- Quantify and explain the relationship between bicycle gears, revolutions per minute, and speed. What is needed for racing, recreation, and touring? Measure several actual bicycles and discuss their potential performance
- Analyze rent versus buy decision for a home taking taxes and inflation into account.
- Analyze the difference between a 15 year and 30 year mortgage taking taxes into account.
- Analyze the number of years required to breakeven if you refinance your home at a lower interest rate. Take into account taxes and front end points.
- Explain the theory behind asset allocation as an investment methodology.
- Describe measures for quantifying volatility of the stock market.
- Analyze and compare interest rates charged on car loans from various sources.
- Analyze and compare the costs associated with several cell phone plans. Evaluate the plans based upon several different sets of assumptions. Graph the breakeven points for various plans.
- Analyze interest rates charged on credit cards from various sources.
- Quantify the effect of sales tax on rich versus poor people.
- Analyze percent of total tax revenue received from rich people.
- Analyze the volume and cost of water lost from a dripping faucet.
- Do a correlation analysis of electrical usage in your home, outside temperature, and time of day. Test whether a fireplace reduces your heating bill? Explain how to read an electric meter on a house.
- Write a quick reference guide for math for carpenters. Give examples of how to use your formulas.
- Analyze one of the magic numbers: pi, e, phi, or i. Describe their history and method of computation
- Develop a statistical profile of how students differ by major, age, or some other characteristic.
- Categorize and explain examples of linear equations applicable in everyday life.
- Do a probability analysis of a casino game such as 21.
- Explain the relationship between latitude and longitude and surface distance on the earth, including a discussion of land versus nautical miles. Explain the relationship between longitude and time. Why was it difficult to determine the longitude at sea?
- Explain the geometry associated with fixing a postion with GPS.
- Based upon historical data over several years from an almanac, try to fit the data to a population growth model.
- Explain how mathematics is used to quantify supply and demand curves in economics.
- Explain and quantify the tradeoffs between front end loaded and back end loaded mutual funds.
- Explain how a car measures speed. What is the relationship between distance, time, speed, and acceleration? Why would one want to measure acceleration in cars? How is it done?
- Explain how to quantify the motion of an ocean wave. Give examples.
- Explain the orbits of the planets. Include a discussion of Kepler's Laws.
- Explain how surveyors measure the height of mountains.
- Explain what is meant by parallax and give examples.
- Explain aspect ratios and give examples in everyday life.
- Analyze the weather data reported by the Thomas Point Lighthouse.
- Explain the geometry of fixing a position with GPS.
- Examine the electrical panel in your home and explain how it relates to the electrical usage in your home.
- Explain the probabilities of you favorite card or board game.
- Explain how probability and statistics are used in stocks, sports, weather, traffic, astronomy, sociology, psychology, gambling, economics, or some other favorite subject.
- Explain how to figure the break even cost of a college education. Apply the methodology to your personal situation.
- Draw a decision tree of you life choices and quantify the implications of each decision.
- Maintain a math journal (diary) of the mathematical situations you incounter in your reading and dailing life. Critically evaluate and explain what you are recording.
- Compile a list of examples with explanations of how you see math misused in news and advertising.
- Describe how magic squares work and give examples. Specify a set of rules (an algorithm) for making magic squares. Try to implement your ideas in EXCEL.
- Emperically demonstrate Zipf's Law. Compare frequency distributions of words used by students based upon their gpa or other pertainent measure.
- Explain why tides occur and describe formulas for estimating what the tidal height will be between low and high tide points.
- Gather data on at least 20 dating couples and record their height, majors, current gpa, annual salary they expect upon graduation, and any other statistic of interest. Analysis and summarize the data. What correlations did you find? Can you form any conclusions or generalizations from your data? Do your couples represent a good sample of the entire student body?
- How do science majors differ from non-science majors? Collect and analyze data on at least 20 students from each group to support your conclusions. Explain what variables you chose to use to make your comparisons.
- Define prime numbers and describe a set of rules for calculating them. Try to implement your ideas in EXCEL.
- Do a scientific analysis of your diet or exercise program. Prove with measurement data which diet or exercise program works best.
- Develop an equation or quantitative methodology to express some non quantitative concept like happiness, motivation, or success. Explain your logic and give examples of applying it to yourself and people you know.
- What type of statistical or quantitative analysis could be used to automatically evaluate the quality of someone's writing. Apply your methodology to some graded papers and test whether or methodology has merit.
- Develop a quantitative method for evaluating persons for a job, for school admission, for a credit card, as a prospective juror in a crimal case, or as prospective dating partners. The normal technique is to identify the most important attributes and assign numerical weights to them. Apply your technique to some actual people and evaluate its usefulness.
- Explain the binomial probability distribution. Give ten examples of how it can be applied in real life. Explain any assumptions for your examples. One example might be the probability of a batter getting a hit.
- Explain how standard deviation can be used to quantify the risk associated with an investment.
- Discuss the impact of income tax rate on your investment return. Create a table with gives the effective return of an investment based on various tax rates. Under what conditions are tax free municipal bonds a good investment.
- Compare the lotteries from several states. Explain the odds of winning each game. Explain which states/games are better for the player and why.
- Are you still stuck for an idea? Look at your hobbies or pastimes. There must be some quantitative aspect to them that you can summarize or research.
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