MATH 472 Ideas for Paper/Presentation

The following are some ideas for your Paper/Presentation for MATH 472.  The purpose of you doing this paper and presentation is to learn, and be able to communicate to others, about probability and/or statistics in an area of your interest (teaching mathematics, applied areas such as business and economics, physics, computer simulation, etc., and more theoretical/pure mathematics topics).  The following are ideas for various project topics and an indication of what would be expected for those projects.  All topics must be cleared with me in advance!  This is not an exhaustive list and you are certainly free to chose another idea (once you clear it with me first, of course).  Around midterm you will be required to hand-in a one-page abstract of your proposed topic that includes the references you will be using.   To reduce your workload, I strongly encourage you to work with a partner on this project!  Please come see me as soon as you can to start discussing your options.   Here is a suggested schedule/pace for working on your paper.

Topics for those who are interested in teaching mathematics:

1.  Learn about the AP Statistics exam.  I would expect students who choose this topic to write a short paper about the history of the AP Statistics exam, what the AP Statistics exam covers, and as an appendix to that paper, work through an example AP Statistics Exam showing the details of the solutions (sample tests with solutions can be found on the AP Statistics Website and I also have some in my office).  Your presentation might consist of a brief overview of the AP Statistics program and show some of the types of problems (with solutions) that appear on the exam.

2.  Create (not copy one that already exists) a teaching module about some particular topic of interest in probability and/or statistics.  The module should be well-documented and researched regarding how it satisfies NCTM standards and good pedagogy.  The module should incorporate different learning styles,  and of course, should have significant mathematical content appropriate for the grade level for which it will be used.  There is a plethora of information on the web about teaching introductory statistics.  I can help get you started on where to look.

Topics for those who are interested in applied mathematics:

1.  If you are interested in pursuing a career in business or economics, a possible topic is to learn about is a career as an actuary.  I would expect students who choose this topic to write a short paper about what an actuary does and as an an appendix to that paper, work through the first test that actuaries must take (the one that covers undergraduate mathematics including probability and statistics) showing the details of the solutions (sample tests with solutions can be found on the on the Society of Actuaries webpage and in my office.).

2.  Take a substantial data set of interest to you and analyze it using the tools we will develop in this class.  The data set should contain a reasonable number of variables of different types (discrete, continuous, categorical, etc.).  Part of this project will necessarily be learning and using SPSS beyond what we do in class.  The final paper should show your data analyses with any interesting observations and conclusions you reach about the data.  Your data analysis must include both descriptive and inferential statistics.  You will decide what questions to ask and what statistical methods to use to answer those questions.  I can help guide you on where to find "good" data sets.

3.  Learn about the topic of Monte Carlo simulation.  Write a (relatively simple) simulation (which you can do in Excel!) and show the results to the class!

4.  Learn how probability and statistics is used in quantum mechanics.  This is a difficult topic requiring knowledge in both physics and mathematics, and would definitely need the help of a willing physics professor. 

Topics for those who are interested in going to graduate school and like pure/theoretical mathematics:

1.  Take some of the more well-known results in probability and statistics and rigorously prove them.  For instance, if one is currently taking (or has previously taken) Advanced Calculus, then a good project would be to go through the proof of the Central Limit Theorem (Section 6.7 of our text) being sure to "cross every t and dot every i."  Part of this would probably include going through the proof of Taylor's Theorem (which is used in the proof of the CLT in our textbook -  the proof of Taylor's Theorem should be in your Advanced Calculus text - if not, I can provide you with a proof.).  This would be an excellent exercise for those interested in graduate school in pure mathematics!

2.  Related to Monte Carlo Simulation - Learn about the theory of random number generation (how do "they" do that?)?  How do "they" know it works? 

Suggested Schedule/Pace for Working on Your Paper: