Math 645: A Survey of Mathematical Problems I
Frank Sottile

•   I am assuming that you now have the course packet.
    Consequently, I am assigning some readings that I skipped last week, starting with Stephen Maurer's discussion of recursion in mathematics, particularly at the level of school mathematics.
    Robert Louis Stevenson's short story "The Bottle Imp", with a little bit of mathematics woven into this story of human greed.
    The main reading, on "Chance and Chanceabilty" is a discussion of probability, both its philisophical underpinnings and the theory of mathematical probability. This is a subtle topic that many of us get wrong, and I do not think is so well-taught in the curriculum. While I cannot say anything about you, I remain at a loss as to what is meant in a weather forecast, when it is declared that "there is a 60% chance of showers at 9 AM", except that perhaps I should have an umbrella handy. This is to set up Chapter 2, where we go next week, after more work on Mathematical Induction.
• Reading:
  • Dr. Geller's Lecture 2.
  • Stephen Mauer,
  • Robert Louis Stevenson's short story "The Bottle Imp",
  • Chapter VII of "Mathematics and the Imagination" on "Chance and Chanceability", (the last three are from the course packet)
  • Chapter 1 of A Survey of Mathematical Problems.
• Assignment: Due Monday, 10 September at 23:59. (HW 2) To hand in: Email a .pdf toTaylor Brysiewicz tbrysiewicz@math.tamu.edu.
  1. What Mathematical Principle that underlies Induction is on display in the "The Bottle Imp"? Explain this.
  2. Exercises 1.8 – 1.15 and Problems 1.3 and 1.5.