Homework

Syllabus

Get Your Grades

Lecture: Tuesday, Thursday 1:30-2:45, in Keller 413
Instructor: Ralph Freese
      Office: 305 Keller
      Phone: 956-9367
      email: email me
      Office hours: T-Th 2:45-3:30, and by appointment

• Notes on partially ordered sets
• Lattice Drawing. On the last page of this paper are two diagrams of the lattice described in problem 51 of Chapter 4. So you just need to label each element with a permutation. Volume 3 of Knuth's The Art of Computer Programming also has a diagram.
• Computing congruences efficiently. This paper has some partition algorithms.

• Exercises on Ramsey Theory
• Proof that R(3,4) = 9

At the time of writing, even the exact value of R(5,5) is unknown, although it is known to lie between 43 and 49 (inclusive); barring a breakthrough in theory, it is probable that the exact value of R(6,6) will remain unknown forever. To quote Paul Erdős,

"Imagine an alien force, vastly more powerful than us landing on Earth and demanding the value of R(5, 5) or they will destroy our planet. In that case, we should marshal all our computers and all our mathematicians and attempt to find the value. But suppose, instead, that they asked for R(6, 6), we should attempt to destroy the aliens".

On August 2, 1876, James Butler "Wild Bill" Hickock (1837-1876) was shot and killed while playing poker in Deadwood, Dakota Territory. He was shot by Jack McCall while holding the ace of diamonds, the ace of clubs, the 8 of spades, the 8 of clubs, and queen of hearts. Since then a poker hand with two pairs, aces and eights, is called "dead man's hand."