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 May 10 Final exam research presentations.
• Thur May 3 Share from project 4. Pants research: an analogy for class. Share final exam research presentations topic. Evaluations.
• Tues May 1 Share from project 3. Go over the test. Discuss the Bradford-Hill_criteria. Discuss the lab. Finish discussing Andrew Wiles. Time to discuss questions on project 4 and the final exam research presentations.
• Mon Apr 30 Class Statistics and What is Mathematics lab
• Thur Apr 26 Finish David Blackwell.
Andrew Wiles and The Proof video and questions.
• Tues Apr 24 Test 3
• Mon Apr 23
Statistics Detective Lab
• Thur Apr 19
Take questions on the study guide or ASULearn review.
Predicting height and solving a crime
Case studies: College Success
Discuss mathematical breakthroughs and revolutions.
David Blackwell.
• Tues Apr 17 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

Discuss the interactive regression.

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

Discuss correlations versus causations

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 Apr 16 Can We Predict the Future? Stocks, Class Data, and Raw Egg Regressions
• Thur Apr 12
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

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

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

3.4 #11.
Look at succeeding in mathematics: Here's Good News... SAT scores are declining at a slower rate.
• Thur Apr 5 Begin the 1969 Vietnam draft data, introduction to scatterplot, line of best fit, and boxplots via Starr
• Tues Apr 3 Go over the lab and iclicker question on all data and stock graph. Stock:
a) lost money
b) gained money

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

Music choices and compatibility issues (measuring "difference" in music tastes via looking at vertical distance between points) music 1, music 2.
• Mon Apr 2 Representations of Data lab
• Thur Mar 29 Discuss the HDYK readings.
Discuss the measures of centers homework and share from How Do You Know.
a) mean
b) median
c) mode
GE experiment
Review boxplots
Search google news for "box plot"
Search google scholar for "box plot" and boxplot
Boxplot and baseball
• Tues Mar 27 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. a href="wc/stats/barcharthome.PDF">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. 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?)
• Mon Mar 26 Stock Graph and ASULearn anonymous data collection.
• Thur Mar 22 Test 2
• Tues Mar 20 Review via clickers:
a) lump sum
b) periodic payment
c) loan payment
d) combination
e) other

If time remains then begin the statistics of nature
• Mon Mar 19 Condo and Car Purchases: Decisions, Decisions (Part 2)
• Thur Mar 8 Discuss project 4. The people mentioned in the finance segment...
Begin the stock market: stock graph.
Take questions and review:
1. lump sum
2. periodic payment
3. loan payment
4. total interest earned for lump and periodic
5. total interest paid for loan
6. month 1 interest paid for lump and periodic
7. month 1 interest paid for loan
8. First row of an amortization table for a car
9. Total paid when there is a negative balance the last month
10. Benjamin Franklin
11. Joan invested for 10 years but then went on vacations
12. Thrifty Savers account: \$100 invested, earn an extra nickel with 2.3% instead of 2.5%
13. month 1 interest on a credit card
14. finance charge on a credit card
Work on hw for Tues.
• Tues Mar 6 Look at debt hw and You Try It 3.4 page 30.
Go over the condo/car lab part 1 from Monday: 1, 4, 7, and 9-13 via the clickers.
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.
Student loan statement. 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

Credit cards and finance charges. If time remains, then work on homework for Thursday on reviewing formulas and beginning to collect information for project 4.
• Mon Mar 5
1. Take out your formula sheet and calculator
2. 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).
3. Condo and Car Purchases: Decisions, Decisions (Part 1) lab
4. Take a look at hw for tomorrow from the calendar page

• Thur Mar 1 Finish car question. Car loans.
Philosophy of loans
Student loan statement.
• Tues Feb 28 Take questions on project 2.
Continue lottery questions. Discuss real-life rates. Search google news for lottery winner lump. Picture of Excel work, Excel work file. Picture of Excel solutions, Excel solution file.
• Mon Feb 27 Collect hw. 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
• Thur Feb 23
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. Search google news for lottery winner lump.
• Tues Feb 21 Review the lump sum equation via clicker questions. Review the Lump sum philosophy.
History and ethics of charging interest for the use of land, animals, money.
Plimpton Cuneiform 322 and interpreting data
Usury is Piracy
Go over the lab.
Quotes on taxation. Local to global taxes.
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.
• Mon Feb 20 Benjamin Franklin's Will - Part 1 (Lab)
• Thur Feb 16 Collect hw. Finish equations
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.
• Tues Feb 14 Test 1
• Mon Feb 13 Take questions on project 4. Look at the class highlights page below for review and take notes on items for Project 4.
• Thur Feb 9 Futurama: I, Roommate. Rob Kirschner's Supernovae results related to whether brightness=1/distance2. Discuss test 1 and the study guide. 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 Reflect on equations in the context of "what is mathematics."
• Tues Feb 7 Go over the lab. Discuss the readings from lab on Monday and the Jeff Weeks interview. clicker question Continue to discuss the video.
Portal.
• Mon Feb 6 Universe Lab
• Thur Feb 2 Continue going over the global questions from Project 1. Discuss the homework readings including Gauss' experiment and MAP data (WMAP) and the Planck Probe. clicker question.
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.
Begin second video:
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.
• Tues Jan 31 Discuss the lab and the Klein bottle. Use tape to make an equator. Begin going over Project 1.
• Mon Jan 30 2-D universe lab
• Thur Jan 26 Take questions on Tuesday class 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,

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 Jan 24 Register the i-clickers. Review Euclidean geometry, 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.
• Image of Shortest Distance Paths.
• Image of Angle sum
• Image of Pythagorean theorem
discuss local (close to Euclidean geometry) to global (geometry is very different) perspectives
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.
Go over the lab.
• Mon Jan 23
Take out notes from homework.
Perspective lab activities
Take the ASULearn Mathematical Experiences reflection
• Thur Jan 19 Share from the syllabus or the last class.
Are The Simpsons 2D or 3D?