Satisfying Topics and Objectives and A Note on the Commonalities of Mat 1010s
All Mat 1010s must satisfy the three designators, must use the How do You Know? book, and must cover the statistics segment and financial mathematics segment. After that, instructors are free to choose segments that they want to cover. Hence, for most of the semester, during the financial mathematics and statistics segments, this section looked much like any other Mat 1010. We differed slightly by taking an interdisciplinary approach, combining financial mathematics with political science in the Ben Franklin lab, and statistics with a real-world view via Heart of Math readings and the stock market. In addition, we began examining some of the course themes - what mathematics is, what it is useful for, and how people succeed in mathematics. For the remainder of this semester, we took an interdisciplinary approach combining the fields of mathematics, sociology, African American studies, women's studies, and history in the What is a Mathematician? segment, and the fields of geometry, visualization, art, history, philosophy and physics, in the Geometry of the Earth and Universe segment.
Reviewing Material
Financial Mathematics
Take out your financial mathematics test, and look up the lump sum, periodic payment and loan payment formulas from your cheat sheet. Write them down on a separate piece of paper:- lump sum formula
- periodic payment formula
- loan payment formula
Keep America Rolling
Since September 11th, you may have seen television commercials from the car companies offering 0% interest on new cars. GM was first to start this with its "Keep America Rolling Program," which offers interest-free financing on all new cars and trucks for certain loan periods. Zero-percent financing can save customers thousands of dollars over the life of the loan. Many of these loans were even extended into this year. I used our effective web searching techniques in order to find the details on the length of an interest free car loan. By searching with
+"Keep America Rolling Program" +"0%"
I found out that GM cancelled the program in January, but brought it back in March. Recall from when you searched for real-life rates, you saw that normally 3 year loans compound monthly at somewhere around 8%. In the "Keep America Rolling Program" these 3 year loans charge 0% interest over the life of the loan. - Use the loan payment formula in order to determine how much
a customer will save - ie calculate the monthly payment assuming
an 8% interest loan of $20,000
compounded monthly for 3 years
and then calculate the interest over the life of the
loan - this interest is the amount the customer would save in the
"Keep America Rolling Program".SHOW WORK
Statistics
- Do stock update number 4
and show it to me so that I can check it off on your sheet.
Recall that the stock market is unpredictable in the short
term, but, in the past,
over the LONG TERM (10 years), stocks that don't go out of business
have historically performed better than
savings accounts. I encourage you to check your stock again in 6 months
and a few years from now.
Various Perspectives Using Statistics
We have seen that the media often misrepresents statistics, and that one must dig deeply to fully understand the (often contradictory) issues involved.
Bin Laden
For example, you may have heard about the 25 million dollar reward offered for information leading to the capture of Bin Laden. After searching for +reward +"Bin Laden" from www.google.com, I found that this reward is actually worded as "up to $25 million", which means that the reward could actually be any amount of money less than or equal to $25 million. By searching further, I happened across an NPR report on this that clarified that the state department will decide on the actual amount of the reward after Bin Laden is captured.
Flu
A second example relates to statistics of deaths from a disease. I search with +2000 +"number of deaths" +influenza +"united states" to find out that there were 91,871 deaths from influenza and pneumonia (which sometimes results from influenza) in the United States in 2000. I also found that there are 94,800,000 flu/pneumonia cases each year. I found out that since the late 1940s, the flu vaccine has been the best way to prevent influenza or lessen its severity and that the vaccine prevents over 90% of the influenza/pneumonia deaths. I was surprised by these statistics since I didn't realize that so many people died from complications of the flu. I then looked up the population of the United States via a search with +"census 2000" +"total population" +"United States", and obtained 281,421,906 people. So, one statistic is that # deaths from the flu / total population of the united states = 91,871 / 281,421,906 = 3.26...E-4 (E-4 is scientific notation meaning that I go 4 decimal places over to the left - ie .000326...) = .0326% of the United States Population dies from influenza and pneumonia each year. Try this on your calculator and make sure you understand before moving on. There are also other perspectives to examine:
- What is the percentage of cases of flu out of the total
population of the United States? SHOW WORK.
- What is the risk of dying from the flu
(as a percentage) once you already have it?
Calculate this
by taking the number of deaths, dividing by the number of
cases and then turning this into a percentage.
SHOW WORK.
Anthrax
Let's see why people are so afraid of anthrax when the chances of getting the disease are so small: I used effective web searching techniques to find the number of anthrax cases in the United States since September 11th. There were 11 cases of inhalation anthrax infection and 5 deaths. There were 12 cases of cutaneous anthrax infection and 0 deaths.
- Use this information
and the population of the United States (found above) to
determine the percentage of cases of anthrax out of the total population of
the US.
This statistic could be used to calm the public.
Note that this
is much, much smaller than the corresponding flu percentage.
SHOW WORK.
- Determine the risk of dying once you have the disease
as a percentage.
Notice that this is much, much larger than the percentage of
risk of dying once you have
the flu, which explains why people are so afraid.
SHOW WORK.
What is a Mathematician?
- Go to this
text transcript of the 3-d Homer segment
and Did You Notice? by James A. Cherry, and find the exact
numbers in the equation shown above
where numbers are raised to a power of 12.
Verify that this matches what you see in the picture and
write the equation here.
- Is the right hand side of the equation even or odd? Why?
- Is the left hand side of the equation even or odd? Why?
- Use the answers to the last two questions to explain why
this equation cannot hold.
- What is the statement of Fermat's Last Theorem?
If you don't remember, look it up in your notes or on the web.
- Use Fermat's Last Theorem (which Andrew Wiles proved was true) to explain why this equation cannot be true.
An Equation Flying Passed 3D Homer
Peer Review of Effectiveness of Groups
For each of the major projects that you had a partner for (Ben Franklin, Statistics report, Mathematician presentation and worksheet, Geometry of the earth and universe report), I want feedback from you on group effectiveness. Go to the WebCT newsgroup forum containing JUST you and Dr. Sarah and choose from the following: (you may copy and paste from here into WebCT)Take Home Part of the Final - 2 Parts
Final Exam
Your final exam grade will be determined by a take-home portion and an in-class portion. Recall from the syllabus and past grades assignments that the comprehensive final exam is worth 20% of your course grade, while 20% of your grade was determined by the combination of test 1, test 2, and your mathematician presentation. While this percentage is relatively small (many other 1010 sections have exams count for 45-60% of the course grade), your performance on the final exam is important since it demonstrates your mastery of the course material and provides you with an opportunity to pull everything together. I do take improvement over the course of the semester into consideration.For the in-class part of the final, one 8.5*11 sheet with writing on both sides allowed. 1 calculator and straight edge mandatory. More details on this part in class tomorrow.
Read through the following directions for the take-home part of the exam now, including the underlined links. This is due on the day of the final
Part 1 of Take Home Portion of Exam - Style
We have seen that there are many diverse styles that lead to success in mathematics. Choose a mathematician** whose mathematical style you identify with and find most rewarding. While geometry is actually the most difficult for me, I chose it as my specialization because it is the most rewarding for me. Identify the mathematician, describe his or her style briefly, and then give specific examples from your life of how the mathematical style applies to you and leads to your success in mathematics and in other areas of your life. Suggested length: 1 page typed.** The mathematician will be chosen from among: Andrew Wiles, Carolyn Gordon, Thomas Fuller, Maria Agnesi, Gauss, Sophie Germain, Georg Cantor, Ramanujan, Paul Erdos, David Blackwell, Mary Ellen Rudin, Frank Morgan, Ingrid Daubechies, Tom Banchoff, Jeff Weeks, or Dr. Sarah.
Part 2 of Take Home Portion of Exam - What is Mathematics?
We have examined the questions of "What is Mathematics?" and have also looked at many applications of math to real life. Using ideas indiscuss how your personal view of mathematics and its usefulness in your life has changed over the course of the semester. Suggested length: 1 page typed.