An explorer is trying to reach the Holy Grail, which she believes is located in a desert shrine d days walk from the nearest oasis. In the desert heat, the explorer must drink continuously. She can carry at most 1 gallon of water, which is enough for 1 day. However, she is free to create water caches out in the desert. For example, if the shrine were 2/3 of day's walk into the desert, then she could recover
1 Induction Recall the principle of induction: Principle of Induction. Let P(n) be a predicate. If ·P(0) is true,an for all nE N, P(n) implies P(n+1), then P(n) is true for all nE N As an example let's try to find a simple expression equal to the following sum and then use induction to prove our guess correct 1·2+2·3+3:4+…+n·(mn+1) To help find an equivalent expression, we could try evaluating the sum for some small n and(with the help of a computer) some larger n sum
Lecture 3: Degradable Materials with Biological Recognition Last time: Theory of hydrolytic polymer erosion Enzymatic degradation of polymers Designing Biodegradable Macromolecules Today: Biological recognition in vivo Engineering biological recognition of biomaterials: cell adhesion/migration Reading: S.E. Sakiyama-Elbert and J.A. Hubbell, 'Functional Biomaterials: Design of Novel
I. Preparation Warm-up Activities 1. Pair Work: Talk with your neighbor about someone you love most. Words you may refer to: considerate patient a great helper generous housework hard-working point out one's mistakes a good cook encouraging tender honest gentle respectable easy to get along with a good listener kind caring
