Read Appendix A and Chapter 1.
p. 4 # 1, 2, 4; p. 517 # 1, 5;
plus the following problem
A) What is wrong with the following proof by mathematical induction?
We claim that we can show that in any room of n people all of them have the same birthday.
Step 1. Check the case n=1. This is clear.
Step 2. Show the (n-1)st case implies the nth case.
Note that if a room has n people, we can send person A out. There are (n-1) people left. By the induction assumption, each of these (n-1) people remaining must have the same birthday. Now bring person A back and send person B out. Then, by the induction assumption, person A must have the same birthday as the rest of the people in the room. So all have the same birthday!