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
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
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
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 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.
- 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.
- 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, 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.
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
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",
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.
- 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:
- In addition, prepare to share something in class tomorrow on each of
these readings - take notes on what you plan to share.
Complete the informal learning evaluation.
If time remains, work on the personal reflection or
final project (see the main web page).