What is Mathematics?
Even though we don't have a final exam (we'll use the exam period for
the final project research sessions), it is still important to step
back and see where we have been, and
the purpose of today is to do so as we reflect on what mathematics is.
Discuss in groups:
What was the purpose of the Geometry
of the Earth and Universe segment?
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,
while also examining local (laws from high school) to global (new laws)
issues as we explored
how we view the world around us and what it actually looks like.
In the process we developed
creative inquiry techniques.
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.
Interest formulas as they apply to the real world
Keep America Rolling
After September 11, 2001, GM created a
"Keep America Rolling" program, which offered interest-free
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
6% 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 applying statistical techniques.
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
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.
Some webpages state:
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.
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 US.
cases that year.
"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 = .000326 = .0326%
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 different kinds of mathematics, applications
to real-life, along with the diverse ways that people succeed.