### Class Highlights

Class Highlights
• Thur Jun 21 Pants research: an analogy for class. Discuss the final project topics.
• Wed Jun 20 Go over project 3 topics. Discuss project 4. Discuss the research project presentations. Time to work on the final exam research presentations.
• Tues Jun 19
Lab Work: Class Statistics and What is Mathematics lab

Come back together and discuss project 3 and the lab. Liz Colman and Education
• Mon Jun 18
David Blackwell.
Andrew Wiles and The Proof video and questions.
• Fri Jun 15 Test 3
Case studies: College Success 3, 5, 6
Success in mathematics reading
Discuss mathematical breakthroughs and revolutions.
David Blackwell.
Andrew Wiles and The Proof video and questions.
Class Statistics and What is Mathematics lab

• Thur Jun 14
Finish Lab Work:
1. Can We Predict the Future? Stocks, Class Data, and Raw Egg Regressions
2. Purchase your stock
3. Statistics Detective Review
4. If finished before we come back together, then review the class highlights page and take notes for project 4.

Come back together. 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

Predicting height and solving a crime
Case studies: College Success 3, 5, 6
Take questions on the studyguide, ASULearnquestions or any other material.

• Wed Jun 13 Go over the lab and iclicker question on all data and stock graph. Stock:
a) lost money
b) gained money
c) stayed about the same
Elections continued: 2000 election between Bush and Gore

Discuss the hw readings
Finish 3.4 #11.
Look at succeeding in mathematics: 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.

Lab work:
1. Can We Predict the Future? Stocks, Class Data, and Raw Egg Regressions

• Tues Jun 12 Meet in 205.

Lab Work: Representations of Data lab
If finished with the lab early, then begin working on project 3.

Back to the classroom. 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
Discuss correlations versus causations
Discuss the Bradford-Hill_criteria

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

Continue 3.4 #11.

• Mon Jun 11 Worst graph intro, worst graphs cover.
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

Search google news for "box plot"
Search google scholar for "box plot" and boxplot
Google images for boxplot
Boxplot and baseball
Begin the 1969 Vietnam draft data, introduction to scatterplot, line of best fit, and boxplots via Starr
Elections:
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

How many different items were you able to find in the books that related to the 2 articles on the McCain and Obama election?
a) 0
b) 1-4
c) 5-9
d) 10-14
e) 15 or over

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.
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

clicker questions
Go over the hw readings.
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.
• Fri Jun 8
Finish the statistics of nature
Discuss the hw readings and mention project 3.
Discuss the measures of centers homework and share from How Do You Know.
a) mean
b) median
c) mode
Histogram of the ASULearn random number from 1 to 10. 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?)
Discuss bar chart of volume of stocks from lab including how you can tell whether the mean will be above or below the median using the idea of a scale balance. Distance from home bar chart. Armspan bar chart. Height box plots.
• Thur Jun 7 Test 2 for 1 hour

1. Stock Graph
2. ASULearn anonymous data collection.
3. Work on hw for tomorrow if you are finished before we come back together
4. statistics of nature

• Wed Jun 6 Collect hw.
1. Finish #8 on Condo and Car Purchases: Decisions, Decisions (Part 2)
2. 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.

Credit cards and finance charges
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.
statistics of nature

• Tues Jun 5 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)

Together, go over the condo/car lab part 1: 1, 4, 7, and 9-13 via the clickers.
Student loan statement.
Look at debt hw and You Try It 3.4 page 30.
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.

Credit cards and finance charges.

Lab work: 1: Condo and Car Purchases: Decisions, Decisions (Part 2)
2: If finished early, then go through the class highlights page and begin to collect items for Project 4

• Mon Jun 4 Philosophy of loans Student loan statement.

Lab work: Take a look at my feedback to you on ASULearn on your Friday try of Jane and Joan. Then take another try.
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).
Condo and Car Purchases: Decisions, Decisions (Part 1)
• Fri June 1
Review the lump sum equation via clicker questions
Discuss clicker questions #2.
Compare the philosophy to the lump sum formula derivation and to Jeff Weeks.
Search google news for lottery winner lump.
Continue lottery questions.
Picture of Excel work, Excel work file. Picture of Excel solutions, Excel solution file. Discuss real-life rates.

Jane and Joan on ASULearn. If you are finished early, then continue working on Project 2 (see the main calendar page)
Review the Jane and Joan extra credit.

• Thur May 31
Review the Pythagorean Theorem from the test.
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.

Benjamin Franklin's Will - Part 1 (Lab)
If finished before we come back together, Choose a city - Boston or Philly. As you read through the following links, take notes on or copy any info into a Word processor that relates to your city (directly or indirectly):
Benjamin Franklin's Will - News Article Web Readings
If time remains, 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

• Wed May 30 Test 1. Finance continued. 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.
Plimpton Cuneiform 322 and interpreting data
Usury is Piracy
• Tues May 29
Go over the Universe lab
Portal and Futurama: I, Roommate.
Discuss test 1 and the study guide.
Discuss the homework reading interview with Jeff Weeks.
Mention Project 4.
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 the equations in this segment.
Reflect on equations in the context of "what is mathematics" and as a way to connect from the geometry segment to finance.
• Mon May 28 Finish the video. Discuss the methods and experiments used to explore higher dimensions, 2-D and 3-D universes, including Rob Kirschner's Supernovae results related to whether brightness=1/distance2.
Discuss each of the hw readings, including Gauss' experiment and MAP data (WMAP) and the Planck Probe.
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.

Universe lab
If time remains before we come back together, take a try of the ASULearn practice quiz.
• Fri May 25 clicker questions
Use tape to make an equator. Begin going over Project 1 and the global questions from Project.
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: testing2.mov [32 min]
• What are the methods and experiments that researchers, artists and others use to explore and represent higher dimensions in the video?
• What are the methods and experiments that researchers, artists and others use to explore and represent the shape 2-D and 3-D universes?

• Thur May 24 Take questions on Tuesday class, homework or project 1.
Lab Clicker questions
In the Poincare disc computer model of hyperbolic geometry, which is like Escher's Heaven and Hell work:
a) The Pythagorean theorem holds
b) They Pythagorean theorem fails since a2+b2 > c2
c) They Pythagorean theorem fails since a2 + b2 < c2
d) The Pythagorean theorem is sometimes satisfied but other times violated
e) There is no way to determine whether it holds

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.

2-D universe lab If finished before we come back together, work on project 1.

• Wed May 23 Go over the webpages and ASULearn messages and share from the syllabus or yesterday's class. What does a space look like, how do we know, and how do we represent it...

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
3) Are The Simpsons 2-D or 3-D? Dutch graphics artist M.C. Escher and the mathematical clues he left in his work: Sun and Moon (1948) 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.
Where is North? Register the i-clicker. Review Euclidean geometry including angle sum and the Pythagorean theorem. Escher's space and perspective geometry, including angle sum and the Pythagorean theorem.
Escher's space and 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
• Pythagorean theorem and Image of Pythagorean theorem
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.
Discuss physical models of small pieces of hyperbolic space. Crochet model of hyperbolic geometry Reef Crochet reef.

• Tues May 22 Index sheet. Overview of the course. Discuss How could we tell that the earth is round instead of flat without using any technology (ie if we were ancient Greeks)? Make a list of ideas on the board. Watch 10 minute video excerpts lifebynumbersintro.mov and prepare to share something to discuss: Life By the Numbers Shape of the World (maps of the earth) and Seeing is Believing (perspective). Write down something you found interesting, disagreed with, or that you wish had been shown. 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. 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. Perspective Drawing and Projective Geometry
Think of your favorite cartoon. Is it 2-dimensional or 3-dimensional?
Lab work in 205:
1) ASULearn Mathematical Experiences Reflection
2) Perspective lab Activities
3) Are The Simpsons 2-D or 3-D?
If time remains before we come back together, then work on homework for tomorrow. Review the activities.