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Consortium for Mathematics and its Applications

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Chloroform Alert! (ILAP)

AAA Chemical Inc. operates two chemical plants in the town of Bayou St. Edwards, home of Dixieland State University. New pollution monitoring equipment has shown elevated concentrations of chloroform in the air over the university. These concentrations...

Tuition Prepayment Plan (ILAP)

You have heard about the South Carolina Tuition Prepayment Program (SCTPP) (htpp://www.scgrad.org), but you wonder if it is a good deal. It allows you to prepay your daughter's college tuition and guarantee payment to attend any South Carolina public...

Reed-Solomon Codes: A Tutorial and a Java Toolbox

Introduction to Coding Theory A code is a set of messages, called codewords, that can be transmitted between two parties. One form that codewords can take is of bitstrings (i.e., strings of 0s and 1s), as in Reed-Muller and Hamming codes. A notable use...

Universal Language: Role for Mathematics

Introduction While relatively few people (just a million or two) in our world of more than six billion people actually know the language of Esperanto, many people realize that it is an attempt to establish an international language- one of many such...

Searching for Text in Vector Space

Introduction Submitting a query to a search engine is a common method of information retrieval. Companies compete to be listed high in the rankings returned by a search engine. In fact, some companies' business is to help raise the rankings of a paying...

Biomath Genetic Inversion

This-and other BioMath Modules under development-arose from a conference in April, 2005, held at the Center for Discrete Mathematics and Theoretical Computer Science (DIMACS) at Rutgers University, organized by Fred Roberts and Margaret Cozzens (both...

Biomath Evolution by Substitution

This-and other BioMath Modules under development-arose from a conference in April, 2005, held at the Center for Discrete Mathematics and Theoretical Computer Science (DIMACS) at Rutgers University, organized by Fred Roberts and Margaret Cozzens (both...

Biomath Imperfect Testing

This-and other BioMath Modules under development-arose from a conference in April, 2005, held at the Center for Discrete Mathematics and Theoretical Computer Science (DIMACS) at Rutgers University, organized by Fred Roberts and Margaret Cozzens (both...

The Mathematical Sorting Hat

Introduction The most well-known matching problem in recent popular culture is in J.K. Rowling's Harry Potter series [Rowling 1998]. Each year, roughly 40 new first-year students at Hogwarts School ofWitchcraft andWizardry are assigned to one of the...

The CWS Model of Alzheimer's Disease

Alzheimer Disease (AD) is the most common form of dementia and the sixth leading cause of death in America. Currently there is no cure. Alzheimer's involves a debilitating loss of brain function that affects memory, thinking, and behavior. Harry Johns,...

Cutting Diagnostic Tests by Half

Abstract We propose a protocol for Bayesian Differential Diagnosis (BDD) that cuts the average number of diagnostic tests by half. Introduction In the television series House, the eponymous protagonist constantly demands that his protégés perform...

21st-Century Problems

Introduction We have put people on the moon, eradicated smallpox, increased food production to feed a burgeoning world population, and developed transportation and communication systems that connect the world. However, most of the really large problems...

Mr. Markov Tours Candy Land

Introduction Candy Land TM is a classic children's board game marketed in 1945 by Milton Bradley, now owned by Hasbro. Each player follows a multi-colored path through Candy Land TM to reach the Candy Castle, with each move determined by the draw of...

You Only Need a Bit of Luck To Win MTVs Are You the One?

Introduction Are You the One? is an MTV reality show in which a cast of single women and single men try to discover their "perfect" opposite-sex matches within the cast and earn money for doing so. MTV claims to use an extensive match-making process to...

Optimizing Disaster Relief From a Navy Aircraft Carrier

Abstract We discuss maximizing delivery of aid from an aircraft carrier to people in an area hit by a disaster, such as an earthquake, a hurricane, or a tsunami. We propose a diffusion model for the movement of critical supplies once they are delivered...

Fish Allocation KKT to the Rescue

Abstract We solve an actual practical problem for a fish farm. We model the problem as an inequality-constrained profit-optimization problem that includes a nonstandard smallest-order constraint. Both the Karush-Kuhn-Tucker (KKT) theorem and software...

Alice in E-Voterland

Introduction Early in February 2019, the Swiss postal authority announced a challenge: for four weeks, starting later that month, all interested parties would be welcome to take part in a so-called "intrusion test" of their proposed electronic voting...

Modeling CO2 Concentration

Introduction One consequence of the COVID-19 pandemic was an increase in interest in the ventilation of buildings. One way of gathering information about ventilation is to monitor the carbon dioxide (CO2) level of a room [CDC 2023]. Maintaining proper...