Dr. Sarah's Math 1010 Class Highlights
Dr. Sarah's Math 1010 Class Highlights Spring 2003 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.
Mon Apr 28
Review Lab
Thur Apr 24
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. (20 minutes)
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.
(45 minutes - stop at Jeff Weeks segment since we watched this part in lab.)
Mon Apr 14 Give back lab 9 (2D Universes)
and give groups a chance to review incorrect answers.
Briefly go over problems 8-11.
Shape of Our Universe Lab,
worksheet.
Tues Apr 15
Oral quiz on questions 0-7 on the geometry of the earth.
Intro to hyperbolic geometry continued via sketchpad -
Sketchpad Playfair's
Playfair's Image,
Sketchpad Sum of Angles
Sum of Angles Image
Sketchpad Pythagorean Theorem
Pythagorean Theorem
Image
(and relate to Introduction to hyperbolic
geometry from lab.)
Sketchpad Euclid's 5th
Postulate
Euclid's 5th Postulate
Image.
Highlight
differences between
Euclidean, hyperbolic and spherical geometry.
Worksheet on Escher.
(solution to number 2)
Polygonal tiling models of the sphere, the plane and hyperbolic space.
Crochet model of hyperbolic space.
Thur Apr 17
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.
Mon Apr 7
Finish going over Ingrid Daubechies, Review the Homer questions,
IDS Viewpoint Readings,
2D Universes,
web research for the geometry report.
Tues Apr 8
Review What is a Mathematician? segment via the segment themes as they
relate to the entire group of mathematicians.
Thur Apr 10
Collect geometry reports and go over problems 1-7.
Mon Mar 31 Finish up RSA coding from Thursday.
Presentations and worksheets on Georg Cantor and Srinivasa Ramanujan.
Intro to hyperbolic geometry worksheet.
In the time that remains, read the web readings for tomorrow and then
complete the worksheets and give suggestions for improvement.
Tues Apr 1 Presentation and worksheets on
Paul Erdos and David Blackwell
Thur Apr 3
Presentations and worksheets on Mary Ellen Rudin, Frank Morgan, and Ingrid Daubechies
Mon Mar 24 Lab Directions
(Perspective Drawing, Problem 0 of the geometry of the earth and universe,
stock market update, web readings, and Are The Simpsons 2-D or 3-D?)
Tues Mar 25 Presentations and Worksheets on Thomas Fuller and
Maria Agnesi.
Thur Mar 27 Collect Tuesday's worksheets. Presentations and
Worksheets on Carl Friedrich Gauss and Sophie Germain.
RSA Coding Continued
Decode the Message
RSA on the internet via Bank of America's website.
Mon Mar 17Go over the
logistics for the What is a
Mathematician? segment, and discuss
Microsoft PowerPoint features for
your presentations.
Each person practices putting a picture into powerpoint.
Intro to
The Pythagorean Theorem and Fermat's Last Theorem.
Andrew Wiles
Tues Mar 18
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.
Worksheet on Andrew Wiles
If time remains, then begin
Dodge Ball
Thur Mar 20
Collect preliminary writeup of answers to math questions.
Collect any remaining Wiles' worksheets and then discuss the concept of
proof and possible answers to those questions.
Work on Dodge Ball. Intro to the geometry of the earth and universe.
Spring Break
Mon Mar 3
Statistics Detective Review Lab.
Tues Mar 4
Intro to the mathematician segment via powerpoint on
Dr. Sarah,
classroom worksheet on
Carolyn Gordon.
Pick groups for the mathematician segment. (Students decide how to choose).
Questions on statistics segment.
Thur Mar 6
Test 2 on statistics.
Mon Feb 24
**Lab 5*
* on regression
(Part 1 and
Part 2). When you have completed
the Excel portions, then work on the "Worth More" parts or homework for
the end of the week.
Tues Feb 25
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.
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.
In groups of 2 or 3:
Discuss situations where text anxiety or performance anxiety have
hindered you. Discuss whether you or someone you know have ever
experienced something similar to stereotype vulnerability
as part of some kind of group (for example, gender, race, math phobic,
"good" or "bad" student...)
where external expectations
from someone else (teacher, society, parents, friends... )
affected your performance.
Groups share their experiences with the class.
Relate to MRT test. Discuss things we would like to see
to back up the articles.
Look at decreasing pipeline for women in the sciences graph and
discuss what it missing.
Thur Feb 27
Collect hw, discuss how tv guide misrepresented stats for their
advertising purposes,
review literary digest poll on Roosevelt/Landon election from 1937.
Discuss linear regressions of Buchanon votes in Palm Beach and the
butterfly ballot.
Review boxplot problems from the WebCT quizzes.
Discuss HIV testing issues and unintended consequences
of medical and educational testing and policy descisions such as
raising airline prices via heart of math reading and stereotype
vulnerability.
Mon Feb 17
Snow Day - University Cancelled Classes
Excel credit card checker,
Mean, Median and Mode lab (stock update and graphs).
Stock Update
Tues Feb 18
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 (class year), "bad" graphs.
Intro to Boxplots via a boxplot of height separated by gender,
and the meaning of boxplots.
Thur Feb 20 Collect and then go over hw,
boxplot of distance from home
and of height separated by gender that includes outliers (ie how the
boxplot changes when the outlier is removed).
Music choices and compatibility issues (measuring "difference" in
music tastes via looking at vertical distance between points)
Begin linear regression via p. 209 # 11, does armspan predict height, and
the worksheet on interpreting the results of regression.
Mon Feb 10
Collecting Data
Tues Feb 11
Collect hw. Go over How Do You Know homework problems, common sense
for matching WebCT quiz 2 problem 6. Highlight the review sheet
and the answers on the main web page.
Go over credit card statement, payday lending offer, credit card offers,
real-life rates and ways to build good credit.
Thur Feb 13
Test 1 on Finance
Mon Feb 3
Lab 3: Dr. Sarah's Condo
Finish up to the designated point and then work on hw for Tues or
WebCT quiz 2.
Tues Feb 4
Collect homework. Go over 1) If I can afford to save $100 per month for a
$50,000 car, in an account compounding monthly at 8%, then how long will
it take for me to save up? Set up the formula for the problem but do not
solve. If I told you that the answer was approximately 18.38 years would
that make sense? Show work to explain why. 2)What will my monthly payment
be if I take out a car loan at 8% compounded monthly for $50,000 for 18.38
years? 3) Use the Sept 2000 interest rate of 8.25% compounded monthly for
the 105265 condo with a loan of 80%. What is the monthly payment? What is
the 1st months interest? What is the total interest over the life of the
loan? Compare to chart on condo lab. Review clarity and depth of lab
answers by highlighting some student answers to the Ben lab (which are
also on a WebCT posting). Finish Dr.
Sarah's condo part 2. If finished before class ends, work on the finance
review sheet.
Thur Feb 6
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. Discuss
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. If time remains, then students
work on homework.
Mon Jan 27
Collect homework.
Lab 2:
Stock Market Lab and
Ben Franklin's Will - Part 1.
Tues Jan 28
Go over $37 problems. Go over
Jane and Joan extra credit (excel sheet)
by using goal seek to discuss
what interest rate would result in equal savings for them both.
Do problems by hand and/or
on Excel.
Picture of Excel work,
Excel work file,
Picture of Excel solutions,
Excel solution file.
Go over main class web page and Ben Franklin and Stock Market lab.
Highlight the Dec 2002 $315 Powerball winner in Hurricane, West
Virginia who had a choice of 30 annual payments or one
lump sum payment of $170.5 million.
Thur Jan 30
Loan payment formula.
Student loan statements.
Begin condo lab.
If time remains, then examine credit card statement.
Tues, Jan 21
Collect homework.
Students begin working on:
If $100 is deposited into an account and left alone for 25 years,
compounded monthly at 5%, how much will we end up with?
How much will be interest ($)?
Review lump sum formula and the philosophy we used to come up with it.
Discuss homework reading.
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.
Transparencies from class
$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
until the final answer.
Thur Jan 23
The University cancelled classes.
Collect homework and go over.
Hand out 3 handouts. Begin working on the problems on
the back of the lump sum versus periodic payment handout.
Go over
Jane and Joan extra credit (excel sheet)
by using goal seek to discuss
what interest rate would result in equal savings for them both.
Do problems by hand and/or
on Excel.
Picture of Excel work,
Excel work file,
Picture of Excel solutions,
Excel solution file.
In the time that remains, discuss lab on Monday and model
stock market and Ben f work in Excel.
Mon Jan 13
Intro to the course. Begin financial mathematics
via How Do You Know? section 2.1.
Web searches for
history of interest:
+history +"interest rates"
521,000 pages
+"history of interest rates" -200*
649 pages
+"origins of banking" +interest 308 pages
Origins of Banking
+"history of interest rates" +babylonian
7 pages
Financing Civilization
+"cuneiform" +babylonian +interest
3160 pages
CUNEIFORM TABLET
+usury +interest +Babylonian
+money 1060 pages
Usury is Piracy
Fill out
index sheet. Work on
Wile E. Coyote.
Come back together to discuss Wile E.
Work on Homer tax homework.
Read through the
main class web page and
Presenting Homework and Writing Assignments. Begin working on
homework.
Tues Jan 14
Collect homework. Review course web pages via volunteers from class.
Have student enter WebCT, post a test message, read message, and look at
quizzes. Show clip of Homer getting into trouble with the IRS.
Turn back Homer homework.
Homer's Taxes.
If time remains then begin working on homework by reading the syllabus
carefully, and then reading through
Dr. Sarah's Sheet on the Main Web Page and WebCT Use, and
the survey assignment.
Thur Jan 16
Collect homework.
Review big picture of Homer tax.
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?
Use remaining time to
review Presenting Homework and Writing Assignments
and then work on homework.
