Mathematical Intuition (Poincaré, Polya, Dewey),
2011
University of Montana
Mathematical Intuition (Poincaré, Polya, Dewey), Reuben Hersh
The Mathematics Enthusiast
Practical calculation of the limit of a sequence often violates the definition of convergence to a limit as taught in calculus. Together with examples from Euler, Polya and Poincare, this fact shows that in mathematics, as in science and in everyday life, we are often obligated to use knowledge that is derived, not rigorously or deductively, but simply by making the best use of available information— plausible reasoning. The “philosophy of mathematical practice” fits into the general framework of “warranted assertibility,” the pragmatist view of the logic of inquiry developed by John Dewey.
Parts Of The Whole : Cognition, Schemas, And Quantitative Reasoning,
2011
Dartmouth College
Parts Of The Whole : Cognition, Schemas, And Quantitative Reasoning, Dorothy Wallace
Numeracy
Based loosely on ideas of Jean Piaget and Richard Skemp, this Parts of the Whole column considers the construction of knowledge in mathematics and quantitative reasoning. Examples are chosen that illustrate an important cognitive difference between quantitative numeracy and classical mathematics, and which illuminate the particular choices instructors must make in order to teach either or both of these.
Blood Alcohol Content,
2011
University of South Florida
Blood Alcohol Content, Chris Ludwin
Undergraduate Journal of Mathematical Modeling: One + Two
Given a set of differential equations describing blood alcohol content as a function time, we integrated the equations to obtain a general solution. The general solution equation depends on three free parameters: the initial concentration of alcohol in the stomach after ingestion, the rate of alcohol absorption into the blood stream and the rate at which the alcohol is metabolized by the liver. We fitted our solution to experimental data to determine the unknown parameters for a particular subject.
Correlation Among Different Variables And Life Expectancy,
2011
University of South Florida
Correlation Among Different Variables And Life Expectancy, June Liu
Undergraduate Journal of Mathematical Modeling: One + Two
The purpose of this project is to show how heart rate, blood pressure, and weight of different species correlate with their life expectancy. We perform graphical analysis and compute Pearson's Product-Moment Correlation Coefficient to show that the heart rate has the highest degree of correlation with life expectancy.
Retroactive Interference And Forgetting,
2011
University of South Florida
Retroactive Interference And Forgetting, Vinishaa Ankala
Undergraduate Journal of Mathematical Modeling: One + Two
Retroactive interference is the amount of information that can be forgotten by a person over time due to newly learned material. In this paper we establish a relationship between the amount of information forgotten by college students while they read and watch television and the time taken to forget it. We equate these numerical equations to solve for the unknown constants. By doing so, we can find the exact equation and also the amount of forgetting information due to retroactive interference.
Mathematical Analysis Of Genomic Evolution,
2011
University of South Florida
Mathematical Analysis Of Genomic Evolution, Cedric Green
Undergraduate Journal of Mathematical Modeling: One + Two
Changes in nucleotide sequences, or mutations, accumulate from generation to generation in the genomes of all living organisms. The mutations can be advantageous, deleterious, or neutral. The goal of this project is to determine the amount of advantageous mutations it takes to get human (Homo sapiens) DNA from the DNA of genetically distinct organisms. We do this by collecting the genomic data of such organisms, and estimating the amount of mutations it takes to transform yeast (Saccharomyces cerevisiae) DNA to the DNA of a human. We calculate the typical number of mutations occurring annually through the organism's average life span …
Optimization Of A Wall Built On A Slope,
2011
University of South Florida
Optimization Of A Wall Built On A Slope, John Hanna
Undergraduate Journal of Mathematical Modeling: One + Two
This project focuses on optimizing the construction of a wall with identical segments built on a slope. Faced with certain variable and fixed cost limitations, one can find the width of a segment that will minimize the total production cost. In this case, the lowest total cost comes from using 10 segments of width 3m.
Study Of Consciousness,
2011
University of South Florida
Study Of Consciousness, Samuel Lee
Undergraduate Journal of Mathematical Modeling: One + Two
The human brain is a powerful organ that controls most of the body. Researchers around the world have long tried to uncover how the brain operates, how memories are formed and stored. Our understanding of neurological diseases such as Alzheimer's and Parkinson's disease has been rapidly improving, yet much remains to be done. In this work, we attempt to study changes in intracranial pressure (ICP) for a 12-hour period and discuss whether the resulting estimates could be used as a measure of consciousness.
Blood Glucose Levels,
2011
University of South Florida
Blood Glucose Levels, Carlos Estela
Undergraduate Journal of Mathematical Modeling: One + Two
The purpose of this study was to establish a mathematical model which can be used to estimate glucose levels in the blood over time. The equations governing this process were manipulated with the use of techniques such as separation of variables and integration of first order differential equations, which resulted in a function that described the glucose concentration in terms of time. This function was then plotted, which allowed us to find when glucose concentration was at its highest. The model was then used to analyze two cases where the maximum glucose level could not exceed a certain level while …
Arc Length Of A Pipe Needed For A Directional Drill,
2011
University of South Florida
Arc Length Of A Pipe Needed For A Directional Drill, Kenneth Cabana
Undergraduate Journal of Mathematical Modeling: One + Two
Underground contracting has come a long way in recent years. As communities and buildings are being built, services like water, sewer, and gas are needed to allow people to perform their day to day activities. This research has led to the idea and design of a way to find the arc length of the pipe put into the ground at given points. The pipe length was estimated using the formulas for distance and arc length together with two different modeling methods: Lagrange interpolation and polynomial regression. Both techniques yielded similar results; however this may be situational and in other circumstances …
Pallet Physics,
2011
University of South Florida
Pallet Physics, Lauren Woodbridge
Undergraduate Journal of Mathematical Modeling: One + Two
This project explores whether it is safe to unload a 907kg pallet from a supply truck with a bed 1.5m off the ground by sliding it down a metal ramp. First we calculated the critical angle for which the pallet would overcome the friction of the wood on the metal and begin to slide. Next we calculated velocity of the pallet as it reaches the bottom of the ramp. Finally we calculate the distance the pallet travels on the concrete after leaving the ramp. Based on these calculations of acceleration, velocity, and displacement, we conclude that it would not be …
Sizing Of An Ammonia Discharge Tank,
2011
University of South Florida
Sizing Of An Ammonia Discharge Tank, Tuliagenda Beckfords
Undergraduate Journal of Mathematical Modeling: One + Two
Phosphate companies use well-stirred tanks to regulate the concentration of ammonia they discharge via their wastewater, preventing ammonia spikes from exceeding the cap set by the Environmental Protection Agency. This report discusses the methods used to determine the minimum possible volume of the tank required to regulate wastewater discharge. With this information, it was determined that the use of a stirring tank is an efficient and cost effective way to regulate ammonia discharge. Based on these results many other companies may use this method to decrease the negative effects of ammonia on the environment.
Comparison Of First Gear Performance For Manual And Automatic Transmissions,
2011
University of South Florida
Comparison Of First Gear Performance For Manual And Automatic Transmissions, Kyle Stottlemyer
Undergraduate Journal of Mathematical Modeling: One + Two
The purpose of this project is to compare the first gear performance of an automobile for both its manual and automatic transmission options. Each transmission type has a different gear ratio, which yields a different acceleration curve for each transmission throughout the torque-rpm curve of the engine. The method of integral calculus was used to find an equation which could be used to solve for time at any point in the car's acceleration. The automobile velocity versus time was then graphed to compare each transmissions acceleration trend. This process is similar to that which automotive companies may use when determining …
Optimization Of A Pressure-Treating Process,
2011
University of South Florida
Optimization Of A Pressure-Treating Process, Josean Velez
Undergraduate Journal of Mathematical Modeling: One + Two
A company that pressure-treats wood wants to minimize its annual cost without using more than 250 days of operation per year. In addition, they want to find the corresponding value of time, batches and cost for each category. We develop an expression in terms of boards per batch to model the total cost of the treatment process. We then take the derivative and use Newton's Method to find the number of boards per batch that minimizes total cost.
Length Of A Hanging Cable,
2011
University of South Florida
Length Of A Hanging Cable, Eric Costello
Undergraduate Journal of Mathematical Modeling: One + Two
The shape of a cable hanging under its own weight and uniform horizontal tension between two power poles is a catenary. The catenary is a curve which has an equation defined by a hyperbolic cosine function and a scaling factor. The scaling factor for power cables hanging under their own weight is equal to the horizontal tension on the cable divided by the weight of the cable. Both of these values are unknown for this problem. Newton's method was used to approximate the scaling factor and the arc length function to determine the length of the cable. A script was …
Design Of A Rainwater Catchment System,
2011
University of South Florida
Design Of A Rainwater Catchment System, Neil Cammardella
Undergraduate Journal of Mathematical Modeling: One + Two
Certain dimensions of a rainwater catchment and storage system were optimized using climatological and sociological data. Using only daily demand and average daily rain fall data, the following dimensions were optimized: 1) The horizontal roof area needed to collect the daily demand of water, 2) The tank size needed to store all the water collected during a heavy rain event, 3) When full, how long the tank will be able to provide water without rain, and 4) The diameter of the outlet flow orifice. With these calculations, we can design a rainwater catchment system that can capture the daily demand …
Optimal Operation Of A Concentrator,
2011
University of South Florida
Optimal Operation Of A Concentrator, Katrina Stine
Undergraduate Journal of Mathematical Modeling: One + Two
Concentrators are used in the industrial world to remove water from a chemical or substance by heating the liquid until the water evaporates thereby concentrating the remaining substance. The goal of this project is to find the optimum cycle time, number of cycles per year, and the heating element area that would minimize the total annual cost and hours of operation of an industrial concentrator. It was found that the specified concentrator would achieve a minimum total cost of $48,720.50 per year and take 993.8 hours to meet the production goal of evaporating one million kilograms of water.
Average Light Intensity Inside A Photobioreactor,
2011
University of South Florida
Average Light Intensity Inside A Photobioreactor, Herby Jean
Undergraduate Journal of Mathematical Modeling: One + Two
For energy production, microalgae are one of the few alternatives with high potential. Similar to plants, algae require energy acquired from light sources to grow. This project uses calculus to determine the light intensity inside of a photobioreactor filled with algae. Under preset conditions along with estimated values, we applied Lambert-Beer's law to formulate an equation to calculate how much light intensity escapes a photobioreactor and determine the average light intensity that was present inside the reactor.
The Effects Of Age On Short-Term Memory Loss Due To Proactive Interference,
2011
University of South Florida
The Effects Of Age On Short-Term Memory Loss Due To Proactive Interference, Alisha Berkauzer
Undergraduate Journal of Mathematical Modeling: One + Two
This project focused on how proactive interference affects the short-term memory of people based on their age. The goal was to find the prime age for learning information and storing it in one's memory. Seven people from ages fifteen to forty were tested individually, using a set color pattern, in order to see how well each individual could remember the different color patterns as difficulty of the pattern increased. The obtained data was fitted by the polynomial regression. The “fitted” curve shows that as age increases, the individual's performance in memorizing the more difficult patterns decreases. Also, the peaked level …
Going Ballistic: Bullet Trajectories,
2011
University of South Florida
Going Ballistic: Bullet Trajectories, Amanda Wade
Undergraduate Journal of Mathematical Modeling: One + Two
This project seeks to answer at what angle does a gun marksman have to aim in order to hit the center of a target one meter off the ground and 1000 meters away? We begin by modeling the bullet's trajectory using Euler's method with the help of a Microsoft Excel spreadsheet solver, and then systematically search for the angle corresponding to the center of the target. It was found that a marksman shooting a target 1000 meters away and 1 meter off the ground has to aim the rifle 0.436° above horizontal to hit the center.
