Algebra Math Games For 9Th Graders latest 2023

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Playing Games – What John Nash Was Actually Famous For

Like Chariots Of Fire did for Eric Liddell and Braveheart for William Wallace, the 2002 film A Beautiful Mind made mathematician John Forbes Nash a household name – without necessarily making his life or work much better understood. Audiences and critics have received the film well – it won an Oscar in 2004 – but enthusiasts of Nash’s work insist that even greater rewards await those who study Nash’s real work and the esoteric discipline, game theory, in which he made his name.

Born in Bluefield, West Virginia, in 1928, Nash was already performing science experiments in his bedroom when he was twelve years old. He didn’t excel at sports or other stereotypical youthful pursuits, instead focusing on ET Bell’s book Men of Mathematics with the same intensity a potential young guitarist might bring to, say, Led Zeppelin IV. . While still in high school, he took college-level math courses, and a Westinghouse scholarship to the Carnegie Institute of Technology (a school known and revered today as Carnegie Mellon) seemed to confirm his calling. mathematician – a calling only confirmed when Princeton aggressively recruited him for his doctorate. mathematics program. He completed his doctorate in 1950.

Much of his important early work – including the three scientific papers that defined and explained the trend known as “Nash equilibrium” and which (many years later) helped him win a Nobel Prize in 1994 – concerned game theory, a branch of mathematics that analyzes how people interact. Game theorists construct equations that reflect people’s supposed motivations when they enter a situation, and then analyze the range of possible actions they can take. They use mathematical modeling to determine what the actual outcomes of the situation will be then.

A logic puzzle known as the prisoner’s dilemma offers a good quick example of how basic game theory works. Imagine two prisoners arrested near the scene of a burglary and arrested by the police. The cops know they’ve found their suspects, but they can’t get anyone to admit their guilt, so they offer everyone a deal. As Michael AM Lerner, writing in Good Magazine, describes: “If they both confess and cooperate, they will both receive a five-year minor sentence. If neither man confesses, they will not get both only a year – But, and this is where it gets interesting, if one confesses and the other does not, the one who confesses gets away with it while the other will do 10 years. Are they going to trust each other and do what is obviously in their best interests, which is not to confess?” Game theorists assume that each person in this dilemma is self-free; By assigning values ​​accordingly, they come up with equations that predict that the two burglars will betray each other – even if it makes more sense to cooperate.

It might sound crazy – how on earth can something that seems as simple as math create successful predictive models of how humans will behave in a real-life situation? But mathematicians, economists and political scientists have used game theory to produce surprisingly accurate predictions. Game theorist Benito de Mesquita used his own equations to predict Ayatollah Khomeini’s successor, in 1984; when his answer proved, several years later, to be correct, he launched a career that now includes a wealthy consulting firm and several collaborations with the Pentagon. Game theory may not be without controversy, but it seems to be here to stay.

Nash’s most famous work concerns how we can assume people will behave in certain “uncooperative” games, that is, situations in which people compete against each other. He showed, in general, that there are limits to how successful people can be in competing against each other – that, unlike Adam Smith (the father of modern economics), certain types of competition tend to reduce the amount of goodies available to everyone (rather than increase the total size of the pot, as Smith is generally supposed to have taught). It was the insight for which – decades later, after his protracted struggle with schizophrenia, and together with Reinhard Selten and John Harsanyi – he won the Nobel Prize. It might not be as photogenic as Russell Crowe (who played Nash in the film), but it’s – who knows? – probably more relevant to your life.

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