Math 645: A Survey of Mathematical Problems I
Frank Sottile

• Now that I have gotten to this part of the course, I see that we do not do any coding theory (we are skipping Section 5.3.3, as there are no readings on codes). Instead, we explore several related topics. One is very fun and quite interesting, called the game of Nim. Play this with members of your family or your students and colleagues.
• Another reading is about factoring polynomials, which a neat bit of algebra.
• Also the reading about infinite sets. Apparently the author is Stanislaw Lem, a Polish science fiction writer whom I read as a teenager. This topic, the infinite hotel, is popular with students. It is also called Hilbert's Grand Hotel, or simply the Hilbert Hotel.
• Finally, a tiny bit of deductive reasoning in Chapter 8.
• Lastly, this is the last homework of the semester. Now all you have to do is your papers. With this much time for you to work on them, I look forward to reading them.

• Reading number 29, Sue Geller's notes on factoring, and then for fun number 30 on the infinite hotel.
• Chapter 5.3.3 and 8.3.1 of A Survey of Mathematical Problems.
• Dr. Geller's Lecture 13.

1. Exercise 5.11, as well as numbers 8.1 and 8.2, and then problems 1–3 at the end of Geller's notes on factoring.