A jigsaw puzzle is put together by successively joining pieces that fit together into blocks. A move is made each time a piece is added to a block, or when two blocks are joined. Use strong induction to prove that no matter how the moves are carried out, exactly n ? 1 moves are required to assemble a puzzle with n pieces.

Lecture 1: Statistics Info and some Basic Principles -‐ Statistics is the most important science in the whole world: for upon it depends the practical application of every other science and of every art: the one science essential to all political and social administration, all education, all organization based on experience, for it only gives results of our experience." Florence Nightingale, Statistician -‐ Statistics are numbers measured for some purpose. -‐ Statistics is a collection of procedures and principles for gathering data and analyzing information in order to help people make decisions when faced with uncertainty. -‐ Course Goal: Learn various tools for using data to gain understanding and make sound decisions about the world around us. -‐ Chapter 1 starts out with eight statistical stories with morals, presented as seven case studies. -‐ In each, data are used to make a decision, a judgment, about a situation. These case studies follow a wide range of ideas and methods and introduce a lot of statistical language. -‐ 1. Who are those speedy drivers Principle: Simple summaries of data can tell an interesting story and are easier to digest than long lists. 2. Safety in the Skies Principle: When discussing the change in the rate or risk of occurrence of something, make sure you always include baseline or base rates. 3. Did anyone ask whom you’ve been dating Principle: A representative sample of only a few thousand, or perhaps even a few hundred, can give reasonably accurate information about a population of many millions. 4. Who are those angry women Principle: An unrepresentative sample, even a large one, tells you almost nothing about the population. 5. Does prayer lower blood pressure Principle: Cause-‐and-‐effect conclusions cannot generally be made on the basis of an observational study. 6. Does Aspirins reduce heart attack rates Principle: Unlike with observational studies, cause-‐and effect conclusions can generally be made on the basis of randomized experiments. 7. Does the internet increase loneliness and depression Principle: A statistically significant finding does not necessarily have practical significance or importance. When a study reports a statistically significant finding, find out the magnitude of the relationship or difference. 8. Did your mother’s breakfast determine your sex Principle: For studies that found a relationship or difference, find out how many different things were tested. The more tests done, the more likely a statistically significant difference is a false positive that can be explained by chance. Watch out if many things are tested and only 1-‐2 of them are statistically significant.