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Lecture 5 - Mathematics and the World

Lecture 5 - Mathematics and the World - 00:39...

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Mathematics and the World  00:39 Mixed Mathematics Mixed Mathematics: included just about any field that you could think of that  focused on the quantities characteristics of things themselves  o Geometric optics (rays etc) o Mechanics (forces with masses) o Astronomy (geometric astronomy, movements of lights in the sky,  modeling etc)  o Less obvious examples: the science of music, acoustics and harmonics,  navigation, fortification (architecture etc), ballistics, artillery Mixed mathematics is not the same as applied mathematics. You develop  some mathematical theorem and then you go and apply it to some specific  subject matter. Mixed mathematics refers to the mathematics of real things.  They are not distinct from those things themselves. There isn’t mathematical  application to actual “stuff.”  o Ex. Rational mechanics: invention of appropriate mathematical techniques  and ideas, with specific reference to mechanical problems. You don’t have  pure mathematics being worked on independently and then being used to  apply to mechanic problems when appropriate. o Mixed mathematics involves quantities OF something, and therefore when  you talk about quantities of something, you have to take into account  considerations of the actual objects themselves for example when you talk  about mechanics you have to talk about mass. (properties are mixed  together with the pure mathematical ideas, arithmetic and geometry)  Probability; Statistical Probability (a mixed mathematical science) Insurance statistics, gambling games, etc.  o Pascal, Fermat, Huygens  o Jakob Bernoull Ars Conjectandi (1713) Published by the Swiss mathematicians Application of mathematical probability to human situations of  uncertainty 
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The first proper systematic theory on probability. This meant the art of  conjecturing, the book treats coin tossing and dice games as  exemplars of problems where the calculus was appropriate but the  ultimate aim of the book was to point the way toward the application of  mathematical probability towards human circumstance.
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  • Spring '09
  • DEAR
  • St. Petersburg paradox, Arbuthnot, statistical probability, Mathematical probability, underlying probability theory, Arbuthnot’s argument

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Lecture 5 - Mathematics and the World - 00:39...

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