Lecture 5 - Mathematics and the World

Lecture 5 - Mathematics and the World - Mathematics and the...

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Unformatted text preview: 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 isnt mathematical application to actual stuff. o Ex. Rational mechanics: invention of appropriate mathematical techniques and ideas, with specific reference to mechanical problems. You dont 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 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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This note was uploaded on 09/30/2009 for the course STS 2821 taught by Professor Dear during the Spring '09 term at Cornell University (Engineering School).

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Lecture 5 - Mathematics and the World - Mathematics and the...

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