Transcript Here - Millersville University

Delaware Valley University
November 14, 2015
An Interesting Mixture:
Incorporating Statistical History
into a
History of Mathematics Course
Kevin S. Robinson, PhD
Millersville University of Pennsylvania
INVITATION TO PRESENT …
From - Ximena Catepillan, Ph.D. Professor
When - Fall 2014, Spring 2015 – One Day Presentation
Course - MATH 301/603 credits 3.0
History of Mathematics
Course Description:
The progression of mathematical concepts in the context of the thought and civilization of
the time, from the Babylonians to the 20th century. Focus on the contributions of the
Hellenic and Alexandrian Greeks as a point of departure for the evolution of geometry,
number theory, analysis and logic. Proofs of some of the great theorems.
Prereq: COMM 100, ENGL 110, MATH 151 or 156 or 161 or 163, and junior status.
General Education - Perspectives Course: interdisciplinary and/or multicultural course.
to apply analytical and critical thinking abilities in resolving major social,
cultural, scientific/technological and/or aesthetic problems.
PRELIMINARIES
Readings:
1) Read Math Through The Ages
Chapter 21 what's in a game - the start of probability theory
Chapter 22 making sense of data - statistics becomes a science
2)Read 2 Articles:
Polling, Polling, Polling – November 2008 Devlin's Angle by Keith Devlin
Significance,
December 2012
PRELIMINARIES
Grappling:
RED vs. BLUE
Does uniform color give athletes an advantage over their competitors? To
investigate this question, Hill and Barton (Nature, 2005) examined the records in
the 2004 Olympic Games for four combat sports: boxing, tae kwon do, GrecoRoman wrestling, and freestyle wrestling.
Competitors in these sports were randomly assigned to wear either a red or a blue
uniform. The researchers investigated whether competitors wearing one color won
significantly more often than those wearing the other color. They analyzed results
for a total of 457 matches. The researchers found that the competitor wearing red
defeated the competitor wearing blue in 248 matches, and the competitor wearing
blue emerged as the winner in 209 matches. The skeptics claim this is ridiculous
saying that nothing is going on - The researchers claim that something is going on …
What is the thought process of the skeptics?, What is the argument of the skeptics?
What is the thought process of the researchers?, What is the argument of the researchers?
What is/are the crucial assumption(s) for the skeptics/researchers?
PRESENTATION
IN-CLASS – 75 Minutes
Discuss Preliminaries … Highlight: DATA – CHANCE – UNCERTAINTY …
Demonstrations – Active, Participation … Coin (two-headed), Die (unfair), …
Motivation of DATA …
Motivation of Probability,
Modeling Randomness …
Motivation of Decisions and Estimating
in the Face of Uncertainty …
Presentation of Statistical Development Timeline … (Example Slides Follow …)
Girolamo Cardano lived from 1501 to 1576, Italy
Cool Fact:
consulted by Leonardo da Vinci on questions of geometry
In addition to Cardano's major contributions to algebra he also made important
contributions to probability, hydrodynamics, mechanics and geology. His book Liber de
Ludo Aleae was published in 1663 but the book on games of chance was probably
completed by 1563.
Cardano makes the first ever foray into the, until then untouched, realm of probability
theory. It is the first study of things such as dice rolling, based on the premise that there are
fundamental scientific principles governing the likelihood of achieving the elusive 'double
six', outside of mere luck or chance.
Normal Distribution (1808)
Carl Friedrich Gauss
&
Pierre-Simon Laplace
A very readable article about the Normal Distribution: http://tinyurl.com/normal-ksr
Misconception:
Something is “wrong” if the distribution is non-normal ...
Often, distributions other than the normal
are more appropriate for a given set of data.
Normality is a myth;
there never has, and never will be, a normal distribution.
Roy C. Geary (1896 - 1983)
Roy C. Geary was undoubtedly the most eminent Irish
statistician and economist of the twentieth century.
Sir Ronald Aylmer Fisher - 1890 to 1962 - English
a genius who almost single-handedly created
the foundations for modern statistical science
&
the greatest biologist since Darwin
… important contributions to statistics, include
the analysis of variance (ANOVA),
method of maximum likelihood,
experimental design.
Cool Fact:
Fisher had poor eyesight, which made reading difficult;
so he learned through listening to others read aloud to
him. He started out studying mathematics (and excelling
at it) but began to focus on statistics because of his
interest in evolutionary theory.
RESOURCE – Timeline of Statistics
Download Here: http://tinyurl.com/timeline-stat
FOLLOW-UP ASSIGNMENT
Part 1
From the timeline of statistics –
select an individual (bubble) not covered in class and create a PowerPoint slide.
Provide additional information that is not on the timeline of statistics –
be creative, be investigative, …
Email the PowerPoint slide (as attachment) to [email protected] –
place STAT HIST in the subject line.
FOLLOW-UP ASSIGNMENT
Part 2
Do voters make judgments about political candidates based on his/her facial
appearance? Can you correctly predict the outcome of an election, more often than
not, simply by choosing the candidate whose face is judged to be more competentlooking? Researchers investigated this question in a study published in Science
(Todorov, Mandisodka, Goren, and Hall, 2005). Participants were shown pictures of
two candidates and asked who has the more competent looking face. Researchers
then predicted the winner to be the candidate whose face was judged to look more
competent by most of the participants. For the 32 U.S. Senate races in 2004, this
method predicted the winner correctly in 23 of them. The skeptics claim this is
ridiculous that nothing is here - The researchers claim that something is here.
a) What is the thought process of the skeptics? …
b) What is the thought process of the researchers? …
Include your responses to a) and b) in your email to [email protected]
– place STAT HIST in the subject line.
http://sites.millersville.edu/krobinson/STATHIST/
•Presentation (PowerPoint) - EPaDel MAA November 2015
•Presentation (PowerPoint) - DATA, DECISIONS, UNCERTAINTY -- A HISTORY
•Preliminaries (PDF)
•Follow-Up (PDF)
•Timeline of Statistics Information