Class Highlights
Mon Dec 10 6-8:30 pm: Final exam research presentations.
Thur Dec 6 Pants.pdf research. Share your final exam research
presentation topic. Assign sessions. Evaluations.
Tues Dec 4
Turn in project 4
Discuss the final research presentations
Discuss the themes from project 4
Mon Dec 3
1. On the front board, mark off whether
you gained or lost money by adding them to the relevant gain/loss columns.
2. Turn in homework.
3. On ASULearn take the Anonymous Advice for Next Semester survey.
4. If finished before we come back together, then work on the project
for tomorrow on the calendar page.
We'll watch together:
Liz Colman and Education
Discuss hw readings, Liz Colman and project 4
Thur Nov 29 Research and meetings day
Tues Nov 27
Discuss The Proof video from lab
David Blackwell
mathematical
breakthroughs and revolutions
Mon Nov 26
Andrew Wiles and The Proof
video and questions.
Tues Nov 20 Test 3
Mon Nov 19
1. Purchase your stock
2. Statistics Detective Review
Thur Nov 15
Take questions on test 3
statistics of nature
Discuss the
Bradford-Hill_criteria
Predicting height
and solving a crime
Case studies: College Success
Tues Nov 13
Discuss the lab: Can We Predict the Future? Stocks, Class Data, and Raw Egg Regressions
In the egg bungee experiment the similarity of the rubber bands led to an almost constant slope for the change in distance dropped / change in rubber bands.
a) Agree
b) Disagree
If your stock market r2 value was 99.9%, would you be assured to make money in the stock market by using the line to predict the future performance and investing accordingly?
a) Yes
b) No
As a researcher, was it ethical to remove the points that I eliminated and keep the remaining points?
a) Yes
b) No
Finish election issues:
2000
election between Bush and Gore and Pat Buchanan's impact in Florida
Continue looking at succeeding in mathematics:
Circle an A.
Here's Good News... SAT scores are declining at a slower rate.
Discuss the SAT and whether the SAT should predict college scores.
Review the biased MRT instructions and relate to
stereotype vulnerability.
Mon Nov 12
Can We Predict the
Future? Stocks, Class Data, and Raw Egg Regressions
Thur Nov 8
How many different items were you able to find in the books
that related to Exposure to letters A or F can affect test performance
a) 0
b) 1-4
c) 5-9
d) 10-14
e) 15 or over
Discuss How Do You Know 3.4 #15
Interpret the negative slope of the best fit line in this context.
a) As the policeman has more experience he gives out more tickets
b) As the policeman has more experience he gives out less tickets
The r2 value is strong but the line predicts that the policeman
receives tickets. Resolve the apparent conflict.
a) There is a typo in the book - the actual r2 value is
weak or not a predictor, so the prediction does not hold up.
b) The mathematics of the r2 value and the prediction
are correct: the policeman gets sloppy
as he gets older, causing him to be penalized.
c) Other
GE experiment
In the hw reading on the unintended consequences of HIV testing the
entire population in the Heart of Mathematics
a) the large numbers of HIV negative people can have
false positives and make what seems like an accurate test percentage-wise
problematic
b) A positive result becomes relatively meaningless because one
only has a small chance of actually having HIV
c) Testing the entire US population leads to the (unintented) problems
d) More than one, but not all of the above
e) a, b and c
Begin the
1969 Vietnam draft
data,
introduction to scatterplot, line of best fit,
and boxplots via
Starr
Discuss correlations versus
causations on why birds fly south during colder weather
Regarding the themes of
Collecting and Presenting Data
Predictors
Boxplots
Unintended Consequences
discuss the hw readings in that context
Tues Nov 6
How many different items were you able to find in the books
that related to the 2 articles on the 2008 McCain and Obama election?
a) 0
b) 1-4
c) 5-9
d) 10-14
e) 15 or over
Which author did you find most credible?
a) The Straight-Ticket Youth Vote, by Patrick Ruffini
b) Young voters not essential to Obama triumph by Tom Curry
c) They were both equally credible
With regard to the 2008 election between McCain and Obama, which of the following are true
1. Both articles claimed that younger voters were essential in North Carolina and Indiana.
2. The exit poll data may not be representative.
3. The authors disagreed about the impact of young voters in Florida and
Ohio.
a) Only 1
b) Only 2
c) Only 3
d) Only two of the three statements are true
e) All three of the statements are true
With regard to the 1936 Landon and Roosevelt election Literary Digest poll,
which predicted the winner as Landon
a) The sample size was not large enough
b) The sample size was not diverse enough
c) Landon should have won - Roosevelt's win was due to a last minute
change in sentiment
Go over the lab and iclicker question on all data and stock graph.
Stock over all time that you sketched by hand on the lab:
a) lost money
b) gained money
c) stayed about the same
Over the time period of the stock graph, the highs:
a) lost money
b) gained money
c) stayed about the same
Worst graph intro,
worst graphs
cover.
Music choices and compatibility issues (measuring "difference" in
music tastes via looking at vertical distance between points)
music 1,
music 2.
Begin 3.4 #11.
Regarding the themes of
Collecting and Presenting Data
Predictors
Boxplots
Unintended Consequences
discuss the hw readings in that context
Mon Nov 5 Representations of
Data Lab
Thur Nov 1 Turn in hw.
Discuss the measures of centers homework and share from How
Do You Know.
Typical waiting time at a doctor's office:
a) mean
b) median
c) mode
Hair color:
a) mean
b) median
c) mode
A realtor wants to advertise how inexpensive it is to live in an area:
a) mean
b) median
c) mode
Nielsen ratings.
a) ABC
b) CBS
c) NBC
Nielsen ratings using a
scale balancing idea for CBS (the middle graph).
a) Mean is higher than the median
b) Mean is lower than the median
c) Mean equals the median
Discuss the literature review/connection component of
proj 3 as related to the themes of
Collecting and Presenting Data
Predictors
Boxplots
Unintended Consequences
Mention google news for "box plot" or boxplot,
google scholar [any time since 2012], including connections to the
social sciences, medicine and sports
google images including the
Michelson-Morley experiment 1887 led to the acceptance of special
relativity...
Histogram of the ASULearn random number from 1 to 10 and
unintended consequence of deductive knowledge seeming like magic [stock
wiz reading too]
experiment and Excel analyses.
Discuss whether the human mind can
provide a random number.
Discuss sampling versus census. Discuss mathematical proof versus
statistical significance and randomness.
Discuss the expected value (sum/10) and briefly mention the chi test [(B2-C2)^2/C2, CHITEST(B2:B11,C2:C11)] and p-value (are the observations statistically significant or can the differences be ascribed to random variations of chance?)
Distance from home bar chart.
Armspan bar chart.
Height box plots.
Tues Oct 30 Snow Day
Mon Oct 29
1. Show my your hw and begin working on below:
2. Stock Graph
3. ASULearn anonymous data collection.
4. Work on hw for tomorrow if you are finished before we come back
together
Thur Oct 25 Test 2
Tues Oct 23
Review via clickers:
a) lump sum
b) periodic payment
c) loan payment
d) combination
e) other
Answer questions on the study guide, ASULearn activities and go over
the homework.
Mention upcoming hw:
Find the stock symbols of a few companies that are actively traded and
that you are interested in "buying" -
for example, you might search
http://finance.yahoo.com/lookup for stocks with certain names
or www.google.com for
"stock symbol" "COMPANY NAME"
where COMPANY NAME is the name of the company that you are interested in.
stock graph
statistics of nature
Mon Oct 22
1. Condo and Car
Purchases: Decisions, Decisions (Part 2)
2. Take a look at my message to you on ASULearn
3. Take a look at hw for tomorrow and ask me any questions before you
leave
Thur Oct 18
Student loan statement.
Credit cards and finance charges.
Discuss project 4.
The people mentioned in the finance segment... Equations in this segment.
Begin the stock market: stock
graph.
Tues Oct 16 Review the lab questions:
1, 4, 7, 8 and 9-13 via the clickers.
In the derivation of the loan formula, we used:
a) x/(x+1) = 1/(1+1/x)
b) the bank earns interest on the lump sum amount while we pay it back
via the periodic payment formula so that our payments plus resulting interest
equals the lump sum amount plus interest.
c) neither a) nor b)
d) both a) and b)
Student loan statement.
Discuss local debt. Discuss debt in NC, the US, and the world.
Richard Feynman quotation:
There are 1011 stars in the galaxy. That used to be a huge
number. But it's only a hundred billion. It's less than the national
deficit! We used to call them astronomical numbers. Now we should call them
economical numbers.
Payday lender in Boone:
What is the annual rate?
a) 17.5%
b) 24%
c) 117.5%
d) 455%
e) none of the above
Student loan statement.
Mon Oct 15
1. Take the Car Loan Practice Problem on ASULearn. Keep track of your calculations on a sheet of paper (if you scroll over an answer box after you submit it, you will receive feedback and hints, and you can resubmit the correct answers online).
2. Condo and Car Purchases: Decisions, Decisions (Part 1)
Tues Oct 9
Take questions on project 2.
Review Jane and Joan extra credit on Excel
Picture of Excel work,
Excel work file.
Picture of Excel solutions,
Excel solution file.
Car loans.
Philosophy of loans
Student loan statement.
If time remains, begin
Condo and Car Purchases: Decisions, Decisions (Part 1)
Mon Oct 8
Jane and Joan on ASULearn - use your formula sheet and calculator to
help you.
You can ask me questions on project 2 before you leave if you have any.
Thur Oct 4 Take questions on project 2.
Look at the following statements:
1: Looked at the total for each compounding period
2: Looked at the future value of money
3: Found a common piece (1 + rate)
4: Multiplied by the common piece (1 + rate) to obtain a
second, similar but shifted viewpoint equation, and
then subtracted to significantly reduce the number of terms
5: Took a solution that originally had too many terms and reduced it to
something manageable
In the derivation of the lump sum formula, we
a) All of the above
b)All but 4
c)All but 3
d)All but 2 and 4
e)All but 1 and 3
Begin
the lottery
questions. Search google news for lottery winner lump.
Picture of Excel work,
Excel work file.
Picture of Excel solutions,
Excel solution file.
Tues Oct 2 Review the lab.
a) The earned rate of a fund is the same as the rate that is charged to
borrow the money in the fund.
b) To find the earned rate of a fund, we can calculate a weighted
average rate using the rates each part of the fund actually receives.
c) To find the earned rate of a fund, we can use the beginning and ending
values of the fund and calculate the rate in Excel using the lump sum formula.
d) Both a) and c)
e) Both b) and c)
Collect the hw.
What about $100 deposited every month into an account for 25 years, compounded monthly at 5%?
Work towards periodic payment understanding and compare the philosophy to the lump sum formula derivation and to
Jeff Weeks.
Transparencies from class
lump and periodic clicker questions
Mon Oct 1 Benjamin Franklin's
Will - Part 1 (Lab)
Thur Sep 27
Review the lump sum equation via clicker
questions
Plimpton Cuneiform 322 and interpreting data
Usury is Piracy
Quotes on taxation. Local to global taxes.
Review the
Lump sum philosophy.
Discuss other possibilities for unknowns in lump sum -
the time length, the rate, or the number of times compounding per year.
Intro to Goal Seek and Solver in Excel via Lisa's Thrifty Savers savings
account from Bart the
Fink.
Tues Sep 25
Discuss test 1. Collect hw.
Begin finance.
Charlie Rose -
An exclusive conversation with Warren Buffett [first 54 seconds and
then from 3:30-5:18].
http://video.google.com/googleplayer.swf?docid=4537231419795681197
Discuss 142 years compounding monthly versus annually.
Lump sum philosophy.
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?
(a) 1000(1+.08)8
(b) 1000(1+.08/8)8
(c) 1000(1+.08/12)8*12
(d) 1000(1+.08/12)8
(e) none of the above
What did the bank really mean?
History and ethics of charging interest for the use of land, animals,
money.
Mon Sep 24
Collect real-life rates hw.
Reflect on equations
in the context of "what is mathematics."
Thur Sep 20 Test 1
Tues Sep 18
Go over the lab.
http://www.youtube.com/watch?v=5u7hFQy9Mt0&feature=related
From 47:46 onwards
Portal
and Futurama: I, Roommate.
My own research as part of a
theme of success in mathematics for Project 4.
Discuss percentages and the prevalence of equations
in and outside of mathematics. Review equations from the geometry
segment: Eratosthenes proportion to calculation the circumference of the
earth, perspective equations to calculate 2d coordinates from a 3d model,
calculating angles in Escher's artwork, sum of the angles in
various geometries, fitting spaces together in various geometries,
Pythagorean theorem in various geometries,
density equation from WMAP data, brightness ~ 1/dist^2
in various geometries from Kirschner's
research on supernova explosions
Discuss test 1 and the study guide.
Mon Sep 17 Universe Lab
Thur Sep 13
Discuss homework readings on Heart of Mathematics and Jeff
Weeks and project 4.
visualizing a hypersphere: Jeff Weeks
worksheet [Einstein based his theory of relativity off of Riemann's work
on this space]
Rob Kirschner's
Supernovae results related to whether
brightness=1/distance2.
The Shape of Space Video - this 11-minute animated video produced by The Geometry Center introduces the two-dimensional space of flatland, looks at possible shapes for flatland from the perspective of three dimensions, and represents those shapes of space in two dimensions. Then the animation uses the same kind of representation to look at possible shapes for three-dimensional space. Viewers are taken on a ride across the boundless three-dimensional surface of a three-torus and a four-dimensional Klein bottle. As viewers see these imaginary universes from inside the spaceship, they experience the illusion of seeing copies of the universes.
http://www.youtube.com/watch?v=Uzd484Mvm2k
Continue discussing the universe questions from
Project 1
Tues Sep 11
Discuss the lab and the Klein bottle.
clicker question.
Continue going over the global questions from Project 1.
Discuss the homework readings including Gauss'
experiment and MAP data (WMAP) and the
Planck Probe.
Discuss other methods and
experiments used to explore higher dimensions, 2-D and 3-D universes,
including
Mon Sep 10
2-D universe lab
Thur Sep 6 Begin going over the first four questions from project
1 - geometry of the earth.
Tues Sep 4 Review.
What does our universe look like, how do we know, and how do we represent it?
Selections cut from PBS Life by the Numbers: Seeing is Believing Video: 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. Tom Banchoff as a mathematician. Shape of the World video: Viewers see how mathematics has become a tool to explore the heavens as the cosmos is charted. Class concentrates on what our universe looks like, how we know, and how we represent it. Discuss the video, including Tom Banchoff, Rob Kirschner,
and Jeff Weeks, Riemann and Einstein, high dimensions, experiments and
representations. notes
Thur Aug 30
Pythagorean theorem and
Image of Pythagorean theorem
In the weeks to come, we will see that there are many real-life
applications of hyperbolic geometry, such as models of the internet that
hope to reduce
the load on routers,
building crystal structures to store more hydrogen or absorb more toxic
metals, mapping the brain, mapping the universe, and modeling Mercury's orbit.
Discuss physical models of small pieces of hyperbolic space.
Crochet model of
hyperbolic geometry
Reef
Crochet reef.
PacMan
sequence from Futurama (Anthology of Interest
II) and a tiling view versus folding up the space (where PacMan would see
his back which would look like a piece of a circle or a flat line to him).
Watch an excerpt from Flatland: The Movie.
Discuss what a 2-D creature would see if an orange passed through the
plane of existence, including 2-D creature movements of the caterpillar turning into a 3-D movement butterfly,
Davide Cervone's Cube Projections.
Highlight some books from my office that are useful for the project.
Sphere questions:
Experiencing Geometry by Henderson
Geometry Theorems and Constructions by Berele and Goldman
The Heart of Mathematics by Burger and Starbird
Symmetry, Shape and Space by Kinsey and Moore
Universe questions:
Beyond the Third Dimension by Banchoff
Exploring the Shape of Space by Weeks
Geometry, Relativity and the Fourth Dimension by Rucker
The Heart of Mathematics by Burger and Starbird
Hyperspace by Kaku
The Math Book by Pickover
Shape of Space by Weeks
Symmetry, Shape and Space by Kinsey and Moore
Tues Aug 28 Go over the lab.
Lab Clicker questions.
Finish where is North?
M.C. Escher and the mathematical clues he left in his work:
Sun and Moon.
Worksheet on Escher.
(number 2).
Quotes from Escher on how he does mathematics
and where it comes from. Discuss whether mathematics arises from nature
or whether we impose our mathematical discoveries onto nature.
Review
Euclidean geometry including angle sum and the Pythagorean theorem.
Poincare's disk model of
hyperbolic geometry.
Escher drawing
Sphere with Angels
and Devils, 1942.
Sphere
Surface with Fish. 1958
Discuss a computer model of Escher's space called hyperbolic geometry.
Sketchpad Shortest
Distance Paths
and Image of Shortest
Distance Paths.
Angle sum and
Image of Angle sum
discuss local (close to Euclidean geometry) to global (geometry is
very different) perspectives
In the weeks to come, we will see that there are many real-life
applications of hyperbolic geometry, such as models of the internet that
hope to reduce
the load on routers,
building crystal structures to store more hydrogen or absorb more toxic
metals, mapping the brain, mapping the universe, and modeling Mercury's orbit.
Mon Aug 27
1. Do you have a class or lab Mondays anytime 6 or later? We may have
a choice about when thefinal research presentations are held. On
the front board mark off whether you do or not.
2. Perspective lab
activities
3. Take the ASULearn Mathematical Experiences reflection
Thur Aug 23
Fill out index sheet.
Share from the syllabus or class on Tuesday. Take questions on project 1.
Review geometery segment themes: What does a space look like, how do
we know and how do we represent it?
Register the i-clicker
Of the following, what is the most compelling argument (to you)
about ways we could know that the earth was round without modern technology?
a) The sun and moon are round so the earth should be (originally attributed to Pythagoras)
b) Ships disappearing on a clear day appear to sink
c) Stars change as we change latitude and overlaps flip when we pass over the equator
d) Directions of hurricanes change from Northern to Southern Hemisphere (Coriolis force)
e) On midsummers day at noon, Syene (Aswan) made no shadows, while Alexandria did (Eratosthenes used this to calculate the circumference of the earth)
Julian Beever's pavement drawings:
Butterfly
Globe wrong
view
Globe correct
view
Accident
I decided to get into 3D after seeing the effect of tiles being removed
from the street, and later trying to recreate the sense of depth in a drawing.
Once I realised you could make things go down, I realised you could make
them appear to go up and I began experimenting.
Think of your favorite cartoon. Is it 2-dimensional or 3-dimensional?
a) 2-D
b) 3-D
c) unsure
Are The Simpsons 2D or 3D?
http://www.youtube.com/watch?v=TKQ8Ilr6PgU
Where is North?
If time remains, go over
perspective drawing and
projective geometry
Tues Aug 21
Overview of the course including the
attendance policy.
Discuss How could we tell that the earth is round instead of flat
without using any modern technology (ie if we were ancient Greeks)?
Make a list of ideas on the board.
Watch 10 minute video excerpts and prepare to share something to discuss:
Life By the Numbers Shape of the World (maps of the earth) and
Seeing is Believing (perspective).
Take notes. Highlight the questions of what our world
looks like, how we know, and how we represent it.
Highlight Danny Glover's discussion that the earth is finite but has
no edges, that a flat map of the earth must contain some distortion, and
Sam Edgerton's views that
perspective -> industrial revolution, that perspective is
learned - not innate, and that we must
distort the work to give the illusion of depth.
Advice from last semester.
