week 14 notes
TRANSCRIPT
8/9/2019 Week 14 Notes
http://slidepdf.com/reader/full/week-14-notes 6/24
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.
8/9/2019 Week 14 Notes
http://slidepdf.com/reader/full/week-14-notes 8/24
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.
8/9/2019 Week 14 Notes
http://slidepdf.com/reader/full/week-14-notes 9/24
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
8/9/2019 Week 14 Notes
http://slidepdf.com/reader/full/week-14-notes 10/24
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.
8/9/2019 Week 14 Notes
http://slidepdf.com/reader/full/week-14-notes 11/24
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.
8/9/2019 Week 14 Notes
http://slidepdf.com/reader/full/week-14-notes 19/24
From http://math.ucsd.edu/~crypto/Monty/montybg.html
8/9/2019 Week 14 Notes
http://slidepdf.com/reader/full/week-14-notes 20/24
From http://math.ucsd.edu/~crypto/Monty/montybg.html
8/9/2019 Week 14 Notes
http://slidepdf.com/reader/full/week-14-notes 21/24
8/9/2019 Week 14 Notes
http://slidepdf.com/reader/full/week-14-notes 23/24
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?