Dr. Sarah's Math 1010 Class Highlights
### Dr. Sarah's Math 1010 Overnight Assignments
and Class Highlights Spring 2001 Page

See Main Class Web Page or
WebCT calendar for longterm project due dates.
See WebCT calendar for quiz retake due dates.

### Geometry of our Earth and Universe

**Mon, April 30**

Finish up Geometry of the Earth and Universe via Dr. Sarah's
Geometry of the Universe.

Look at Syllabus and Summarize the Course

Course Evaluations

Hand out Final Exam Review Sheet

Stock Market Update

New Scientist Planet Science: Ghosts in the sky
**Homework** Think about what kind of mathematcial style that we've
seen/used works best for you.
**Tues, May 1**
Review for Final Exam - Last Day of Class!

**Mon, April 23**WebCT quiz 8, Web readings on 2d, 3d and 4d,
and 3-d into 4-d Homer.
**Tues, April 24** Seeing is Believing video from the
Life by the numbers series.
**Thur, April 26** Shape of the World video from the
Life by the numbers series. Talk about how to construct a cylinder from
a strip in the plane by identifying the edges, and how we could
explain this to 2d Marge.

**Thur, April 19**Finish Geometry of our Earth and Universe
presentations.

**Mon, April 9** WebCt quiz on first 3 days of the presentations,
2-d into 3-d homer.
**Tues, April 10** Presentations on Daubechies and Morgan.
Review Gender and Multicultural Issues and the diverse styles of all the
mathematicians that we saw.
**Thur, April 12** Collect Geometry of our Earth and Universe
reports and references. Begin presentations.

### What is a Mathematician?

**Mon, April 2** Icosahedron sheet, WebCT quiz,
begin Geometry of
our Earth and Universe.**homework** Work on classroom worksheet
from presentations, What is a Mathematician? Geometry of our Earth
and Universe, and WebCT quiz retakes.
**Tue, April 3** Presentations on Gauss, Ramanujan and Erdos.
**Homework** See WebCT calendar
**Thur, April 5** Presentations on Blackwell, Rudin and Gordon.
**Homework** See WebCT calendar and study for WebCT quiz on the first 3
days of presentations on mathematicians (Muhammed up to Gordon).

**Mon Mar 26** Dr. Sarah goes over
PowerPoint, and then student groups work on What is a Mathematician?
**Tues Mar 27**
Begin
Dr. Sarah's mathematics and mathematical style (and contrast with
Andrew Wiles)
Discuss diameter of spaces,
the diameters of a sphere, a football made from a sphere,
and a three-cornered pillow shaped object made from a sphere by using an
icosahedron.
**Thur March 29** Presentations on
Muhammad ibn Muhammad al-Fullani al-Kishnawi (-1741) Magic Squares,
Maria Agnesi (1718-1799) Witch of Agnesi, and
Sophie Germain (1776-1831) Modular Arithmetic,
Sophie Germain Primes and Coding Theory. Dr. Sarah goes over
ideas and mathematics involved after each presentation.
**Homework** Do classroom worksheets from presentations, work on
What is a Mathematician?, test revisions, and study for WebCT quiz
on Dr. Sarah's and Wiles' mathematics.

**Mon March 19** Hand out remainder of Mathematician Folders,
Statistics Test **Homework for Tues**
grades assignment.
**Tues Mar 20**
The first few
minutes of The Royale - Star Trek Next Generation's 1989 episode
from Stardate 42625.4
- Picard
- Fermat's Last Theorem. Familiar With it?
- Riker
- Vaguely. I spent too many math classes daydreaming
about being on a starship.
- Picard
- When Fermat died, they found this equation scrawled in
the margin of his notes-

X to the Nth plus Y to the Nth equals Z to the Nth
where N is greater than two, which he said had no
solution in whole numbeers but he also added the phrase
"REMARKABLE PROOF."
- Riker
- But no proof was included.
- Picard
- And for 800 years people have tried to solve
it.
- Riker
- Including you.
- Picard
- I find it stimulating. It puts thing in
perspective. In our arrogance, we feel we are so
advanced yet we still can't unravel a simple knot tied
by a pert-time French mathmatician working alone
without a computer.

Discuss Pythagorean Thm,
why a computer can't check all the cases, and the mathematical style of
Pierre de Fermat.
begin
The Proof -
A Nova video about Princeton University
Professor Andrew Wiles and his solution
of Fermat's Last Theorem.

**Thur Mar 22** Finish The Proof Video
Discuss
Then we discuss the mathematical style of Andrew Wiles
Fermat's Last Theorem,
how a mathematical proof will demonstrate that there are no solutions without checking all the cases, Taniyama-Shimura conjecture and the Epsilon conjecture. By looking at the example If I get a speeding ticket, then I was driving too fast, we demonstrate how If A then B is logically equivalent to If not B then not A, but that these are different statements then If B then A. Then, We apply this to the Epsilon conjecture to see that the conjecture is logically equivalent to If Taniyama-Shimura is true then Fermat is true.
Dr. Sarah's Worksheet on Andrew Wiles

### Statistics

**Over spring break - study for test 2 on statistics, do WebCT quiz
5 retakes (due Mon at 2pm), and start working on
What is a Mathematician?**

**Mon, Mar 5**
Go over linear regression on excel via
p. 209 number 11, and
how to use the equation of the line to make predictions, and
highlight situations where the prediction makes sense versus those that
don't (stocks, p. 209 number 11 prediction for 15 hours, 30 hours and 100
hours).
Measure some students armspan and height, discuss
why it makes sense that there should be a correlation between them
and then linear regression. Students give data to Dr. Sarah for input
into Excel.
Egg bungee jump lab, then WebCT quiz.
**Homework for Tues**
Need Internet Explorer for
Problem 3.5,
Problem 4.1,
Problem 4.2,
Problem 4.3,
Problem 4.4, **also do
p. 209 number 12 parts b) and c)
using the line and p. 186 #15 (given Thur)**.
**Tues, Mar 6**
Go over p. 185 #16, and p. 209 number 12 b) and c).
Do linear regression by hand via p. 208 number 11 and compare to Excel
work.
Have students do p. 209 number 12 part a) by hand.
Go over this and discuss actual predictor value,
estimated predictor values from a graph or via a line fit by eye,
and related issues
such as the fact that if someone had 10 absences in our class
then they wouldn't even be taking the midterm!
Hand out Does Armspan predict Height?
regression graph from Excel based on data taken in lab yesterday.
Go over WebCT quiz 5 problem on SAT score boxplot,
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
**Homework**WebCT quiz 4 retake due Tues night.
Work on stock lab (you may pick up your draft after
1pm on Wed on my door). For Thur, bring stock draft to class,
bring WebCT quiz 5 handout to class. WebCT quiz 5 retake due before
class on Mon after spring break, and test on stats is during that lab.
**Thur Mar 8**
Go over stock lab, go over WebCT quiz 5,
Hand out What is a Mathematician projects,
review for Statistics Test.**Homework** See Tues HW,
read
this website on linear regressions of Buchanan votes in Palm Beach,
read
Hispanics Draw Even With Blacks In New Census (washingtonpost.com)

**Mon, Feb 26** Stock Statistics lab
**Tues, Feb 27**
Students called on to go over HW from Tues, Feb 20, discuss examples
of data for p. 185 number 6.
For class data, do a pie chart and then a boxplot.
Compare to histogram for the class data.
Review NITE graphs
**Homework for Thur**See WebCT calendar for other HW,
**Need to use Internet Explorer for web based problems**,
Problem 3.2
,
Problem 3.3,
Problem 3.4,
p. 186 number 14.
**Thur 3/1**
Students put homework on the board.
Discuss standard deviation for the class data,
discuss standard deviation of Web Based Problem 3.1 from last
HW, continue analyzing what kind of info one can read from
different statistical representations,
begin linear regression.
**Homework for Mon** Work on stock lab which is due on Monday,
Study for WebCT quiz - notes on stock graphs and statistics,
histogram, pie chart, boxplots, mean, median, standard deviation,
linear regressions.**Homework for Tues**
p. 186 #15

**Mon, Feb 19** WebCT quiz 4, stock intro, web polls.
**Homework** See WebCT calendar (Feb and March)
**Tues, Feb 20** Survey: How far away
(in miles) is each student's hometown? Discussed biases in the data.
Order the data. Find the mean and median.
Do one histogram at a bin width of 100.
Discuss the difference between the book and the computer on histograms.
Each group does a different bin width.
Discuss measures of center and related ideas.
**Homework for Thur**
See WebCT Calendar, p. 151
You try it 2.1, p. 160 You try it 2.5,
(answers are in the back of the book), p. 168 number 12,
p. 185 number 6,
Use **Internet Explorer** for this
Web based problem (bras should be bias!)
Problem 1.1,
Problem 3.1 (see my WebCT posting on the
errors in here!).
**Thur, Feb 22**Go over HW, Dr. Sarah models stock lab
process for NITE, and discusses related issues.

### Financial Math

**Mon, Feb 12** Homer Tax lab, finish up Dr. Sarah's condo lab
from 2 weeks ago.
**Tues, Feb 13** Review major ideas from Homer Tax lab, including
28% bracket. Review major ideas from end of the condo lab. Discuss
Real life rates.
Analyze credit card statement. Analyze
Payday Lender info. Analyze credit card offers.
**Homework for Thur**
Where did 449.67 balance subject to finance charge come from
(extra credit if you find the correct calculation before we go over
it on Thursday)? Review Payday Lender and Credit Card calculations.
**Thur, Feb 15**Finish up credit card calculation, discuss
benefits and negatives of credit cards versus debit card,
wrap up financial math and give overview of that style of doing mathematics.
Transition into statistics by looking at MSFT stock price on the
web and modeling what the students will do at the begining of lab
on Monday (Each student will choose a different stock to track).
Begin statistics via samples, polls and census, explain how the
Random Digit Table is used in sampling.**Homework for next week**
Study for WebCT quiz, look up stocks that you might be interested in
via stock intro,
work on test 1 revs,...

**Mon, Feb 5** WebCT quiz 3, car lab
**Tues, Feb 6** review
**Thur, Feb 8** Test 1 on Finance

**Mon, Jan 29** WebCT quiz 2, Dr. Sarah's condo
**Tues, Jan 30** Go over homework,
web pages,
Jane and Joan extra credit (excel sheet) - using goal seek to discuss
what interest rate would result in equal savings for them both.
condo lab (excel sheet) - go over amortization table, and discuss
when the loan would be paid off if we pay an extra $20 each month,
and how much interest we would pay. Discuss
payment formula for
Look at Dr. Sarah's Condo
(costs $105,265, putting 20% down, at 6.75% compounded monthly)
with the payment formula and compare to Excel.
With a loan of 84,212, what is the monthly payment and total interest?
What if buy down the rate to 6.25%, which is the monthly payment and
total interest?
Hand out
test 1 review sheet, and car lab hw.
**Homework for Thursday (3 web based problems, and 3 by-hand problems)**
Web based problems ** need to use Internet Explorer **,
Problem 2.3 #1,
Problem 2.3 #2,
Problem 2.3 #3.

**Set up formula and solve on your calculator:**
what is the monthly payment for Dr. Sarah's condo if
we keep the rate at 6.75%, but instead take out a smaller loan of 82,212?
How much would she pay total? What is the 30 year interest?
What would have happened if I had waited until today to buy
the condo? Assume that the price of the condo had remained the same
(which it wouldn't have!). What is the monthly payment if we use today's
mortage rate of approximately 7.5%.
How much would I pay in total?
How much of that would be interest?
(I obtained this rate at
Bank of America Page by choosing Conventinal Fixed and looking at the
30 year rate.)
If I can afford to save $100 per month for a $50000 car, in an
account compounding monthly at 8%, then how long will it take
for me to save up?
**Either go to a bank sometime in the next week or search on the
web to find
real rates on
savings, checking & money market accounts, cds, & student, house and car loans.
Write up or print out your findings.**
**Thur Feb 1**
Go over homework,
look at the third 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? Compare this to the $100 savings per month
above and discuss. Analyze Dr. Sarah's student loan statements,
analyze past student Mark's student loan statement.
**Homework** See WebCT calendar. For WebCT quiz 3, study
webct quiz 2 and know loan payment formula setup and common sense.

**Mon, Jan 22** Work on Ben F. lab due next Wed.
**Tues, Jan 23** Continue log problems.
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 car if we put in $200 a month into a 6% compounded
monthly account if we need $22,000?
Students work on problems, and then we go over them as a class.
**Homework for Thur**See HW from Tues the 16th (below),
and also Internet Explorer
Problem 2.2 #12
(be prepared to present hw problems), work on Jane and Joan due Fri,
work on Ben F.
**Thur, Jan 25** Students called on randomly to present hw,
Math Whiz Contest. **Homework for Mon** See Tues hw,
study for WebCT quiz (know how to match formula to problem,
and common sense), and for Tues
p. 91 #17 and 20 and redo all the web based problems
as a review.

**Tues, Jan 16**
Review formulas, go over homework,
hand out Ben Franklin Lab,
Jane and Joan sheet.
How much do we need to invest now for Dr. Sarah to give her niece
100,000 at her niece's retirement?
Assume that she has found an account that will pay 6.5% interest,
compounded monthly.
We used algebra. How about if Dr. Sarah
will deposit a certain amount per month?
How much must she put in?
The problem
with this scheme is that Dr. Sarah will be making payment for the next
60ish years! Instead, let's say she 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 Dr. Sarah to save 100,000 for her niece
if she puts 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.
**Homework for this and next week** Wile E. Final Version due by Friday by
5pm on to my door 326 **along with draft**. You may turn it in early.
For Mon, read text of Ben Franklin lab and do quiz 1 retakes.
Also,
p. 90,
8 and 10 -13,
You Try It 2.8, 2.9 and 2.10 (solutions are on page 306),
Internet Explorer web based problems
Problem 2.2 #7
Problem 2.2 #8
Problem 2.2 #9,
Problem 2.2 #10,
Problem 2.2 #11.
Work on Joan and Jane sheet.

**Mon January 8** -
Section 2.1, and
Web based problems on % ** need to use Internet Explorer **, problem
1.1
(Click on the word PROBLEM and use the down arrow key to view the 2nd line),
problem
1.2,
and problem
1.3
(.91 is the correct answer - notice that the problem incorrectly
identifies .2, .3, .4, ... as correct answers also).
Intro to course via the syllabus and policies. Follow
Lab 1 Directions
**HOMEWORK for Tues** p. 69-71 # 1, 17, 20,
review syllabus and class notes.
Bring the textbook and a scientific calculator
(with y^x, x^y, or ^) to classes.
**Tues Jan 9**
Go over homework problems, via randomly picking on students
to present them. Fill out index sheets.
Begin lump sum formula via $20 in an interest bearing acount for 5 years,
compounding annually at 2%. How about compounding monthly?
If you win a lottery, is it better to take 10,000 now, or wait 12 years and
get 30,000 then
(assume that if we take the 10,000 now, then we won't spend any of
the money and instead will compound monthly at an interest rate of r%).
Each
group of 2 does
this for a different r ranging from 6% to 11.5%.
**HW for Thur
**Web based problems on % **need to use Internet Explorer**
problem
1.4,
and problem
1.5
and Web based problems on savings accounts, problem
2.2 #1 and problem
2.2 #2,
read pages 72-76, do page 90
numbers 1 and 2.
**Thur 1/11**
Review lump sum formula.
Students present hw.
Real Life Bank formula. 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.

The bank means 8% is the annual rate!
Discuss periodic payment formula.
If 100 is deposited into an account and left alone
for 25 years, compounded monthly at 5%, how much do we have?
Compare to 100 deposited every month into an account and left alone
for 25 years, compounded monthly at 5%.
Discuss solutions and calc keys.
We'll do an exercise to show that the number of digits we use does
matter! 100 is deposited each month for 25 years into an account compounding
5% monthly. What do we have at
the end? The interest rate is .05/12=.004166666...
Each group used a different number of digits (ie 0, .004,.0041,.00416,...) and
we compared the final answers to show that we should **never round**.
**HW for Tues **
Problem 2.2 #3,
Problem 2.2 #4
Problem 2.2 #5
Problem 2.2 #6 (the answer to the last question is wrong -
9% we would choose 1500 a month and 8% 30,000 later,
Put in $37 each month for 2 years,
at 12.99% compounded monthly. Compare this with putting in
$37 and leaving it there for 2 years, at 12.99% compounded monthly.
Read pages 77-79.