Srini Devadas and Eric Lehman Lecture Notes Induction III 1 Two Puzzles Here are two challenging puzzles. 1.1 The 9-Number Puzzle

Why do you believe that 3+3=6? Is it because your second-grade teacher, Miss Dalrymple, told you so? She might have been lying, you know Or are you trusting life experience? If you have three coconuts and someone gives you three more coconuts, then you have--ahal--six coconuts. But if that is the true basis for your belief, then why do you also believe that

1 Induction A professor brings to class a bottomless bag of assorted miniature candy bars. She offers to share in accordance with two rules. First, she numbers the students 0, 1, 2, 3, and so forth for convenient reference. Now here are the two rules:

1 Streaks someone tapping the H and t keys in a what felt like a random way?0 Nas the table of H's and T's below generated by flipping a fair coin 100 times

1 The Number-Picking Game Here is a game that you and I could play that reveals a strange property of expectation. 3, First, you think of a probability density function on the natural numbers. Your distri- bution can be absolutely anything you like. For example, you might choose a uniform distribution on 1, 2, ... 6, like the outcome of a fair die roll. Or you might choose a bi- probability, provided that,...,n. You can even give every natural number a non-zero nomial distribution on 0, 1 he sum of all probabilities is 1

1 Logic A proposition is a statement that is either true or false. Propositions can be joined by \and\, \or\, \not\, \implies\, or \if and only if\. For each of these connective, the defini- tion and notational shorthand are given in the table below. Here A and B denote arbitrary propositions

1 Case analysis The proof of a statement can sometimes be broken down into can be tackled individually 1.1 The method In order to prove a proposition P using case analysis Write, We use case analysis Identify a sequence of conditions, at least one of which must hold. (If this is not obvious, you must prove it

assets An asset is a commodity that provides a flow of services over time. +E.g. a house, or a computer. .A financial asset provides a flow of money over time -a security

在现今多元化、科技化、便利化的金融服务市场,每家银行业者莫不想找到能给予客 户最便利服务的通路,加强与客户间之互动,藉由创新的工具提升服务品质,创造客户满 意度。 由于电子科技的快速发展,传统的银行业务推展方式已开始面临科技化服务的巨大 战,计算机与电话系统的整合(Computer Telephony Integration)创造了一种全新的服务通 路,过去需要客户亲临银行办理的业务,现今只需要一支行动电话(call phone)或手提电 脑( notebook)与几个输入的动作,弹指之间即能获得银行周全的服务,因此,未来的银 行经营规模与良已不是取决于分行家数的多寡、业务人员的数量,而是谁能充分应用计 算机科技的优势,创造银行核心竞争力,并提供最适切之服务给客户,创造极大化的银行 服务价值

Hobby: reading, listening to the music, using computer, watch original American movies, shopping, walking, travelling Family: 3 members, husband, twelve year-old son