What is Mathematics?

Even though we don't have a final exam (we'll use the exam period for final project poster sessions), it is still important to step back and see where we have been, and the purpose of today's lab is to do so as we reflect on what mathematics is. Read through the following and click on any underlined links. You should answer any questions on a piece of paper and be prepared to share your answers and discuss the readings in class tomorrow.

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.


    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 years later. 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 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 of the life of the loan - this interest is the amount the customer would save in the "Keep America Rolling" program. SHOW WORK

  2. Often customers are offered a 0% loan or a cash rebate instead. What issues would go into deciding which you would take?


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

    Stock Update

  3. 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, 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.


    For example 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 were
    94,800,000 flu/pneumonia cases that year.
    Some webpages state that since the late 1940s, the flu vaccine has been the best way to prevent influenza or lessen its severity and that in many years 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 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:

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

  5. 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.

  6. What are some risks or problems with the flu vaccine?

    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, along with the diverse ways that people succeed in math. Here are some readings for use in your personal reflection:

  7. In addition, prepare to share something in class tomorrow on each of these readings - take notes on what you plan to share.
  • Adding up Fuzzy Math: Teaching the Basics.

  • Quantitative Literacy reading.

  • Creative Inquiry Lessons for Life list.

  • What is Mathematics? reading on ASULearn.

  • Complete the informal learning evaluation.
    If time remains, work on the personal reflection or final project (see the main web page).