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
3. Introduction to Proof By Induction
Click here for the sum of cubes
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. 42 Methods of Mathematical Proof
7. Assignment:
p. 383 (1, 3, 4, 5, 6, 11, 13)
Do #1, #2, and #3 on the worksheet
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