Invitation to Mathematics
主 题: Invitation to Mathematics
报告人: Prof. Kishna B. Athreya (Iowa State University)
时 间: 2011-04-29
地 点: 理科一号楼1114（数学所活动）
Consider the following three problems.
1a). An analysis professor walks from home to her office. At halfway points to where she is aiming for she changes her mind and reverses her direction. Where does this professor end up?
1b). A probability professor does the same but uses a coin toss for the decision on direction.Where does she end up?
2. . The unit ball Sn in n space is the set of all points in n space within a length of one from the origin. The length of the unit ball Sn for n=1 is 2, the area of the unit ball for n=2 is pi. The volume of Sn for n=3 is 4Pi/3 .It is thus increasing with n. What happens to the\"volume \"of Sn as n goes to infinity? (This was posed by the computer scientist Prof John Hopcroft of Cornell University).
3. Consider an old fashioned market where a seller and a buyer meet. The seller starts with a price s and the buyer offers b