M1030:Introduction to Quantitative Reasoning
Working in groups of two to three students, group members select a question or problem to investigate from a list of topics approved by the course instructor. In their investigation students apply the techniques studied in the M1030 course and then present their results or conclusions in a typewritten paper. As a research report the paper is to include a discussion of the background of the problem, the approach the group has taken in their investigation, a discussion of the mathematical techniques used, and a summary of the results of the group's research. All members of the group read the final draft of the project and approve it before it is submitted. The analysis of the problem, organization of work, grammar, and spelling are all considered in the project grade.
Some examples of past project topics are:
1. Many practical questions arise in dealing with one's finances. Pick a newspaper or magazine article published during the past year that discusses the savings patterns of Americans (provide the name of the newspaper/magazine and the date of the article). Examine the article in your group, summarizing the points made, and then do the following problem. Suppose that Julia, age 35, opens a bank account paying 5% annual interest compounded monthly. She plans to deposit $100 each month in the account. Assuming the interest is the same for the next 30 years, how much will Julia's account be worth when she retires at age 65? Compare her accumulation to her total investment. Now do the same analysis for Bob who is 25 and for Beth who is 45. Were there any connections between your calculations and the article you've read?
Now, determine how much you think you can afford to save per month and determine what kind of interest rate you could get at your bank. Depending on how old you are and when you want to retire, determine how much savings you could accumulate. Determine your accumulation both in terms of face value and after adjusting for inflation (assume 2% annual inflation). Suppose you plan to live on the interest from your accumlation when you retire. Estimating a 5% APY at that time, what will your annual interest amount to when you retire? Present a summary of your calculations, connecting your results to points made in the article. What factors do you think might impact your estimate of income from interest? What other methods are generally used to save for retirement? Discuss some of these briefly and present their benefits and drawbacks. Finally summarize any conclusion(s) your group has made.
2. First, describe in your own words the effect of scaling on the lengths, area, and volume of three-dimensional shapes. Give specific examples including measurements and then summarize your results in formulas for a general scaling factor, s. Then read the article, "Size and Form", in the book, Possible Worlds by Haldane. A copy of this book can be found in Marriott Library and 5 copies of the article itself are on reserve (file M1030) in the Mathematics Library in the basement of the JWB, the building where the Mathematics Department is located. Summarize what the author says about the surface area to volume ratio and about the effect of size on the form of living creatures giving an example of each effect. Now consider the following question. Cold-blooded reptiles bask in the sun to raise their temperatures so that basic metabolic processes can take place. The Sun's heat must be used to raise the temperature of the entire volume of the body, but it is absorbed only by the reptiles surface.We will assume that the rate at which the Sun warms the reptile is proportional to its surface area to volume ratio. Explain why this imples that the time a cold-blooded reptile must bask in the Sun is proportional to the volume to surface area ratio and that for a particular cold-blooded reptile the time required in the Sun is roughly proportional to its linear size. Now, if a 10 cm long Fence Swift lizard lounges in the Sun 10 minutes each day to raise its body temperature, explain how long you might expect a 1 meter long Monitor lizard to bask in the Sun. If we assume dinosaurs were cold-blooded, how much time in the Sun would you expect a 5 meter long dinosaur to require each day? Does your answer make you question whether dinosaurs were cold-blooded creatures? In responding to this last question think over the assumptions made in comparing a Swift lizard to a dinosaur. Finally present some of the current beliefs of researchers on the question of whether dinosaurs were warm-blooded or cold-blooded creatures. (adapted from the text, Using and Understanding Mathematics )