Quote of the Day: "Mathematics -- this may surprise or shock some -- is never deductive in creation." -- Paul Halmos Objectives: The student will learn the difference between inductive reasoning and deductive reasoning. The student will prove theorems using induction. 1. Collect Homework. 2. Discuss Sigma Notation and give examples
What is the sum of the numbers from 1 to 100?Click here to learn about Gauss' answer Click here for a comic about Summation
3. Introduction to Proof By Induction
4. Discuss example from The Imp In The bottle.
5. Inductive Logic Applied to Y2K For those of you who can remember all the fuss about Y2K, here is application of Inductive reasoning to flying on the airlines. On January 1, 2000, nobody will fly because that is the first dangerous day. As a result, the system will remain untested until January 2, so nobody will fly then either, as that is now the first dangerous day. Similarly, nobody will fly on January 3, 4, 5, etc. Thus we have the end of aviation as we know it! 6. Show comic strip about proof by induction. 7. 42 Methods of Mathematical Proof 9. Assignment: p. 383 (1, 3, 4, 5, 6, 11, 13)Do #1, #2, and #3 on the worksheet |