Mathematics 451
Projects from Previous Terms
Applications and Modeling

Math 451 pages: [ HomeGrading Rubric | Project Schedule | Previous Projects | Small Model List ]

Over the last few years we have had a variety of projects: some have worked well, others have not.  Usually the most difficult aspect of writing an "A" paper, is to have sufficient and enlightening mathematics (see the rubric).  For this reason, those models focusing on the physical and mechanical often have an advantage.  Sports and business models have presented some difficulty.  However, given a sufficient statistical background, a student could develop a reasonable sociological... model.

Below are selected models (selected only because I could find these easily) from the last few years.

  • Going the Distance -- Jimmy, Tiffani and Lance attempted to determine the distance traveled by a golf ball as a function of the speed of the club and the club used. They also compared the data they collected to the model used by a laser swing monitor.
  • To Teach or not to Teach; an Investigation into the Trends of the Salaries of America's Secondary Teachers -- Jimmy, Gary and Matt used data (corrected for inflation) to estimate the future salaries and lifetime earnings of grade-school teachers.
  • Condenser Bushing -- Bridget, Jay and Jennifer discovered the equation relating the radius of a condenser bushing and the electrical charge to the field intensity surrounding the bushing.
  • The Probability of Winning the Superbowl -- Can we use team statistics through the last week of regular play (such as rushing yards and pass completion percentage) to predict the winner of this year's Superbowl? Keri Bailey and John Bush used logistic regression to determine the most important team statistics for "predicting" the previous Superbowl winners. They then used these statistics to develop a logistic model for predicting the probability each team will win the Superbowl this year.
  • The Perfect Bat -- Melissa Rudy and Tommy Elliot first explore the relationship between a female baseball player's build (height to weight ratio) and their batting speed, and find a roughly linear relationship. (UTM's softball team was kind enough to be the subjects of this trial.) They then seek the optimum bat for a player, based on the player's batting speed and the "weight-length ratio" of the bat.
  • Outbreak: Is this the End? -- A severe pandemic in 1918 infected at least one-fifth of the total human population and took more than 20 million lives. Anisha Mabry and Jerrica Wall estimate the number of sick, contagious, immune, susceptible and deceased individuals at several susceptibility rates, then predict the daily population over the next few months.
  • Draining Oil -- The students drained a cylindrical tank of oil through a horizontal pipe and modeled the height of the oil in the tank as a function of the oil's viscosity, density, and temperature. 
  • Parachutes -- After making small parachutes and quickly learning why parachutes have a hole in the center, these students added a hole, then modeled the terminal velocity as a function of the parachute's radius and load.
  • Rat Trap Catapult -- Using a catapult made from a rat trap, two different types of projectiles were launched. A model was developed to find the optimum firing angle.
  • Choose your Club Wisely -- The distance a golf ball travels as a function of type of club (wood, steel and titanium) and swing speed.
  • Flight Time of Paper Helicopters -- Flight time of a paper helicopter as a function of the wing length, weight and height from which it is dropped. 
  • That's the Way the Ball Bounces -- The height a basketball bounces as a function of velocity and pressure.
  • You Spin Me ‘Round -- an analysis of how long it takes clothes to dry in a dryer (does it take twice as long to dry a load twice as big?)  Pat used dimensional analysis to develop a mathematical model, then empirically fit this model using data he collected by drying towels.
  • Evaporating a Puddle -- an effort to model the volume of a puddle as a function of several variables including time, temperature and the specific heat of the fluid.  The students heated alcohol to get their data that was fit to a mathematical model derived by a dimensional analysis.
  • The Melting of An Ice Cube -- beginning with a simple differential model, the students then used dimensional analysis and least squares fit to determine the necessary constants.  The end product is a model that relates the mass of an ice cube to the ambient temperature, time, specific heat and thermal conductivity of water.
  • Free Style Tuning for Guitars -- Determining how to tune a guitar using string tension and linear density.  By using a hook to hang a mass on the string, these students model how many turns of the peg are necessary to bring the string into tune.
  • A Projection of the Deer Population -- Using the Leslie matrix Model, the students estimated the number of female deer in Tennessee over the next few years.
  • The Effectiveness of a Foam Rubber Coolie -- The rate of heat transfer was related to the amount of the surface of the can covered by the "coolie," as well as the specific heat of the soda, and the thermal conductivity of the foam in the coolie.
  • A Spinning Dilemma -- Farmers use paddlewheel spreaders to distribute seed.  This team modeled how far a "seed" (actually a marble) would travel when dropped on to a spinning paddle as a function of the angular velocity, height, gravitational constant, and radius.
  • Let's Go Parking -- The geometry of parking cars.
  • The Average Number of Coins -- If we always give the "best" amount of money to the cashier, what is the average number of coins we will have in our pocket?  Are there other sets of coins (instead of 1, 5 10 and 25 cents) which would reduce this number?
  • To Fold is to Conserve -- How fast will a towel dry as a function of both the humidity? And what is the best way to fold it on a clothes line?
  • To Play are not to Play; How Dangerous are Collegiate Sports -- Using data from the NCAA Injury Surveillance System, this team developed a ranking of collegiate sports from the "most dangerous" (spring football, wrestling and men's soccer) to the least dangerous (women's softball).
  • Electricity, the Energy of Choice -- 
  • Liquid Drain-O --  Models the rate a which a cylinder drains as a function of the size of a hole in the base and the viscosity of the liquid.
  • Crime on Campus -- Compares the crime rate on 150 college campuses to the campus and city sizes, and the crime rate in the city. 
  • Milk Production in Dairy Cattle -- Various data such as cattle age, somatic cell count, and temperature are correlated to average milk production for one dairy farm.
  • Mathematical Relationships of Golf -- Distance a golf ball travels as a function of the face angle of the club and compression of the ball. 
  • To Cut or Not to Cut? -- This project studied the relationship between a cut or scuff on a baseball and its trajectory out o a pitching machine.
  • Bowling Strikes -- Using both a computer model and a mathematical model, this group determined the best angle and location for a straight ball.
  • Efficient Restaurant Service -- A model of restaurant service as a function of the distribution of the customers and the number of employees.
  • Investigating Alternate Methods of Mathematics Placement --