# Algebra level symbolic math

• ### Cartoon: Where the ink falls

A cartoon suitable for use in teaching about various graphic displays. The cartoon is number 688 (January, 2010) from the webcomic series at xkcd.com created by Randall Munroe. Free to use in the classroom and on course web sites under a creative commons attribution-non-commercial 2.5 license.

• ### Quote: Milikan on Theory and Experiment

Science walks forward on two feet, namely theory and experiment ... Sometimes it is one foot that is put forward first, sometimes the other, but continuous progress is only made by the use of both -- by theorizing and then testing, or by finding new relations in the process of experimenting and then bringing the theoretical foot up and pushing it on beyond, and so on in unending alterations. is a quote by American physicist Robert Andrews Millikan (1868 - 1953). The quote comes from Dr. Milikan's May 23, 1924 Nobel lecture.
• ### Quote: Chew on Differences

... if the difference isn't different enough to make a difference, what's the difference? is a quote by American agricultural statistician Victor Chew (1923 - ). The quote is found in his 1980 paper "Testing differences among means: correct interpretation and some alternatives" ("HortScience" pages 467-470). The quote can be used in discussions of practical significance versus statistical significance.
• ### **Histogram Explorer

This applet is designed to allow users to explore the relationship between histograms and the most typical summary statistics. The user can choose from several types of histograms (uniform, normal, symmetric, skewed, etc.), or can create their own by manipulating the bars of the histogram. The statistics available for display are mean, median, mode, range, standard deviation, and interquartile range. Also available is a "Practice Guessing" option, in which the values of the statistics are hidden until the user has entered guesses for each value.

This java applet provides students with opportunities to visualize the Monty Hall paradox (i.e., the famous "three-door" problem often discussed in introductory statistics courses). By going through the simulation and reading the accompanying materials, students can better understand concepts related to probability, and they can also see the need to gather data in order to test theories about what might happen under particular conditions (especially since the outcome of the Monty Hall problem tends to contradict students' initial intuitions).
• ### Quote: Nightingale on Confounding

In comparing the deaths of one hospital with those of another, any statistics are justly considered absolutely valueless which do not give the ages, the sexes and the diseases of all the cases. is a quote by British nursing pioneer and statistician Florence Nightingale (1820 - 1910). The quote appears on page 59 of her 1859 book "Notes on Nursing: What It Is and What It Is Not".
• ### Quote: Cooper on The Law of Large Numbers

Oh, well, this would be one of those circumstances that people unfamiliar with the law of large numbers would call a coincidence. is a quote spoken by Sheldon Cooper (2007 - ) a character on the CBS comedy show "The Big Bang Theory" played by Jim Parsons (1973 - ). The quote occurred in Season 1 episode 4 that first aired in October, 2007.
• ### Cartoon: Random Walks

A cartoon that can be used in teaching about random walks. Cartoon by John Landers (www.landers.co.uk) based on an idea from Dennis Pearl (The Ohio State University). Free to use in the classroom and on course web sites.
• ### Cartoon: Machine Learning

A cartoon that can be used in teaching about Machine Learning estimation techniques. Cartoon by John Landers (www.landers.co.uk) based on an idea from Dennis Pearl (The Ohio State University). Free to use in the classroom and on course web sites.
• ### Cartoon: Redundancy

A cartoon that can be used in teaching about random walks. Cartoon by John Landers (www.landers.co.uk) based on an idea from Dennis Pearl (The Ohio State University). Free to use in the classroom and on course web sites. (note - in the U.K. the word "redundancy" in labor statistics refers to people who have been laid-off because their job no longer exists).