Dr. Sarah's Math 1010 Class Highlights
### Dr. Sarah's Math 1010 Class Highlights Spring 2002 Page

The following is NOT HOMEWORK unless you miss part or all of the class.
See the Main Class Web Page
for ALL homework and due dates.

### Review

**Mon May 6**
Review Lab

**Tues May 7**
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 final exam.

### Geometry of the Earth and Universe

**Mon Apr 29**
Briefly go over problems 8-11. If you are waiting for the video,
do stock update number 3 and look at the main web page for assignments.
The Shape of Our Universe,
worksheet

**Tues Apr 20**
PBS
Life by the Numbers
Shape of the World video
Hundreds of years before Columbus set sail, the Greeks used mathematics to determine the size
and shape of the planet. Viewers see how mathematics has become a tool to explore the earth
and the heavens as the world and the cosmos is charted.
(stop at Jeff Weeks segment since we watched this part in lab.)

Selections cut from
PBS Life by the Numbers
Seeing is Believing Video
The first special effects ever created in
Renaissance paintings also owe their existence to mathematics and
spurred on the industrial revolution.
Modern artists and mathematicians are trying to grapple with
the 4th physical dimension.
Mathematics helps define space and
helps present visions of our world to us.

**Thur May 2**
Review the shape of the universe material.
Euclidean, hyperbolic and spherical geometries,
the 4th physical dimension and its applications,
the hypercube and the hypersphere
via
excerpts from
Davide Cervone's Selected Course Notes
why the universe is not thought to be a hypercube,
and some of the shapes
that might be the shape of the universe
(10 Euclidean possibilities, a number of
the infinite but known spherical possibilities
via excerpts from Week's paper on Topological Lensing in Spherical Spaces
page 1,
page 12, and
current mathematical attempts to classify the
hyperbolic possibilities, including the
Weeks example
, which is the smallest known hyperbolic space),
and
current attempts to determine the shape of the universe.
Brief intro to my own
research and how it fits into these ideas, and my
mathematical style.
Exit survey.

**Mon Apr 22**
Conclude the What is a Mathematician Segment via an
IDS Viewpoint,
2D Universes,
work on WebCT quiz 5, 6 and/or the geometry report.

**Tues Apr 23**
Review Homer questions,
collect geometry reports, go over questions 1-7.

**Thur Apr 25**
2D Universes continued...
Oral quiz on questions 0-7 to finish geometry of the earth.
Intro to hyperbolic geometry via sketchpad -
Sketchpad Playfair's
Playfair's Image,
Sketchpad Sum of Angles
Sum of Angles Image
Sketchpad Euclid's 5th
Postulate
Euclid's 5th Postulate
Image
Sketchpad Pythagorean Theorem
Pythagorean Theorem
Image
and
Escher.
Highlight
differences between
Euclidean, hyperbolic and spherical geometry.
Polygonal tiling models of the sphere, the plane and hyperbolic space.
Crochet model of hyperbolic space.
If time remains,
Review gluing spaces - torus, klein bottle (learn to visualize
this), and a 2-holed torus.

### What is a Mathematician?

**Mon Apr 15**
Readings and Activities on Perspective Drawing and Projective Geometry,
perspective worksheet,
Homer 1. If you are finished
early, then work on WebCT quiz 5 retakes, review of Mathematician
ideas via web references, or homework or projects.

**Tues Apr 16**
Paul Erdos and David Blackwell Presentations. Dr. Sarah reinforces
the material.

**Thur Apr 18**
Mary Ellen Rudin, Frank Morgan and Ingrid Daubechies Presentations.
Dr. Sarah reinforces
the material.

**Mon Apr 8**
Work on a
MathSciNet search for authors (only works from school)
for modern mathematicians (Erdos up until recent
times) and other searches for papers by your mathematician.
Do a stock market update. Winning strategy for "Dodge Ball"
Begin
geometry of the earth and universe segment.
If time remains then WebCT quiz 5. Otherwise take this outside of lab.
Lab Directions

**Tues Apr 9** Gauss and Germain presentations.
Discuss the fact that mathematics research is often completed for
its own sake and not for its usefulness, but that it often ends up
being useful and applicable, sometimes immediately, and at
other times hundreds of years later
(as in the case of research that formed the basis for modern computers,
Sophie Germain primes that are used in RSA coding, Dr. Sarah's research, ...).
Relate statistics to the 55 reasons article.
Go over RSA coding via link from mathematician reference page.
Go over Gauss' mathematics.

**Thur Apr 11** Cantor and Ramanunjan presentations.
Dr. Sarah reinforces the material.

**Thur Apr 4**
Thomas Fuller and Maria Agnesi Mathematician Presentation and
Classroom Worksheet. Dr. Sarah reviews the material after each
presentation. If time remains then begin "Dodge Ball".

**Mon Mar 25**
Go over logistics
for the What is a Mathematician segment,
and discuss
Microsoft PowerPoint features for
your presentations.
Each person practices putting a picture into powerpoint.
Andrew
Wiles lab

**Tue Mar 26**
Andrew Wiles worksheet
Work on What is a mathematician segment.

**Thur Mar 28**
Discuss the fact that in "The Proof" video, we saw very few women, and only
heard about one woman working on the problem, and we saw no African
Americans.
Statistics on women and underrepresented minorities in
mathematics.
Briefly talk about Carolyn Gordon and Can you Hear the Shape
of a Drum?
Carolyn Gordon worksheet

### Statistics

**Mon Mar 18**
Choose mathematician in groups of 2 (additional directions will be
given out on Thursday).
Interactive linear regression plot via heart of math activity.
Statistics Detective Lab
due at the end of lab.

**Tues Mar 19**
Review by calling on students to answer questions based on WebCT quizzes
and review sheet.

**Thur Mar 21** Test 2 on Statistics

Spring Break March 11-15

**Mon Mar 4**
Collect hw, go over linear regression on excel via How Do You Know
p. 209 number 11,
how to use the equation of the line to make predictions, and
highlight situations where the prediction makes sense versus those that
don't (armspan as a predictor of height, p. 209 number 11 prediction for
15 hours and 100 hours, and stocks),
and Does Smoking Predict
Breath Held? graph.
Lab Directions,
Linear Regression Lab,
Egg Bungee Jump Regression

**Tues Mar 5**
Discuss music choices from class survey and compatibility issues
via Music graph 1 and
Music graph 2.
Do linear regression by hand via p. 208 number 11 and compare to Excel
work.
Discuss actual predictor value,
estimated predictor values from a graph or via a line fit by eye,
and related issues.
Discuss Volume/High WORTH MORE from lab via WebCT quiz 4 question 11.
Talk about Does SAT score predict college GPA?
Discuss the fact that more than a dozen studies of large student
groups and specific institutions
such as MIT, Rutgers and Princeton conclude that young women
typically earn the same or
higher grades as their
male counterparts in math
and other college courses despite having SAT-Math
scores 30-50 points lower, on average.
Discuss gender and multicultural issues
on test taking, and discuss stereotype vulnerability via students reading
selections from
FairTest Examiner
Stereotypes Lower Test Scores, and
Claude Steele has Scores to Settle
Groups discuss the article and then discuss whether they have ever
experienced something similar as part of some kind
of group (for example, gender, race, math phobic, ...)
that wasn't expected
to do well on a test or in another situation.

**Tues Mar 7**
Collect hw, discuss HIV testing issues, and discuss unintented
consequences of medical and educational testing and
policy decisions such as raising airline prices
via heart of math reading and stereotype vulnerability.
Discuss literary digest poll on Roosevelt/Landon election from 1937.
Discuss linear regressions of Buchanan votes in Palm Beach.

**Mon Feb 25**
Mean, Median and Mode,
Modular Arithmetic and Check Digits,
Excel credit card checker
**Tues Feb 26**
Continue to use the class data to discuss bar charts
(distance from home and height)
, and how you can tell whether the mean will be above or below the mean, standard deviation (distance from home, height, untimed MRT)
, review the timed and untimed MRT and stats from lab,
histograms (distance from home with a class size of 50 and then 100)
, pie charts (smokers, class year), and then talk about "bad" graphs.
**Thur Feb 28** Collect and then go over hw,
boxplot of female versus male height, boxplot of female versus
male untimed MRT, boxplot of distance from home,
begin linear regression via does armspan predict height, and
the worksheet on interpreting the results of regression.

**Mon Feb 18**
Lab directions,
Class data
collection sheet,
Quantitative literacy,
pinecones

**Tues Feb 19**
Collect real life rates. Go over credit card statement, payday lending offer, credit card offers, real-life rates. Discuss biases related to the
census of class data. Begin sampling.
Review pineapple material.
students look at golden mean poster and pinecones.

**Thur Feb 21**
Look at summary of readings, review survey method
guaranteeing complete anonymity from Heart of Math, use this method on an
embarrasing but interesting survey question,
and then we analyze the survey results.
Perform the same survey method on a non-embarrasing question.
Review the difference between a
census and a survey. Then use the table of random digits to pick
people from the class. Students work
on the circle sampling problem from How Do You Know.

### Financial Mathematics

**Mon Feb 11** Stock Market and
Homer Tax

**Tues Feb 12** Students work on p. 90-92 9 and 14 and p. 1010 number 8,
go over the answers, review parts of the condo lab,
and common sense for matching WebCT quiz 2 questions to the number answers.
In remaining time, students review for Thursday's test or work on the
lab.

**Thur Feb 14** Test 1 on Finance

**Mon Feb 4** Dr. Sarah's condo
continued - at least finish up to and including the car table.
WebCT quiz 2 (take this outside of class if you didn't
have a chance to take it in class).
If you finish both of these work on homework.

**Tues Feb 5** Review condo today problem.
Go over 2nd by-hand problem from the hw (and how much is the total
interest) by calling
on students using the index cards. Also do that to
look at the second by hand homework problem as a loan payment problem -
instead of saving up for the $50000 car, assume that we found a car loan for
18.38 years at 8% compounded monthly. Then what will our monthly payment be?
How much is the total interest?
Compare this to the $100 savings per month option and discuss. Finish
Dr. Sarah's condo part 2 in class.
If finished before class ends, work on the finance review sheet
or other hw.

**Thur Feb 7**
Analyze Dr. Sarah's student loan statements, analyze past
student Mark's student loan statement. p.90-92 problems
19, 21, 22, 23, 24, and 25
- students
worked in groups (counted off and then formed groups via
the whole # remainder of their # divided by 6)
and presented their solutions to the class.

**Mon Jan 28** Lab 2,
Ben Franklin Part 1

**Tues Jan 29**
Go over web pages - main, class highlights,
syllabus, web based problems, WebCT (bulletin board,
quizzes and retakes, and grades).
Use index cards to call on people to answer questions on
Ben F and Jane and Joan.
Go over
Jane and Joan extra credit (excel sheet) - using goal seek to discuss
what interest rate would result in equal savings for them both.

How long does it take to tripple a lump sum
of $1000 at 6% compounded yearly?
How long does it take to tripple a lump sum
of $1000 at 6% compounded monthly?
When can we get our $22,000 car if we can't get a car loan
but are forced to save up $200 a month into a 6% compounded
monthly?
Dr. Sarah read about the 2001 Powerball lottery from usatoday.com.
It said "For the jackpot worth 295 million, if there is one winner, then
they will have a choice between 25 annual payments of 11.8 million each
(25*11.8)=295 or
a single lump sum payment of 170 million".
How can we compare the logical benefits of each choice?
Let's cut off the "million" to make it easier to work with
(if you look at the formulas for lump sum and periodic payment, this
is ok to do, since it is multiplication outside the parenthesis).
Let's assume that if we took the
lump sum then we would leave the 170 in an
account at 5% compounded annually for the 25 years. Let's
assume that if we took the annual payment then
we would deposit each 11.8 annual payment into the same type of account.
Which yields more money?
Which would you choose? Why?
What rate would yield the same amount of money?

**Thur Jan 31** Dr. Sarah's condo

**Mon Jan 21** MLKJ Holiday

**Tues, Jan 22**
Review lump sum formula and the philosophy we used to come up with it.
If $100 is deposited into an account and left alone for 25 years,
compounded monthly at 5%, how much will we end up with?
How much will be interest ($)?
Compare to $100 deposited every month into an account and left
alone for 25 years, compounded monthly at 5%.
Work towards the periodic payment formula and compare the philosophy
to the lump sum formula derivation philosophy.
$100 is deposited each month for 12 years into an account compounding
5% monthly. How much do we end up with?
We'll do an exercise to show that the number of digits we use does matter!
100 is deposited each month for 12 years
into an account compounding 5% monthly. What do we have at the end?
The interest rate is .05/12=.004166666... Each
group of 3
used a different number of digits and rounding versus truncation methods (ie .004,.0041, .0042,.00416, .00417,.004166, .004167, .0041666, .0041667
). The group helped each other with their calculators and made sure that
they all came up with the same answer.
We compared the final answers to show that we should **never round**.
If we have a baby, how much we we need to put in per month in order to
have $100,000 for college (18 years from now) assuming 6%
compounding monthly. How much do we put in total? How much is interest($)?

**Thur, Jan 24**
Review formulas via sheet, go over questions, How much do we need to invest
now to have 100,000 in 63 years at 6.5% compounded monthly?
What if we will
deposit a certain amount per month? How much must we put in per month? The
problem with this scheme is that we will be making payments for the
next 63 years! Instead, let's say we can affort a monthly payment of $20.
How long will it take for the money to grow to 100,000? We set up the problem
and then did Guess and check. Intro to Logs. Solve 5^time=25. Then solve:
How long will it take to save 100,000 if we put in
$20/month at 6.5% interest, compounded monthly. We set up the problem and
then reduced to number^power=number, and then solved for the exact answer
using logs.

**Mon Jan 14** Intro to the course. Begin financial mathematics
via How Do You Know? section 2.1.
Fill out
index sheet. Work on
Lab 1,
Wile E. Coyote, and
complete the
survey. As time allows,
follow the directions at the end of lab 1 to read the
Dr. Sarah's Office Hours and Syllabus and Grading Policies links.

**Tues Jan 15**
Collect homework.
Each group does a problem 2.1 5,6,7,9,10 to turn in and present
to the rest of the class.
Attitude Survey.
Review course web pages. Web searches to find the history of
interest rates and related issues.

+history +"interest rates"
371,000 pages

+"history of interest rates" 693 pages

+"history of interest rates" +loan +credit

FT.Com -
FT Guide to the New Millenium

+"history of interest rates" +babylonian

Financing Civilization

Usury is Piracy

**Thur, Jan 17**
Review and continue with the history of interest. Begin lump sum
formula via compounding annually. Then compounding quarterly,
and then the general lum sum formula. Compounding monthly.
Real-life bank situation.
Past student was told that her c.d. will be
compounded monthly at 8% for 8 months, and is told that this 8% will
apply each and every month.
Let's say that she put in $1000. How much would her c.d. be worth
at the end of 8 months if
-the bank will compound 8% each and every month (ie 96% per year!)
-the bank means that 8% is the annual rate.
Which did the bank really mean?