### 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
2. Statistics Detective Review
• Thur Nov 15
Take questions on test 3

statistics of nature

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

Over the time period of the stock graph, the highs:
a) lost money
b) gained money

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
"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: Within 2 weeks of my next paycheck I can come in and (if I qualify), write a check to them for \$117.50 and receive \$100 cash at that time. Then, when I get paid, I bring \$117.50 in cash to their office and buy back my check. If I don't show up, they deposit my check, and if it bounces I will owe "returned check charges", plus the amount, and then on to a collection agency with potential civil charges if I don't pay. 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
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].
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.
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.
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?