Class Highlights

  • Fri Jun 21 Final research presentations. Final evaluations.
  • Thur Jun 20 Share presentation topics and assign research sessions. Pants.pdf research. Go to the computer lab and work on the research presentations.

    In 205:
    1. Work on and (and as I make my way around the room) show me a list of any mathematical connections/mathematicians you already have so that I can help you add to them.
    2. Sell your stock
    3. On ASULearn take the Anonymous Advice for Next Semester survey.
    4. After I have met with you in lab and you have finished #2 and #3, you may continue working on the research presentations in the lab (I am happy to continue helping!) or elsewhere. Remember to bring printed copies of everything, including your annotated bibliography, to tape up tomorrow.

  • Wed Jun 19 Discuss Project 4 as a review of the course.
    Discuss mathematical breakthroughs and revolutions: changing the world.
    Look at the final research presentations and discuss how to research mathematical connections for a number of class interests.

  • Tues June 18
    Discuss the homework
    General Education and Mathematics in a General Education:
    Liz Colman and Education
    clicker questions #7-11.
    Take any questions

    In 205
    1. Sell your stock
    2. Read through Meeting 21st Century Quantitative and Science Literacy Needs of Appalachian Students and write down (to turn in) a) items that you agreed with (if any)
    b) items that you disagreed with (if any)
    c) items that surprised you (if any)
    d) the most compelling reason to reduce the hours that is listed in the article
    e) the most compelling reason(s) to keep or increase the hours that is listed in the article
    f) Has this article changed any of your thoughts about whether Appalachin should reduce the quantitative literacy credit from 4 hours to 3 hours? If so, describe.
    3. You may work on project 4 or the research presentations (I am happy to help!) in the lab or elsewhere

  • Mon Jun 17 Finish the Andrew Wiles and The Proof video and questions
    clicker questions #1-6. Discuss the What mathematics is research and readings assignment.
    Discuss Project 3 topics
  • Fri Jun 14 Test 2.
    Review the course themes:
    -what mathematics is
    -what it has to offer and why it is useful
    -the diverse ways that people succeed in it and impact it
    -local to global theme
    -truth and consequenses theme

    Mathematicians: David Blackwell and Andrew Wiles
    David Blackwell
    Andrew Wiles and The Proof video and questions
  • Thur Jun 13
    Take a look at homework.
    Look at succeeding in mathematics (Circle lots of As): Here's Good News... SAT scores are declining at a slower rate. Discuss the SAT and whether the SAT should predict college scores. HoM on SAT and GPA. Review the biased MRT instructions and relate to stereotype vulnerability.
    Case studies: College Success #6

    Predicting height and solving a crime

    Clickers for regression lab

    In 205:
    1. Statistics Detective Review
    2. Purchase your stock
    3. If finished before we come back together, then review the class highlights page and take notes for project 4.

  • Wed Jun 12

    GE experiment
    Discuss correlations versus causations on why birds fly south during colder weather
    Exposure to letters A through F
    Discuss the Bradford-Hill_criteria

    In 205:
    1. Can We Predict the Future? Stocks, Class Data, and Raw Egg Regressions

  • Tues Jun 11
    In 205:
    1. Representations of Data lab
    2. If finished before we come back together then work on project 3
    Back to the classroom:

    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

    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 printed stock graph, the highs:
    a) lost money
    b) gained money
    c) stayed about the same

    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

    Discuss the homework readings:
    Golden mean and Fibonnaci
    Mendel and genetics of peas, twin studies, GPA studies and SAT, Visualizing, Vietnam draft
    HIV testing, airplane safety, the price of life - asbestos, pap smears, loss of life expectancy... [unintented consequenses]

    Lady Tasting Tea

    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

  • Mon Jun 10
    Nielsen ratings.
    Use your homework to decide who is the best network?
    a) ABC
    b) CBS
    c) NBC

    Here's good news, we are the best network... (for each network)

    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

    Boxplot and baseball.
    Reminder of google news for "box plot" or boxplot, google scholar [any time since 2013], including connections to the social sciences, medicine and sports and google images including the Michelson-Morley experiment 1887 led to the acceptance of special relativity...

    Anthropology study: width/length of 20 beaded rectangles used in Shoshani leather handicrafts and the relationship to 1/golden mean.

    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 the 1969 Vietnam draft data, introduction to scatterplot, line of best fit, and boxplots via Starr

    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 would have won - but Roosevelt's win was due to a last minute change in sentiment
    d) I did not complete the homework readings

    Discuss the homework readings in light of:
    Collecting and Presenting Data
    Unintended Consequences

    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

    Finish election issues: 2000 election between Bush and Gore and Pat Buchanan's impact in Florida
    Begin 3.4 #11.
  • Fri Jun 7 Discuss the literature review/connection component of proj 3 as related to the themes of
    Collecting and Presenting Data
    Unintended Consequences
    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

    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 Benford's law, where the first digit in many real-life sources of data is not equally distributed, and approximates a logarithmic trend (where 1 occurs about 30% of the time while 9 less than 5% of the time) in data such as street addresses, stock prices, population numbers, death rates, etc...

    Distance from home bar chart. Armspan bar chart. Height box plots.

    Finish the statistics of nature. doodling in math class.

    Discuss 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.

  • Thur Jun 6 Test 2. Meet in the lab.
    In 205:
    1. Work in groups of 2 or 3 people. On the front board, put up the actively traded stock symbol that you wish to track [one stock per group - first come, first served]: for stocks with certain names
    or for
    "stock symbol" "COMPANY NAME"
    2. stock graph
    3. ASULearn anonymous data collection.
    4. statistics of nature
    5. Work on hw for tomorrow if you are finished before we come back together.
  • Wed Jun 5

    Review the Condo lab questions: 1, 4, 7, 8 and 9-13
    a) Option 1
    b) Option 2

    Answer questions on the study guide, ASULearn activities and go over the homework.
    Review via clickers: 1.2 #9, 14, 21, and 24 and 1.3 # 8 and 10
    a) lump sum
    b) periodic payment
    c) loan payment
    d) combination of lump sum and periodic payment
    e) other

    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
    Discuss good credit

    Discuss project 4. The people mentioned in the finance segment... Equations in this segment.
    Begin statistics: statistics in the geometry segment and in finance

    Mention upcoming needed for lab in 2015: Find the stock symbols of a few companies that are actively traded and that you are interested in "buying" - for example, you might search for stocks with certain names
    or for
    "stock symbol" "COMPANY NAME"
    where COMPANY NAME is the name of the company that you are interested in.
    stock graph

    In 205:
    1. Find some stock symbols, as above
    2. Stock Graph
  • Tues Jun 4 Collect the lab and the loan/debt research. Take questions on the homework readings. Clicker questions:

    1. In the derivation of the loan formula, we used:
    a) x/(x-1) = 1/(1-1/x) = 1/(1-x-1)
    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)

    2. To calculate how much I pay in total we use
    a) lump sum
    b) periodic payment
    c) loan payment
    d) one of the above, depending on the problem context
    e) none of the above

    3. If we pay an extra $20 each month on a loan then we will pay
    a) less total interest and I have a good reason why
    b) less total interest but I am unsure of why
    c) more total interest but I am unsure of why
    d) more total interest and I have a good reason why
    e) the same amount of interest

    4. When the loan is set up so that there is a 0 balance in the Excel chart the last month, then we can calculate the total interest via:
    a) monthly payment x # payments - original loan
    b) add the montly interest for each and every month
    c) original loan x monthly rate x #payments
    d) exactly 2 of a, b, c are correct
    e) a, b, c are all correct

    Second Student loan statement, credit cards and finance charges

    In 205:
    1. Condo and Car Purchases: Decisions, Decisions (Part 2)
    2. Jane and Joan on ASULearn - saving for retirement
    3. If finished early, then go through the class highlights page and begin to collect items from finance for Project 4

  • Mon Jun 3 Review lump sum and periodic payment. Complete $37 savings. Show work to determine that the interest is $119.84 and $10.91 respectively.
    Philosophy of loans Student loan statement.

    In 205:
    1. 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)
  • Fri May 31 lump sum clicker
    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

    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

    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.

    In 205:
    Jane and Joan on ASULearn. If you are finished early, then continue working on Project 2 (see the main calendar page)

  • Thur May 30 Collect hw and take questions.
    Lump sum philosophy. Revisit the clicker question from yesterday
    (a) 1000(1+.08)8

    (d) 1000(1+.08/12)8
    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 using todays rate and seeing how long it will take to double our money using her rate, and then today's rate:
    Goal Seek: Data/What-If Analysis/Goal Seek/Set cell...

    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.
    Charlie Rose - An exclusive conversation with Warren Buffett [first 54 seconds and then from 3:30-5:18]. [DVD 4:11 - 5:48]
    Quotes on taxation. Local to global taxes.

    In 205:
    Benjamin Franklin's Will - Part 1 (Lab)

  • Wed May 29 Test 1. Resume class at 1:55.

    Begin finance.
    History and ethics of charging interest for the use of land, animals, money.
    Plimpton Cuneiform 322 and interpreting data
    Usury is Piracy
    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?

  • Tues May 28
    Review the lab. Take questions on the quiz, project 4, or the study guide.
    Discuss the Jeff Weeks Interview.
    visualizing a hypersphere: Jeff Weeks worksheet [Einstein based his theory of relativity off of Riemann's work on this space]
    Discuss the local to global theme in this segment.
    My own research as a part of the ways that people succeed and impact mathematics
    Discuss equations in this segment.
    Reflect on equations in the context of "what is mathematics" and the prevalence of equations in and outside of mathematics. Highlight percentages, fractions and decimals.

  • Mon May 27 Questions or comments on the readings.
    Maddie's video From 47:46 onwards.
    Discuss the density equation WMAP and Planck launches.
    Portal and Futurama: I, Roommate.
    Rob Kirschner's Supernovae results related to whether brightness=1/distance2.
    Gauss and Lobachevsky's measuring the angle sum

    In 205:
    Universe Lab
  • Fri May 25
    Use tape to make an equator. Begin going over the first 4 questions from Project 1

    Hyperbolic geometry: There are many real-life applications of hyperbolic geometry, such as
    1. models of the internet that hope to reduce the load on routers,
    2. building crystal structures to store more hydrogen or absorb more toxic metals
    3. mapping the brain
    4. mapping the universe
    5. modeling Mercury's orbit.
    6. Art: Crochet model of hyperbolic geometry Reef Crochet reef.

    Review starting at about 4:11, including a 3-torus with only 96 stars

    [~32 minutes] 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
    Discuss and share responses to the notes

  • Thur May 24
    In 205:
    1. 2-D universe lab
    2. If finished before we come back together, then work on project 1.

  • Pythagorean theorem and Image of Pythagorean theorem
    discuss local (close to Euclidean geometry) to global (geometry is very different) perspectives
    Crochet model of hyperbolic geometry

    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.
    Review the slinky model of the Klein bottle along with the identifications of the square model.
    Glass model - I have a much smaller model in my office.
    Students create a tiling view of Klein bottle Tic-Tac-Toe to the left and right (same board), and above and below (reflected board).
    Clicker question
  • Wed May 23 Register the i-clicker.
    Go over the webpages and ASULearn messages and share from the syllabus or yesterday's class.

    Lab 1 Clicker questions

    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 in the horizon
    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)

    What does a space look like, how do we know, and how do we represent it...

    Where is North?

    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.

    First 3 questions on Clicker review of Euclidean and Escher
    Escher's space and Poincare's disk model of hyperbolic geometry.
    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
  • Tues May 21 Index sheet. Overview of the course including the attendance policy.
    1. what mathematics is,
    2. what it has to offer and why it is useful,
    3. the diverse ways that people succeed in it and impact it,
    4. local to global theme,
    5. truth and consequenses theme.
    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 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.

    Julian Beever's pavement drawings:
    Globe wrong view
    Globe correct view
    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

    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.