Dr. Sarah's Review Lab
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
Read through the following and click on any underlined links
as they come up.
You should answer any questions on a piece of paper.
Satisfying Course Goals and Objectives
Develop creative inquiry skills.
appreciation of what mathematics is,
what it has to offer, why it is useful, and the diverse ways
that people can be successful at mathematics (including you!).
Develop communication skills by
communicating mathematics to a general audience in writing projects,
group and class discussions and presentations, and on the WebCT bulletin
Develop computer skills and advanced web searching techniques.
has been designated as a
and computer use course.
Watauga College Math 1010
All Math 1010 sections must satisfy the three designators.
This section of MAT 1010 is designed for Watauga College students.
You'll receive full general education math credit
while developing a liberal arts appreciation of mathematics.
While parts of the class are similar to other Mat 1010s,
it differs from other sections via an interdisciplinary and thematically
Syllabus 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...
To recognize misrepresentations of studies and statistical data
in the real world
by understanding statistical techniques and satisfy the numerical
What is a Mathematician? The lives and mathematical
work and styles of some famous mathematicians.
our Earth and universe
You'll become a mathematician with the geometry
of the earth and universe as your field of study, while developing
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
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
and by examining the real-life 14th dimensional heart disease data.
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
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 and
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 political 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
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.
Take out your financial mathematics test, and look up the
lump sum, periodic payment and loan payment formulas from your
Write them down on a separate piece of paper:
- lump sum formula
- periodic payment formula
- loan payment formula
Keep America Rolling
Since September 11th, you may have seen television
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 were even extended
into this year.
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 in January, but brought it
back in March.
Recall from when you searched for real-life rates, you
saw that normally 3 year loans
compound monthly at somewhere around 8%. In the "Keep America Rolling
Program" these 3 year loans charge 0% interest over the life of the loan.
- Use the loan payment formula in order 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 over the life of the
loan - this interest is the amount the customer would save in the
"Keep America Rolling Program".SHOW WORK
- Do stock update number 4
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 (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.
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 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 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.
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
So, one statistic is that # 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% of the United States Population 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 are so afraid of anthrax 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.
What is a Mathematician?
An Equation Flying Passed 3D Homer
- Go to this
text transcript of the 3-d Homer segment
and Did You Notice? by James A. Cherry, and find the exact
numbers in the equation shown above
where numbers are raised to a power of 12.
Verify that this matches what you see in the picture and
write the equation here.
- Is the right hand side of the equation even or odd? Why?
- Is the left hand side of the equation even or odd? Why?
- Use the answers to the last two questions to explain why
this equation cannot hold.
- 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 this equation cannot be true.
Peer Review of Effectiveness of Groups
For each of the major projects that you had a partner for
(Ben Franklin, Statistics report, Mathematician presentation
and worksheet, Geometry of the earth and universe report),
I want feedback from you on group effectiveness.
Go to the WebCT newsgroup forum containing JUST you and Dr. Sarah
and choose from the following:
(you may copy and paste from here into WebCT)
Take Home Part of the Final - 2 Parts
Your final exam grade will be determined by
a take-home portion and an in-class portion.
Recall from the syllabus and past grades assignments
that the comprehensive final exam is worth 20% of your course grade, while
20% of your grade was determined by the combination of test 1, test 2, and your mathematician presentation. While this percentage is relatively small (many other 1010 sections have exams count for 45-60% of the course grade), your performance on the final exam is important since it demonstrates your mastery of the course material and provides you with an opportunity to pull everything together. I do take improvement over the course of the semester into consideration.
For the in-class part of the final,
one 8.5*11 sheet with writing on both sides allowed.
1 calculator and straight edge mandatory.
More details on this part in class tomorrow.
Read through the following directions for the take-home part
of the exam now, including the underlined links.
This is due on the day of the final
Part 1 of Take Home Portion of Exam - Style
We have seen that there are many diverse styles that lead to success in
mathematics. Choose a mathematician** whose mathematical style
you identify with and find most rewarding.
While geometry is actually the most difficult for me,
I chose it as my specialization
because it is the most rewarding for me.
Identify the mathematician, describe his or her
style briefly, and then
give specific examples from your life of how the mathematical style
applies to you and leads to your success in mathematics
and in other areas of your life.
Suggested length: 1 page typed.
** The mathematician will be chosen from among:
Andrew Wiles, Carolyn Gordon, Thomas Fuller, Maria Agnesi, Gauss,
Sophie Germain, Georg Cantor, Ramanujan, Paul Erdos,
David Blackwell, Mary Ellen
Rudin, Frank Morgan, Ingrid
Daubechies, Tom Banchoff, Jeff Weeks, or
Part 2 of Take Home Portion of Exam - What is Mathematics?
We have examined the questions of "What is Mathematics?"
and have also looked at many applications of math to real life.
Using ideas in
Adding Up Fuzzy Math: Teaching the Basics,
What is Mathematics?,
and specific examples of mathematics and its applications,
discuss how your personal view of mathematics and its usefulness
in your life has changed over the course of the semester.
Suggested length: 1 page typed.
Remainder of Lab
Spend the remainder of lab working on WebCT quizzes 6, 7 and/or 8,
revisions for Thursday,
and/or the take home part of the final.
Take advantage of the time you have in lab now since
I am happy to answer questions on anything.
During tomorrow's class we will complete course
evaluations and I will give you
study suggestions for the in-class part of the final
as we continue reviewing for the final.
If you must miss class, you must see me in office hours before the
I will set some extra office hours after classes end once I know
my schedule. Check the main web page for work due.