Review

The purpose of today's lab is to step back and review. Read through the following and click on any underlined links. You should answer any questions on a piece of paper and come to class tomorrow prepared to share your answers.

Satisfying Course Goals and Objectives

We began the semester with an interdisciplinary approach that combined the fields of geometry, visualization, art, history, philosophy and physics, in the Geometry of the Earth and Universe segment, and the fields of mathematics, sociology, African American studies, women's studies, and history in the What is a Mathematician? segment. In the process we developed creative inquiry techniques and examined some of the course themes - what mathematics is, what it is useful for, and how people succeed in mathematics.

More recently we applied the reasoned strategies that mathematics illustrates as a powerful tools that give us surprising strength for analyzing and conquering life's issues in the finance and statistics segments. We have engaged in creative inquiry methods all throughout this class. My hope is that you will take these skills with you and find it helpful to apply them to your own lives in the future.

You'll receive the numerical data, writing, and computer use designators for your work in this class (all Math 1010s must satisfy the three designators). Math 1010s look very much alike in a lot of ways but we differed slightly by taking the interdisciplinary and thematically linked approach throughout the course, for example, by combining financial mathematics with political science and history in the Ben Franklin project.

WebCT Peer Review of Effectiveness of Groups
For each of the major projects that you had a partner for I want feedback from you on group effectiveness.

Using File/New Window, open up a new web browser and enter WebCT. Compose a WebCT posting message to Dr. Sarah by choosing the forum containing you and Dr. Sarah and using the subject "peer review". If you feel you deserve the same grades as your partners(s), just say so. If not, please explain why you deserve a higher or lower grade than your partner(s) and specify which project(s) this relates to and the name(s) of your partner(s).

Reviewing Material:
Answer Questions on a Piece of Paper

Even though we don't have a final exam (we'll use the exam period for final project presentations), it is still important to step back and see where we have been. We developed creative inquiry techniques in the first two segments and examined some of the course themes - what mathematics is, what it is useful for, and how people succeed in mathematics. In addition, you were encouraged to be creative and skeptical thinkers and learners.

Geometry of the Earth and Universe

How we view the world around us and what it actually looks like.
    Read through the worksheet on Jeff Weeks and answer the questions there.



What is a Mathematician?

The lives and mathematical work and styles.
    Jeff Weeks' interview responses already provide a good review of many of the thematic issues from this segment and the course. To review some of the mathematics related to the Andrew Wiles worksheet, old down the control key and then the mouse button and click on this link Homer's blackboard equations. Open the link in a new window and read through it and answer these questions.

  1. Write down the 2nd equation from Homer's blackboard (see the text below the pictures) involving the power of 12.



  2. What is the statement of Fermat's Last Theorem? If you don't remember, look it up in your notes or on the web.



  3. Use Fermat's Last Theorem (which Andrew Wiles proved was true) to explain why the 2nd equation on Homer's blackboard cannot be true.



  4. Yet, we do not need the full strength of Fermat's Last Theorem. Explain how we can show the equation is false if we know only that Fermat's Last Theorem doesn't hold when the power is 3 (proven by Euler) or 4 (proven by Fermat).



  5. Can an odd/even argument be used to justify that the 2nd equation is false? If so, then give the details, and if not, explain why.



  6. Give a different mathematical reasons why the equation cannot hold. Hint: Use the fact that 9 divides a number if and only if 9 divides the sum of the digits.



  7. I decide to calculate the 12th root of the left hand side on my TI-83 Plus calculator. When I do this, it tells me that the answer is 4472, which would imply that the equation was valid. This really did happen on my calculator. Resolve the apparent conflict.



    In class tomorrow, we'll discuss the back story behind the power of 12 references in The Simpsons.
More recently we applied the reasoned strategies that mathematics illustrates as a powerful tools that give us surprising strength for analyzing and conquering life's issues in the statistics and finance segments.

Finance

Interest formulas as they apply to the real world - credit cards, student loans, savings accounts, car and house purchases, taxes, retirement...

    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 2003. 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 at one point, but brought it back again, and that the loan was often for 3 years. Let's assume that the loan would have compounded monthly at 8%. In the "Keep America Rolling" program, these 3 year loans charge 0% over the 3 years.

    Loan Payment Formula:

    Monthly Payment =

                        Loan (rate/12)
                        __________________

                        1 - (1 + rate/12)(- years*12)

    Total Interest Over the Life of a Loan: Interest = Monthly Payment * 12 *years - Loan

  1. Use the loan payment and interest formulas to determind 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 of the life of the loan - this interest is the amount the customer would save in the "Keep America Rolling" program. SHOW WORK


Statistics

To recognize misrepresentations of studies and statistical data in the real world by understanding statistical techniques and satisfy the numerical data designator.

    Stock Update

  1. Take out your stock packet and do another stock update 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 (20 years), stocks that don't go out of business have historically performed better than savings accounts. The stock sheet has additional updates listed so that you can check it again over the long term (after the semester is over) if you like.

    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 searched 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, but in 2004, there was a shortage of the flu vaccine. 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 in the United States.

    One statistic is that the
    # 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%. The is the percentage of the United States population that 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:

  2. What is the percentage of cases of flu out of the total population of the United States? SHOW WORK.

  3. 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 were so afraid of the anthrax mailing 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.

  4. 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.


  5. 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.


  6. We could perform a similar analysis of any disease. Name some other diseases that have been mentioned in the recent news that people are afraid of contracting.

What is Mathematics?

    We have examined this theme and have also looked at many examples of different kinds of math and some applications of mathematics to real-life. Come to class tomorrow prepared to discuss these readings:

  1. Read through Adding up Fuzzy Math: Teaching the Basics.



  2. Read the Quantitative Literacy reading.



  3. Review the Creative Inquiry Lessons for Life list.



  4. Review the What is Mathematics? reading.