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
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 statistics and finance segments.
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, 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 realworld view
via class activities, and the stock market.
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 posting message to Dr. Sarah
by choosing the forum containing you and Dr. Sarah
and using the subject "peer review". You may copy the following
and paste it into WebCT by highlighting the text, and going to
Edit/Copy here, and then Edit/Paste in WebCT.
Final Exam
Final Exam
The final exam will cover What is Mathematics? and
Finance.
While 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 and the
What is Mathematics? theme.
I do take improvement over the course of the semester into
consideration.
One 8.5*11 sheet with writing on both sides allowed and
one calculator mandatory.
More details on this in class tomorrow, where you will also
receive the take home portion of the test.
Reviewing Material:
Answer Questions on a Piece of Paper
Even though the details from the
other topics are not on the final
exam (you are expected to recall the "big picture" themes as part of
What is Mathematics?), 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 skeptical learners.
Geometry of the Earth and Universe
How we view the world around us and what it actually looks like.
As a reminder, skim through the
Shape of our Universe
readings again.
What is a Mathematician?
The lives and mathematical work and styles of some famous mathematicians.
Using the control key, do control and then a mouse click on this link
Homer's
blackboard equations
and then open the link in a new window and read through it.
 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 TI83 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.
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.
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
 Take out your stock packet and
do the
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...E4 (E4 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:
 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?
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.
 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.
 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.
 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.
Your final exam will consist of
material from Finance and What is Mathematics?
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 reallife.
 Read through
Adding up Fuzzy Math: Teaching the Basics.
This is a new reading.
 Review the Creative Inquiry Lessons
for Life list.
 Review the Quantitative
Literacy reading.
 Review the What
is Mathematics? reading.
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 interestfree
financing on all new cars and trucks for certain loan periods.
Zeropercent 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
 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
Ben Franklin
Superscripts in Word
Open up Microsoft Word and type in
1000(1+rate)100=131000
Highlight 100 and under Format, release on Font. Then
check the box next to superscript and hit OK.
 Show Dr. Sarah your professionally formatted equation so that she
can check off that you were able to do this. You will need similar
professional formatting in your report.
Lab answers Take out your Ben Franklin lab and look at your answers for.
Compare your answers to the following:
Next go to the main web page and look at homework for the rest of the
week.
As usual, I'm happy to answer any questions you have as I make my way
around the room, in office hours, or on WebCT. We'll talk more about
the final in class tomorrow.