Mathematics Commons^™

Using Calculus To Model The Growth Of L. Plantarum Bacteria, Erin Carey

Undergraduate Journal of Mathematical Modeling: One + Two

Experimental data for the growth of Lactobacillus plantarum bacteria have been obtained over time, creating the need for mathematical means to model this data. We use the Gompertz model because it is a sigmoid function for a time series, where growth is slowest at the start and end of a time period. The Gompertz model is especially useful because it defines specific parameters that characterize the S-shaped curve. In addition, the Gompertz model uses relative growth, which is the logarithm of the given population compared to the initial population. This reflects the fact that bacteria grow exponentially. The important parameters …

Detecting Edges, Sam Maniscalo

Undergraduate Journal of Mathematical Modeling: One + Two

In human vision the first level of processing is edge detection. Edges are determined by the transitions from dark points to bright points in an image. For this paper, we consider an edge profile model representing a boundary or edge in an image. From this model we can determine the strength of the edge, the width of the edge, and either the transition from dark to bright to dark or the transition from bright to dark to bright. Our first step was to take the given edge profile and determine the type of edge that is represented and the characteristics …

Determination Of Azeotropy, Kyle Cogswell

Undergraduate Journal of Mathematical Modeling: One + Two

The ultimate goal of this paper is the determination of an azeotrope within a methanol-acetone system. An azeotrope is the point in a chemical system at which coexisting compositions of vapor and liquid phases are equal. The importance of this point lies in the fact that azeotropes are undesirable; they prevent one from completely separating a mixture through distillation. This state can occur over a range of temperatures and for the purposes of this paper there is only one azeotrope for each given temperature. All azeotropes occur at relative extrema in pressure. By finding these extrema, we find the mole …

Infection Of A Homogeneous Population By A Known Bacterium, Arthur Maknenko

Undergraduate Journal of Mathematical Modeling: One + Two

In order for the development of antibiotics and vaccines to be successful, the lifecycle and infection pattern of a pathogen must be studied well. In this paper, we study the rate of replication and the pattern of infection in a homogeneous population, which may or may not have an effective immunity or immunization program against the pathogen. We utilize three functions: one will determine the rate with which the pathogen replicates; the second will show the result of an infection by a single individual of a susceptible population without a removal rate; and the third will include the removal rate …

2009 Ford Mustang Performance Test, Daniel Fernandes

Undergraduate Journal of Mathematical Modeling: One + Two

Our goal is to find the time required for a 2009 Ford Mustang to accelerate from rest to 88 feet per second. We begin with three equations involving force, velocity, and force inverse, which is a value derived from Newton's Law, F=ma. The Mustang has three gears with three different gear ratios that must be used as the car accelerates. We found results from 2000 to 6000 RPMs for all three gears. Once the force inverse was found, we plotted the force inverse vs. velocity graph. The area beneath this curve from 0 to 88 feet per second is the …

Modulus Of Subgrade Reaction And Deflection, Austin Potts

Undergraduate Journal of Mathematical Modeling: One + Two

Differential equations govern the bending and deflection of roads under a concentrated load. Identifying critical parameters, such as the maximum deflection and maximum bending moments of a street supported by an elastic subgrade, is key to designing safe and reliable roadways. This project solves the underlying differential equation in pavement deflection and tests various parameters to highlight the importance in selecting proper foundation materials.

That's A Drag: The Effects Of Drag Forces, Shane Maxemow

Undergraduate Journal of Mathematical Modeling: One + Two

Drag is a force that opposes motion due to an object's shape, material, and speed. This project defined what drag force is, derived the governing equation for drag and listed some applications of drag forces. Derivation of the drag equation was achieved using the Buckingham π theorem, a dimensional analysis tool. Lastly, this project explored the problem of how long and how far a dragster takes to stop once its parachute is deployed.

Biodiversity In A Florida Sandhill Ecosystem, Samantha Robertson

Undergraduate Journal of Mathematical Modeling: One + Two

This project compares two transects of land in the University of South Florida's Botanical Gardens for their biodiversity. The transects were chosen to represent a Florida sandhill ecosystem and the individual Longleaf Pine, Saw Palmetto, Turkey Oak, Laurel Oak and Live Oak specimens were counted. All other species above waist height were counted as "other"?. Once the individuals were counted, the Simpson's and Shannon-Wiener indices were calculated. Since the Shannon-Wiener index incorporates several diversity characteristics, it is typically more reliable than Simpson's. However, both biodiversity indices agreed that transect B was more diverse than transect A.

Repeatability Estimates Of Sloped Scattered Data, Angelique Waller

Undergraduate Journal of Mathematical Modeling: One + Two

Repeatability is the variance in data accumulated under fixed conditions. It is important for quality control as it costs both time and money to recalibrate tools and remanufacture machines. This project compares three methods for approximating the repeatability of a sloped scattered data set. The first method uses a linear approximation, the second involves rotating the data points, and the third calculates distance using right triangles. The methods are compared for both precision and ease of use.

Robotics Potential Fields, Jordi Lucero

Undergraduate Journal of Mathematical Modeling: One + Two

This problem was to calculate the path a robot would take to navigate an obstacle field and get to its goal. Three obstacles were given as negative potential fields which the robot avoided, and a goal was given a positive potential field that attracted the robot. The robot decided each step based on its distance, angle, and influence from every object. After each step, the robot recalculated and determined its next step until it reached its goal. The robot's calculations and steps were simulated with Microsoft Excel.

Arsenic And Growth Of Amphistegina Gibbosa, Elise Keister

Undergraduate Journal of Mathematical Modeling: One + Two

A laboratory tested various concentrations of arsenic on the growth of foraminifera and recorded their findings. Upon examination, the plotted probability density function for each of these trials resembled a similar shape. The plots were then characterized in a general model composed of linear segments. Using calculus, statistics such as the expected value, variance and standard deviation were calculated to interpret the collected data. The statistics revealed that arsenic limits the growth of ocean life.

Call Forecasting For Inbound Call Center, Peter Vinje

Undergraduate Journal of Mathematical Modeling: One + Two

In a scenario of inbound call center customer service, the ability to forecast calls is a key element and advantage. By forecasting the correct number of calls a company can predict staffing needs, meet service level requirements, improve customer satisfaction, and benefit from many other optimizations. This project will show how elementary statistics can be used to predict calls for a specific company, forecast the rate at which calls are increasing/decreasing, and determine if the calls may stop at some point.

Transportation Of Machinery Through A Confined Space, Diana Atwood

Undergraduate Journal of Mathematical Modeling: One + Two

Our goal in this paper is to determine whether a packaging machine of negligible width will fit through a hallway and into a certain room (see page 4 for comments about negligible width). Given the width of the hallway and the room, we apply calculus to find the minimum length available between the two. We determine that the machine will successfully fit into the room.

Buoy Dynamics In Subsurface Zones, Randy Guillen

Undergraduate Journal of Mathematical Modeling: One + Two

The objective of this paper is to find the tension acting on a line that anchors a buoy submerged just beneath the surface of the ocean. Since the problem statement only gives the geometric shapes and dimensions of the buoy, we must use calculus to find its volume and surface area through integration of the volumes and surfaces of revolution formed by the specific parts of the buoy along an axis. The volume and surface area determine the buoyancy force and force of gravity, the two forces acting on the buoy that affect the tension in the line. After calculating …

Reconstruction Of Brooksville Ridge Cave Temperatures From Speleothem Samples, Amor Elder

Undergraduate Journal of Mathematical Modeling: One + Two

A problem was proposed to use an adjusted version of Dorale's speleothem delta function to model the temperature fluctuations in the Brooksville Ridge Cave from the Medieval Warm Period to the present. The temperature values reconstructed by the model can be compared to the known temperature trend during the same selected time period. If the results matched the trend, it indicates that the cave's temperature was the dominant influence. If not, a different variable was the main influence of the cave.

Using δ¹⁸O values gathered from a speleothem, past temperatures of the cave were modeled. Results show that …

Calculating Power Of A Co2 Compressor, Jennifer Wedebrock

Undergraduate Journal of Mathematical Modeling: One + Two

In this project the goal is to find the power of a CO₂ compressor used in a process of storing CO₂ underground. Although the compressor is not 100% efficient and does not exist under ideal conditions, the power can first be calculated as if it were under ideal conditions by calculating its enthalpy and entropy. Residual terms are then added to both the enthalpy and the entropy to account for the behavior of CO₂ under non-ideal conditions. Since the sum of the change in entropy under ideal conditions and the residual terms for entropy is zero, a …

Parts Of The Whole: Teachers And The Work They Do, Dorothy Wallace

Numeracy

This introductory column argues the need to study our system of education with the same care we would give any complex system, pointing out some ways in which the educational system functions differently from other managed systems, and concluding that a careful study of the forces shaping education will lead to insight into what makes educational change successful.

Review Of Quantitative Reasoning: Tools For Today's Informed Citizen By A. Sevilla And K. Somers, Aaron G. Montgomery

Numeracy

Alicia Sevilla and Kay Somers, Quantitative Reasoning: Tools for Today’s Informed Citizen. (Emeryville CA: Key College Publishing, 2007). 626 pp. Softcover with Student CD. $79.95 (USA) ISBN 1-931914-90-1. http://www.keycollege.com/catalog/titles/quantitative_reasoning.html

From charts and graphs (Topic 1) to decision making (Topic 21), Quantitative Reasoning offers a good selection of topics that students in a general education mathematics course and other individuals in our society should understand. Organizing the 21 chapters (topics) under the headings of numerical reasoning, logical reasoning, and statistical reasoning, Sevilla and Somers focus their chapters on examples and devote the last 224 pages to 21 Excel activities. Parallel graphic-calculator …

Word Problems: Reflections On Embedding Quantitative Literacy In A Calculus Course, Gizem Karaali

Numeracy

Even though Quantitative Literacy (QL) programs are currently being developed and implemented in several colleges and universities, most schools still depend on traditional mathematics courses to reach their quantitative literacy goals. This note is a case study of how a traditional mathematics course sequence intended for students majoring in social and life sciences may be modified and adapted to at least partially fulfill the need in the absence of a stand-alone QL program. In particular, we focus on a freshman-level mathematics course sequence that serves various client departments. This sequence covers the traditional content of a first-year calculus sequence along …

False Positives And Referral Bias: Content For A Quantitative Literacy Course, Stuart Boersma, Teri Willard

Numeracy

An extended study of accuracy in medical screening is presented as a useful application to increase students’ quantitative reasoning skills. Two detailed examples are presented. The first explores the frequency of obtaining false positive results from a medical screening tool while the second examines the issue of referral bias and its effect on the apparent sensitivity and specificity of the screening tool. Results from student assessments indicate that the activity increases one’s ability to define terms such as “false positive” and “false negative” and increases one’s ability to read and compute with information obtained from a two-way table. Teacher assessment …

Using Local Data To Advance Quantitative Literacy, Stephen Sweet, Susanne Morgan, Danette Ifert Johnson

Numeracy

In this article we consider the application of local data as a means of advancing quantitative literacy. We illustrate the use of three different sources of local data: institutional data, Census data, and the National College Health Assessment survey. Our learning modules are applied in courses in sociology and communication, but the strategy of using local data can be integrated beyond these disciplinary boundaries. We demonstrate how these data can be used to stimulate student interests in class discussion, advance analytic skills, as well as develop capacities in written and verbal communication. We conclude by considering concerns that may influence …

Quantitative Literacy Across The Curriculum: A Case Study, Benjamin Steele, Semra Kiliç-Bahi

Numeracy

We describe a quantitative literacy (QL) program at Colby-Sawyer College, a small, residential, liberal arts college in New Hampshire. This program has grown rapidly from a traditional math curriculum to a college-wide understanding of quantitative literacy and voluntary participation by many faculty members in all departments. More than 80% of the faculty agreed that it would be useful for students to be able to use quantitative skills in their courses, but only 24 % thought students were capable of doing very well in mathematics. Twenty-three faculty members attended a summer workshop, funded by NSF, DUE # 0633133, in which they …

Quantitative Literacy On The Web Of Science, 1: The Bibliography And Its Role In The History Of This Journal, H L. Vacher, Todd Chavez

Numeracy

Prior to deciding to propose in 2006 that the National Numeracy Network (NNN) publish a new journal for quantitative literacy with their support, the University of South Florida Libraries investigated the publication environment of the field on the Web of Science®. Reproducing part of that study in this paper, we present findings from topic searches (March 2008) for “numeracy,” “quantitative literacy,” and “statistical literacy.” These updated results include a combined bibliography of 338 peer-reviewed articles amongst 210 different journals, by 748 authors from 321 institutions in 25 countries, in a total of 87 subjects (34% of the subject classes in …

Abstracts For Numeracy, H L. Vacher

Numeracy

No abstract provided.

Collection Of Nitrate In A Denuder, Hannah Feig

Undergraduate Journal of Mathematical Modeling: One + Two

Data are given for aerosol nitrate (NO_3-) size distributions in the atmosphere as recorded by a cascade impactor and by an annular denuder. Using this data, our goal is to find the percent of nitrate in the atmosphere that the denuder is able to detect. This requires that we find the size distribution of nitrate that enters the denuder. From these data and calculations, we find that 32.8% of nitrate in the atmosphere can be detected by the denuder. Nitrate was measured to study its affects on seagrass in the Tampa Bay and to compare nitrate levels with …

Critical Axial Load, Walt Wells

Undergraduate Journal of Mathematical Modeling: One + Two

Our objective in this paper is to solve a second order differential equation for a long, simply supported column member subjected to a lateral axial load using Heun's numerical method. We will use the solution to find the critical load at which the column member will fail due to buckling. We will calculate this load using Euler's derived analytical approach for an exact solution, as well as Euler's Numerical Method. We will then compare the three calculated values to see how much they deviate from one another. During the critical load calculation, it will be necessary to calculate the moment …

Criteria Pollutant Concentration, Victor Neese

Undergraduate Journal of Mathematical Modeling: One + Two

With the assistance of Assistant Professor Jeff Cunningham (Civil & Environmental Engineering Department, USF) a study was carried out pertaining to the amount of CO and NOx pollutants emitted from a highway having two lanes in each direction. The receptor of the pollutants is a hypothetical housing development located near the highway. The concentrations were found by utilizing information regarding meteorological conditions, estimated emissions rates, and distances from the highway less than or equaling 2 km.

Algae Bloom In A Lake, David Sanabria

Undergraduate Journal of Mathematical Modeling: One + Two

The objective of this paper is to determine the likelihood of an algae bloom in a particular lake located in upstate New York. The growth of algae in this lake is caused by a high concentration of phosphorous that diffuses to the surface of the lake. Our calculations, based on Fick's Law, are used to create a mathematical model of the driving force of diffusion for phosphorous. Empirical observations are also used to predict whether the concentration of phosphorous will diffuse to the surface of this lake within a specified time and under specified conditions.

Review Of The Triumph Of Numbers By I. B. Cohen, H L. Vacher

Numeracy

I. Bernard Cohen, The Triumph of Numbers: How Counting Shaped Modern Life. (New York: W.W. Norton & Company, 2005). 209 pp. $24.95 (USA). ISBN 0-393-05769-0.

The premier historian of science ends his career telling how the world has become awash in numbers—“how numbers entered the conduct of life and of government, the understanding of nature, and the analysis of societies.” The stories begin with Kepler and end with Florence Nightingale. In between, major players include Galileo, Harvey, Leeuwenhoek, and Halley; Graunt and Petty; Jefferson and Franklin; Lavoisier, Sinclair, Pinel and Louis; Guerry and Quetelet. The book tells of the spread …

Birds–Dead And Deadly: Why Numeracy Needs To Address Social Construction, Joel Best

Numeracy

Sociologists use the term social construction to refer to the processes by which people assign meaning to their world. This paper argues that numeracy education needs to address social construction. In particular, thinking critically about the statistics the news media report regarding social issues requires understanding the competitive nature of the social problems marketplace, and the social forces that allow questionable numbers to receive widespread public attention. Such critiques must incorporate more than assessing how the numbers were calculated; they must consider the social construction of particular statistics. Two recent examples—claims about the number of birds killed flying into windows, …