Dr. Sarah's Math 1010 Class Highlights

### Dr. Sarah's Math 1010 Class Highlights The following is NOT HOMEWORK unless you miss part or all of the class. See the Main Class Calendar for ALL homework and due dates.

• Thur Dec 8 Pants research. Oral abstracts. Evaluations.
• Tues Dec 6 Review the lab. Share from project 4. Discuss final project and class on Thursday (present abstract, a metaphor for class, course evaluations).
• Mon Dec 5 Classroom statistics and What is Mathematics continued.
• Thur Dec 1 Finish discussing hw readings and quotation. Proof questions.
a) 0
b) 1
c) 2
d) 3
e) greater than 3
Discuss mathematical breakthroughs and revolutions.
David Blackwell.
• Tues Nov 29
Andrew Wiles and The Proof video and questions. Go over What is Mathematics readings and quotations.
• Mon Nov 28 Use lab time for research and readings on What is Mathematics.
• Tues Nov 22 Test 3
• Mon Nov 21
Statistics Detective Lab.
If you did not already take a try of the ASULearn Review Questions for Test 3 then do so.
Take questions on the study guide or ASULearn review.
• Thur Nov 17 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.

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

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

2000 election between Bush and Gore
If time remains, Case studies: College Success
• Tues Nov 15 Discuss How Do You Know 3.4 #15

Interpret the negativeslope 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
Discuss the interactive regression. Discuss the lab.

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
Can We Predict the Future? Stocks, Class Data, and Raw Egg Regressions

Discuss correlations versus causations

As a researcher, was it ethical to remove the points that I eliminated and keep the remaining points?
a) Yes
b) No

Media Representations: Discuss Exposure to letters A or F can affect test performance and related p. #s from the book.

How many different items were you able to find in the books that related
a) 0
b) 1-4
c) 5-9
d) 10-14
e) 15 or over
• Mon Nov 14 Can We Predict the Future? Stocks, Class Data, and Raw Egg Regressions
• Thur Nov 10 Review 1969 Vietnam Draft [relate to the theme of breaking it up into smaller pieces, like Jeff Weeks, and shifting viewpoints.]
Go over hw readings and clicker questions.
Go over analyses and critiques of the impact of young voters and corresponding page numbers
Music choices and compatibility issues (measuring "difference" in music tastes via looking at vertical distance between points) music 1, music 2.
3.4 #11.
• Tues Nov 8 Go over the lab and iclicker question on 5 years. Go over the hw readings. Review median and quartiles of boxplots via the average of 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
Begin the 1969 Vietnam draft data, introduction to scatterplot, line of best fit, and boxplots via Starr
• Mon Nov 7 Representations of Data Lab
• Thur Nov 3 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 the measures of centers homework and share from How Do You Know.
a) mean
b) median
c) mode
Nielsen ratings.
a) ABC
b) CBS
c) NBC
Take questions on project 3
GE experiment
Statistics of nature
Music choices and compatibility issues (measuring "difference" in music tastes via looking at vertical distance between points) music 1, music 2.
• Tues Nov 1 Discuss the lab. Take questions on the hw readings and mention project 3.
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.
Worst graph intro, worst graphs cover. 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.
• Mon Oct 31 Stock Data and Graph and ASULearn Data Collection
• Thur Oct 27 Test 2
• Tues Oct 25 Review the lab. Take questions on study guide of ASULearn quiz. Discuss the stock market and data collection: model the Stock Graph Begin the statistics of nature.
• Mon Oct 24 Look at #10 in 1.3. Condo and Car Purchases: Decisions, Decisions (Part 2)
• Thur Oct 20 Go over the condo/car lab part 1 from Monday. Discuss loans and the economy. Revisit the second student loan statement along with the Excel file from lab on Monday. Review homework.
a) lump sum
b) periodic payment
c) loan payment
d) combination
e) other
• Tues Oct 18 Collect and then review the lab from yesterday.
Philosophy of loans
Student loan statement. Payday lender. Credit cards and finance charge. If time remains, then work on homework for Thursday.
• Mon Oct 17 First 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) lab
• Tues Oct 11 Take questions on Project 2 and look at ASULearn. clicker review
Philosophy of loans
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.
• Mon Oct 10 Look at
Project Criteria and Rubric
Benjamin Franklin's Will - News Article Web Readings
Ben Franklin's Will Part 1
Lump Sum Philosophy and Derivation
• Thur Oct 6 Discuss the \$37 wording. periodic payment. lottery questions Search google news for lottery winner lump. Picture of Excel work, Excel work file. Picture of Excel solutions, Excel solution file. If time remains, discuss project 2.
• Tues Oct 4 Go over the lab. Review the lump sum philosophy. 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
If time remains, then begin the lottery questions
• Mon Oct 3 Benjamin Franklin's Will - Part 1 (Lab)
• Thur Sep 29 Review the lump sum equation via clicker questions. Review the Lump sum philisophy. Discuss other possibilities for unknowns - 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.
If time remains, then my own research as part of a theme of success in mathematics for Project 4.
• Tues Sep 27
Begin finance. Charlie Rose - An exclusive conversation with Warren Buffett [first 54 seconds and then from 3:30-5:18].
History and ethics of charging interest for the use of land, animals, money.
Plimpton Cuneiform 322 and interpreting data
Usury is Piracy
Quotes on taxation. Local to global taxes. Discuss 142 years compounding monthly versus annually.
Lump sum philisophy.
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?
• Mon Sep 26 Collect homework. Discuss percentages and the prevalence of equations in and outside of mathematics. Reflect on equations. in the context of "what is mathematics." Take notes for project 4. Discuss upcoming homework.
• Thur Sep 22 Test 1
• Tues Sep 20 Go over the lab. Review Rob Kirschner's Supernovae results related to whether brightness=1/distance2.
Portal. Futurama: I, Roommate. Discuss test 1 and the study guide.
Work on the Jeff Weeks worksheet as a review.
• Mon Sep 19 Universe Lab
• Thur Sep 15 Turn in homework. Continue going over the global questions from Project 1. 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. Discuss Jeff Weeks interview.
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.
• Tues Sep 13 Discuss the lab and the homework readings, including 2-D creature movements of the caterpillar turning into a 3-D movement butterfly, Gauss' experiment and MAP data (WMAP) and the Planck Probe. clicker questions.
• Mon Sep 12 2-D Universe Lab
• Thur Sep 8
Use tape to make an equator. Begin going over Project 1.

• Tues Sep 6 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.

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
• Thur Sep 1 Where is North? Review Euclidean 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.
Hyperbolic worksheet.
• Angle sum and Image of Angle sum
• Pythagorean theorem and Image of Pythagorean theorem
• Tues Aug 30 What does a space look like, how do we know, and how do we represent it... Go over the lab. Lab clicker questions 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. Register the i-clickers.
• Mon Aug 29 Take out notes from homework.
Perspective lab activities
Take the ASULearn Mathematical Experiences reflection
• Thur Aug 25 Fill out index sheet. Share from the syllabus or Monday's lab. Think of your favorite cartoon. Is it 2-dimensional or 3-dimensional? Advice from last semester. Finish going over the video... 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. 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. Are The Simpsons 2D or 3D?
http://www.youtube.com/watch?v=TKQ8Ilr6PgU If time remains then go over ASULearn messages, and discuss project 1.
• Tues Aug 23 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). 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. If time remains, Julian Beaver's drawings and perspective drawing and projective geometry