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8/9/2019 Week 14 Notes

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Biographies

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1605 Kepler discovers first law of planetary motion.

1609 Galileo develops his first telescope.

1624 William Oughtred invents a slide rule.

1636 W. Gascoigne invents the micrometer.

1642 Frenchmen, Blaise Pascal invents an adding 

machine.

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By the end of the 17th century, a scientificrevolution had occurred and science had become

an established mathematical, mechanical, and

empirical body of knowledge.

 

Galileo Galilei, René Descartes, Blaise Pascal, IsaacNewton, and others had become noted scientists.

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1704 Isaac Newton publishes Opticks

1712 Brook Taylor develops Taylor's series

1733 Geralamo Saccheri studies what geometry

would be like if Euclid's fifth postulate were false

1750 Thomas Wright discusses galaxies and the

shape of the Milky Way

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1752 Benjamin Franklin shows that lightning is

electricity.

1788 Joseph Lagrange presents his equations of motion in Mechanique Analytique.

1795 Pierre Laplace discusses Newtonian black holes

1798 Henry Cavendish measures the gravitational

constant and determines the mass of the Earth.1799

Karl Gauss proves that every polynomialequation has a solution among the complexnumbers.

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The 18th century was also part of the "The Age of Enlightenment", an historical period characterizedby a change away from traditional religious sourcesof authority, and a move towards science andrational thought.

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From http://math.ucsd.edu/~crypto/Monty/montybg.html

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From http://math.ucsd.edu/~crypto/Monty/montybg.html

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Discussion of Probability

•  Design your own dice game (similar to the one listed on page 165). Describe

the rules of the game, and describe how you would calculate the

mathematical expectation of winning.

•  How could the expected value of a game be related to the cost to play the

game?

•  What advantages became available by looking at the expected outcomes of 

events instead of just describing equally likely outcomes?

Discussion of Statistics

•  What is the relationship between data and statistics?

• How are statistics and probability related?

•  How would you design an experiment to test the fastest route by car from

Brody Hall to Hubbard Hall? How would you control for error? Does this

prove that one route is faster than the other?

o  What different designs did you use?

o  What different variables did you come up with?

o  What can you conclude?

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