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Friday, May 2 The final exam will be cumulative, with the material since the last exam weighted somewhat more heavily. Friday, April 4 The schedule is updated with everything we've covered through today. Friday, April 4On Problem A for this week, you may assume that you have subroutines to handle common linear algebra tasks such as row-reduction, etc. Thursday, February 27Hint on p117 #5d: Let {u, v} be your favorite edge. Let U be the set of all vertices that can be sent to u by an automorphism, and V be similar for v. Show that there are no edges inside U or V. Tuesday, February 25Note that every vertex having the same degree is not sufficient for a graph to be vertex-transitive. For a counterexample, consider the disjoint union of C_{4} and C_{5}. To show the Petersen graph is vertex-transitive, you're actually going to have to exhibit automorphisms... Monday, February 24I was amused to see a graph-theoretic analysis of the role of the Ukraine in the game of Risk. The analysis is (tranlated into more formal terms) that the Ukraine vertex has high degree; and moreover that there are a large number of vertices within a walk of length 2 of Ukraine. Saturday, February 15 Here are some previous exams in upper level courses that I've taught: Monday, February 10 For Exercise 1 on p106, assume that both married couples and dancing pairs are mixed gender. Thursday, February 6 By the way: Tuesday, January 28On 6b, note that "complement" means complement among order pairs (i,j) with i<j. That is, all i < j such that \pi(i) < \pi(j) Saturday, January 25The star on problem 6ab applies to both a and b. Tuesday, January 21On the Fibonacci problem, while it is connected with a deeper result from Chapter 12.3 (and you might find this very interesting), please don't use any unproved results in solving the problem. I recommend a fairly-straightforward mathematical induction, instead! Wednesday, January 15 The first homework is now posted, as promised. Monday, January 13Welcome to MA 4143/6143! The syllabus is linked at the left. Last modified May 04, 2014 |