assign it, or postpone assigning #11 and 12 until you
     do discuss it.)

     Assignment: read pages 5-13 (stop at proving Euler's theorem), do
                 pp. 24-26 #1, 2, 9, 11, 12

Day 2:
     Review definitions of graph, vertex, edge, connected, valence, Euler
     circuit.  Explain the meaning of Euler's theorem and give the idea of
     the proof.  Reassure the students that you're not going to expect them
     to be able to construct or regurgitate such proofs, but that the concept
     of proof is an important one.  Talk about if and only if.  Have the
     students look up "theorem" in the dictionary.

     Assignment: read pages 13-17, do p.27-32 #20, 32, 33c, 36, 42, 48.

Day 3:
     Look at examples of "good Eulerizations" in the text for rectangular
     networks (pp. 18-19) and do the 5 x 6 case on the board.  Then have the
     students work on the 4 x 6 case, and if time permits, #26b (as usual,
     encourage them to compare their solutions with those of the people 
     around them).  Discuss the solutions with the class.

     Assignment: read pages 17-22, do pp.28-32 #22,25-28 (On #28, does it
                 matter where A is?)
     Note: #28 is a variant of the famous K\"onigsberg Bridge problem, not
     mentioned in the text.