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Full-Text Articles in Mathematics
Oh Statistics!, Heather L. Cook
Oh Statistics!, Heather L. Cook
Journal of Humanistic Mathematics
This poem was written about statistics and the usefulness thereof.
So Long My Friend, Bryan Mcnair
So Long My Friend, Bryan Mcnair
Journal of Humanistic Mathematics
No abstract provided.
The Uncertainty Of Confidence, Michael J. Leach
The Uncertainty Of Confidence, Michael J. Leach
Journal of Humanistic Mathematics
This is a free-verse poem about the estimation of population parameters in statistical models. The spacing of words is intended to reflect uncertainty.
Mathematics Versus Statistics, Mindy B. Capaldi
Mathematics Versus Statistics, Mindy B. Capaldi
Journal of Humanistic Mathematics
Mathematics and statistics are both important and useful subjects, but the former has maintained prominence in the American education system. On the other hand, statistics is more prevalent in daily life and is an increasingly marketable subject to know. This article gives a personal history of one mathematician’s bumpy road to learning and teaching statistics. Additionally, arguments for how and why to include statistics in the K-12 and college curricula are provided.
The Battle Against Malaria: A Teachable Moment, Randy K. Schwartz
The Battle Against Malaria: A Teachable Moment, Randy K. Schwartz
Journal of Humanistic Mathematics
Malaria has been humanity’s worst public health problem throughout recorded history. Mathematical methods are needed to understand which factors are relevant to the disease and to develop counter-measures against it. This article and the accompanying exercises provide examples of those methods for use in lower- or upper-level courses dealing with probability, statistics, or population modeling. These can be used to illustrate such concepts as correlation, causation, conditional probability, and independence. The article explains how the apparent link between sickle cell trait and resistance to malaria was first verified in Uganda using the chi-squared probability distribution. It goes on to explain …
A Method For Generating Realistic Correlation Matrices, Johanna S. Hardin, Stephan Ramon Garcia, David Golan
A Method For Generating Realistic Correlation Matrices, Johanna S. Hardin, Stephan Ramon Garcia, David Golan
Pomona Faculty Publications and Research
Simulating sample correlation matrices is important in many areas of statistics. Approaches such as generating Gaussian data and finding their sample correlation matrix or generating random uniform $[-1,1]$ deviates as pairwise correlations both have drawbacks. We develop an algorithm for adding noise, in a highly controlled manner, to general correlation matrices. In many instances, our method yields results which are superior to those obtained by simply simulating Gaussian data. Moreover, we demonstrate how our general algorithm can be tailored to a number of different correlation models. Using our results with a few different applications, we show that simulating correlation matrices …
Mathematics And The Hunger Games, Michael A. Lewis
Mathematics And The Hunger Games, Michael A. Lewis
Journal of Humanistic Mathematics
The Hunger Games plot features a dystopian future in which twelve outer districts are oppressed by a centralized capital. The story focuses on the heroism of a sixteen-year-old girl named Katniss and how she tries to rise above the oppression that she experiences. It also features a special lottery and other twists that are sources of mathematical interest. This essay focuses on some of the mathematical issues raised by The Hunger Games in an effort to show that this story can be used to teach students (as well as other interested parties) some important concepts from mathematics.
Medicine, Statistics, And Education: The Inextricable Link, Katharine K. Brieger '11, Johanna S. Hardin
Medicine, Statistics, And Education: The Inextricable Link, Katharine K. Brieger '11, Johanna S. Hardin
Pomona Faculty Publications and Research
No abstract provided.
Changes Across 25 Years Of Statistics In Medicine, Johanna S. Hardin
Changes Across 25 Years Of Statistics In Medicine, Johanna S. Hardin
Pomona Faculty Publications and Research
[This piece is a series of interviews with giants in the field of medicine on their views of how statistics is changing medicine. I interviewed the editor of the New England Journal of Medicine, a preeminent doctor/researcher of lung cancer, the director of the LA County Department of Public Health, and a Harvard statistician who sits on the editorial board of the New England Journal of Medicine.]
Analyzing Dna Microarrays With Undergraduate Statisticians, Johanna S. Hardin, Laura Hoopes, Ryan Murphy '06
Analyzing Dna Microarrays With Undergraduate Statisticians, Johanna S. Hardin, Laura Hoopes, Ryan Murphy '06
Pomona Faculty Publications and Research
With advances in technology, biologists have been saddled with high dimensional data that need modern statistical methodology for analysis. DNA microarrays are able to simultaneously measure thousands of genes (and the activity of those genes) in a single sample. Biologists use microarrays to trace connections between pathways or to identify all genes that respond to a signal. The statistical tools we usually teach our undergraduates are inadequate for analyzing thousands of measurements on tens of samples. The project materials include readings on microarrays as well as computer lab activities. The topics covered include image analysis, filtering and normalization techniques, and …