Dr. Sarah's Review Lab - USE NETSCAPE!!

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 you go along from this lab, which is accessible from the main web page at http://www.mathsci.appstate.edu/~sjg/class/1010. You are receiving a printed copy of this so that you can study from it, and because there have been server problems all over campus (computer services is working to correct them). This should be completed and turned in by the end of lab. You will receive it back in class tomorrow.
From the syllabus:                               Course Goals
Develop creative inquiry skills.
Develop an appreciation of what mathematics is, what it has to offer, and why it is useful.
Develop communication skills by communicating mathematics to a general audience in writing projects, group and class discussions and presentations, and on the WebCT bulletin board.
Develop computer skills and advanced web searching techniques.
Math 1010 has been designated as a writing intensive, numerical data and computer use course.
From the syllabus:                               Topics 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.
What is a Mathematician? The lives and mathematical work and styles of some famous mathematicians.
Geometry of the Real World Geometry of our earth and universe - doing mathematics the way mathematicians do.

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.
  • We satisfied the writing intensive designator with four different styles of writing - the Ben Franklin summary report, the statistics persuasive report, the mathematician teaching worksheet, and the geometry research report.
  • We satisfied the computer use designator via the web and web searching techniques, bulletin board and online 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, must use the How do You Know? book, and must cover the statistics segment. Most cover the 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 politcal 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.
    Read Through the Following:
  • Quantitative Literacy
  • Adding Up Fuzzy Math: Teaching the Basics (which is attached as the last side of this packet) and then review the
  • Creative Inquiry list.
  • Do stock update number 4 and show it to me so that I can check this off on this 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.

    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, 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.
  • 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. I also found 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 91871/281421906 = 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. I also found that there are 94,800,000 flu/pneumonia cases each year. Hence, the risk of dying once you have the disease is 91871/94800000 = 9.69E-4 = .000969 = .0969%. All of these different perspectives must be taken into account when examining the statistics.
  • Let's see why people are so afraid of anthrax when the chances of getting the disease are so small: Use effective web searching techniques in order to find details on the number of anthrax cases in the United States since September 11th. Be sure that your page is current, and includes the death of the 94-year-old woman who died of inhalation anthrax on November 21.
  • Give the exact phrases and words that you used for your successful search, the total number of cases of inhalation and cutaneous anthrax infection, and the number of deaths.

  • Use your answer and the population of the United States 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 which would be 94800000/281421906 = 33.7%. SHOW WORK.

  • Determine the risk of dying once you have the disease by taking the number of deaths of anthrax and dividing by the number of cases. Notice that this is much, much larger than the .0969% risk of dying once you have the flu, which explains why people are so afraid. SHOW WORK.

    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 here:
  • lump sum formula

  • periodic payment formula

  • loan payment formula

    Skim through this reading on Money Matters from the Heart of Mathematics in order to review the derivations of the formulas, real-life applications and learn some new things too! Notice that the lump sum and periodic payment formulas match our formulas. But, the reading never actually gets to our loan payment formula, although it does get close (on the last page).

    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 have been extended into next year. Use effective web searching techniques in order to find details on the length of an interest free car loan.
  • Give the exact phrases and words that you used for your successful search and the length of time of the 0% loan.

  • Use OUR loan payment formula in order to determine how much a customer will save - ie calculate the monthly payment assuming 8% interest loan of $20,000 compounded monthly for the loan period you found above, and then calculate the interest over the life of the loan - this interest is the amount the customer would save. SHOW WORK

    What is a Mathematician
  • Go to this text transcript of 3-d Homer segment and Did You Notice? by James A. Cherry, and find the equation where numbers are raised to a power of 12. Write this down here.

  • Why is the right hand side of the equation equal to an even number?

  • Why is the left hand side of the equation equal to an odd number?

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

  • What is the statement of Fermat's Last Theorem?

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

    For homework, I asked you to think about what style of doing mathematics is most rewarding for you. Notice that I did NOT ask which segment was most applicable (financial mathematics) or which segment was the easiest for you (recall that while I chose to do geometry, since this is the most rewarding for me, it is actually a part of mathematics that I find most difficult). Instead, I asked what STYLE (we have seen many different styles of people being successful in mathematics) of doing mathematics is most REWARDING for you.
    Open up Microsoft Word and type up a response to this. Be sure to include an in depth response including reasons why the style (NOT the segment) is most rewarding. SAVE OFTEN.
  • When you are finished, copy your work from Word and paste it into a bulletin board posting to the forum containing just you and I. When you are sure that you have chosen the correct forum, post the message. Check to make sure it posted correctly by clicking on Update Listing, selecting the topic (forum) containing just you and I and reading your message.
    Geometry of the Earth and Universe
  • Take WebCT quiz 8. Your grade is the highest of the (up to) 5 tries you complete before this Wed at 11:55pm.
    If time remains in lab, make sure that you have completed WebCT quizzes 6 and 7 (due tonight by 11:55pm). You can retake WebCT quiz 8 (due this Wed by 11:55pm), review or work on extra credit opportunities.