Dr. Sarah's Review Lab

The purpose of today's lab is to step back and see where we have been and where we are going and in the process begin reviewing for the final exam. Read through the following and click on any underlined links as they come up. You should answer any questions on a piece of paper.

Satisfying Course Goals and Objectives

Course Goals

 Develop creative inquiry skills.
Develop an appreciation of what mathematics is, what it has to offer, why it is useful, and the diverse ways that people can be successful at mathematics.
Develop communication skills by communicating mathematics to a general audience in writing projects, group and class discussions and presentations.
Develop computer skills and advanced web searching techniques.
Math 1010 has been designated as a writing intensive, numerical data, and computer use course.

Syllabus and Objectives

Financial Mathematics Interest formulas as they apply to the real world - credit cards, student loans, savings accounts, car and house purchases, taxes, retirement...
Statistics To recognize misrepresentations of studies and statistical data in the real world by understanding statistical techniques and satisfy the numerical data designator.
What is a Mathematician? The lives and mathematical work and styles of some famous mathematicians.
Geometry of our Earth and Universe You'll become a mathematician with the geometry of the earth and universe as your field of study, while developing visualization skills.

Satisfying Course Goals and the Future

  • We have engaged in creative inquiry methods all throughout this class. My hope is that you take these skills with you and apply them to your own lives in the future.
  • By doing mathematics throughout the semester, while also looking at real-life applications, and stepping back to examine what mathematicians are like and what mathematics they study in the What is a Mathematician? segment, I hope that we have developed an appreciation of what mathematics is, what it has to offer, and why it is useful.
  • We developed communication skills in precisely the ways mentioned in the syllabus.
  • We satisfied the numerical data designator within the statistics segment and by examining the real-life 14th dimensional heart disease data.
  • We satisfied the writing intensive designator with three different styles of writing - the Ben Franklin summary report, the mathematician teaching worksheet, and the geometry research report.
  • We satisfied the computer use designator via the web and web searching techniques, WebCT use, and Microsoft Word, Excel and Powerpoint. I specifically chose programs that are widely available, and that you are likely to use again, as opposed to mathematics specific software.

    Satisfying Topics and Objectives and A Note on the Commonalities of Mat 1010s


    All Mat 1010s must satisfy the three designators, and must cover the statistics segment. Most also cover the financial mathematics segment. Hence, for most of the semester, during the financial mathematics and statistics segments, most 1010s look alike. We differed slightly by taking an interdisciplinary approach, combining financial mathematics with political science and history in the Ben Franklin lab, and statistics with a real-world view via class activities, 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 that combined 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.

    WebCT Peer Review of Effectiveness of Groups
    For each of the major projects that you had a partner for (the Mathematician presentation and worksheet, and the Geometry of the Earth and Universe report), I want feedback from you on group effectiveness.

    Using File/New Window, open up a new web browser and enter WebCT. Compose a WebCT mail message to Dr. Sarah at 1339520031 with the subject "peer review".

    On the __________ assignment, I worked with __________________
    (be specific about each assignment and who your partner was)
    and ______________ (choose one of the following):

            I deserve the same grade as my partner
            I deserve a higher grade than my partner
            I deserve a lower grade than my partner

    If you did not choose the "same grade" option, then please elaborate and justify your answer.

    Fill in the above for each assignment for which you had a partner.

    Final Exam

    Final Exam

      The final exam will cover the What is a Mathematician? segment, the Geometry of Our Earth and Universe segment, and What is Mathematics?

      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 15% 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 (since much of your grade was determined by lab work, writing projects, and participation) your performance on the final exam is important since it demonstrates your mastery of the recent course material. I do take improvement over the course of the semester into consideration.

      See the Take Home Part of the Final Exam

      For the in-class part of the final, one 8.5*11 sheet with writing on both sides allowed and one calculator mandatory. More details on the in-class part of the exam during tomorrow's class.

    Reviewing Material:
    Answer Questions on a Piece of Paper

    Financial Mathematics

      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.

      Loan Payment Formula:          

      Monthly Payment =

                            Loan (rate/12)
                          ________________

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

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

    1. 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

      Stock Update

    1. Do the next 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).

      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. 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 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.

    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 a Mathematician?

      Before break, we reviewed some of the segment themes as they related to Dr. Sarah.




      An Equation Flying Passed 3D Homer


    1. Go to this text transcript of the 3D 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 down.



    2. Using only math common sense (without using your calculator), is the right hand side of the equation even or odd? Why? Use your knowledge of the fact that raising a number to a power is the same things as multiplying that number by itself that many times to answer this, since you will not be able to answer this on your calculator.



    3. Using only math common sense (without using your calculator), is the left hand side of the equation even or odd? Why?



    4. Use the answers to the last two questions to explain why this equation cannot hold.



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



    6. Use Fermat's Last Theorem (which Andrew Wiles proved was true) to explain why this equation cannot be true.



    Geometry of the Earth and Universe

    1. Skim through the NYTimes article (Universe as Doghnut: New Data, New Debate) again



    What is Mathematics?

      We have examined "What is Mathematics?" and have also looked at many applications of math to real life.

    1. Read through Adding Up Fuzzy Math: Teaching the Basics. This is a new reading.



    2. Review the Creative Inquiry Lessons for Life list.



    3. Review the Quantitative Literacy reading.



    4. Review the What is Mathematics? reading.

    The Remainder of Lab

    Remainder of Lab

      Take advantage of the time you have in lab now since I am happy to answer questions as I make my way around the room. We will continue reviewing for the final exam in class tomorrow. See the front board for office hours. Check the main web page for work due.

      Spend the remainder of lab working on the Ben F report or Mathematician worksheet revisions for Thursday (along with the paper references for your mathematician), the take home part of the final, or WebCT quizzes 6-8 due next Tuesday (Recall that there are an unlimited number of retakes for quiz 6 only and that (as usual) your grade is the highest of your retakes. Hence, once you receive a perfect score, retaking the quiz for the purposes of review will not hurt your grade. When you retake WebCT quizzes, you should make sure that you understand why each part is correct or incorrect and make sure that you could explain so on the final exam).