Math 2513

Discrete Mathematical Structures

Summer 2013

American crow (Corvus Brachyrhynchos). Crows are actually classified as members of the songbird family, though you might not think of crows' calls as "songs". In fact, since the crow is thought of a rather ugly and ordinary bird, people tend to overlook what an interesting and intelligent creature it actually is. Crows are susceptible to the West Nile virus, and since the introduction of the virus to the United States in 1999, their population has dropped by an estimated 45 percent, though they are not considered to be endangered. (The virus cannot be transmitted from crows to humans.)

Instructor: John Albert
Office: PHSC 1004
Office hours: Mondays, Tuesdays, and Thursdays from 1:00 to 2:00 pm (or by appointment)
Phone: 325-3782
E-mail: jalbert@ou.edu

Announcements

  • Solutions to the third exam.
  • Review sheet for the third exam.
  • Solutions to the second exam.
  • Review sheet for the second exam.
  • First exam: solutions.
  • Review sheet for the first exam.
  • Syllabus for this course.
  • I taught this class in Fall 2012. You can find copies of the tests and homework assignments, along with some other interesting links, at the web page for that course.

    Homework

    Assignment

    Due Date

    Problems
    1 Wednesday, May 15 1.1: 12, 14, 36(b,d,f); 1.2: 19, 20, 25; 1.3: 22.
    2 Friday, May 17 1.4: 28, 32, 50, 51; 1.5: 33, 40.
    3 Monday, May 20 1.4: 62; 1.6: 19; 1.7: 17(a).
    4 Wednesday, May 22 1.8: 27, 34; 2.1: 11, 32(a); 2.2: 18(c,d), 27(a,b).
    5 Friday, May 24 Do the problems on this handout.
    6 Tuesday, May 28 2.4: 15(a,b); 29(a,b,c); 4.1: 21.
    7 Thursday, May 30 4.1: 7, 27, 40, 46.
    8 Wednesday, June 5 4.2: 2, 4, 6(a,b), 21(a,b).
    9 Friday, June 8 4.3: 3, 24, 26, 33.
    10 Tuesday, June 11 4.3: 40(e,g); 4.4: 5(b,c).
    11 Thursday, June 13 5.1: 4, 6, 18, 31.
    12 Wednesday, June 19 5.2: 7, 12, 14.
    13 Friday, June 21 6.1: 1, 7, 8, 9, 10, 11, 16, 32.
    14 Monday, June 24 6.2: 14, 34, 44.
    15 Tuesday, June 25 6.3: 12, 13, 24, 26, 40.
    16 Wednesday, June 26 9.1: 3(a,b,c,d) (skip the "antisymmetric'' question), 9.5: 1(c,d), 2, 27.

    Links

  • The six-people-at-a-party problem is discussed in this Wikipedia article. You can also try the Java applet at this page.
  • In class we randomly picked the three numbers 18, 15, and 29 (in that order) to look up in the Online Encyclopedia of Integer Sequences, to see if there is any interesting sequence in which these three numbers appear in a row. The first sequence that comes up when you search the OEIS for these numbers is number A039752, the sequence of sums of prime divisors of Ruth-Aaron numbers. There is an article by Carl Pomerance available online, "Ruth-Aaron numbers revisited", with some interesting anecdotes about these numbers. You can also read the original paper about Ruth-Aaron numbers, titled "714 and 715"; in the second column of Table 1 you'll find the numbers 18, 15, and 29 listed partway down. Ruth-Aaron numbers also play a role in the recent novel ``The Housekeeper and the Professor" by Yoko Ogawa.
  • Only 20 of the first 10,000 natural numbers are Ruth-Aaron numbers. One of them is 4191. In an eerie coincidence, 4191 is also another iconic baseball number: Ty Cobb's long unbroken record of career hits is officially 4191 (it was finally broken by Pete Rose, who got his 4192nd hit on Sept. 11, 1985). But I have to say "officially" here because there is some dispute about Cobb's actual total; some say it should really be 4189.
  • Here is a photo of Hank Aaron and Paul Erdos signing their joint baseball. (Erdos is at lower left.)
  • What might an 11-set Venn diagram look like?