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
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).
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
Answer Questions on a Piece of Paper
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
Open the link in a new window and read through it and answer these questions.
- Write down the 2nd equation from Homer's blackboard (see the text
below the pictures) involving the power of 12.
- 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 the 2nd equation on Homer's blackboard cannot be true.
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).
- 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.
- 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.
- 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.
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
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
Loan Payment Formula:
Monthly Payment =
1 - (1 + rate/12)(- years*12)|
Total Interest Over the Life of a Loan:
Interest = Monthly Payment * 12 *years - Loan
- 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.
To recognize misrepresentations of studies and statistical data in
the real world by understanding statistical techniques and satisfy the
numerical data designator.
- Take out your stock packet and
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
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.
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 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
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",
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
- 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?
by taking the number of deaths, dividing by the number of
cases and then turning this into a percentage.
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
There were 11 cases of inhalation anthrax infection and
5 deaths. There were 12 cases of cutaneous anthrax infection and
- 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
This statistic could be used to calm the public.
Note that this
is much, much smaller than the corresponding flu percentage.
- 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.
- 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:
- Read through
Adding up Fuzzy Math: Teaching the Basics.
- Read the Quantitative
- Review the Creative Inquiry Lessons
for Life list.
- Review the What
is Mathematics? reading.