Class Highlights and Labs

  • Mon May 6 Research Presentations from 12-2:30
  • Thur May 2 Discuss mathematical breakthroughs and revolutions: changing the world. Pants.pdf research. Share your final exam research presentation topic. Assign sessions. Evaluations.
  • Tues Apr 30
    Discuss the themes from project 4
    Liz Colman and Education
    Discuss the final research presentations

  • Mon Apr 29
    1. Sell your stock.
    2. On the front board, mark off whether you gained or lost money by adding them to the relevant gain/loss columns (one mark per group).
    3. Success in Math video
    4. Class discussion on the videos, what is mathematics homework from Thursday and Andrew Wiles.
    5. On ASULearn take the Anonymous Advice for Next Semester survey.
  • Thur Apr 25 Collect the What is Mathematics research and readings assignment. 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
    Take questions on Project 4 or the Research Presentations
    David Blackwell
    Andrew Wiles and The Proof video and questions.

  • Tues Apr 23 Test 3

  • Mon Apr 22
    1. Purchase your Stock
    2. Statistics Detective Review

    Clicker questions:
    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

    In the egg bungee experiment my group used less than the number of rubber bands that the line predicted for 200 cm:
    a) True
    b) False

    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
  • Thur Apr 18

    Predicting height and solving a crime
    Discuss correlations versus causations on why birds fly south during colder weather
    Discuss the Bradford-Hill_criteria
    Case studies: College Success

    David Blackwell
    Mathematical breakthroughs and revolutions
    Liz Colman and Education

  • Tues Apr 16

    Regarding the themes of
    Collecting and Presenting Data
    Predictors
    Boxplots
    Unintended Consequences
    discuss the hw readings in that context

    Continue looking at the theme of success and impacts 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.

    GE experiment

  • Mon Apr 15 Can We Predict the Future? Stocks, Class Data, and Raw Egg Regressions lab
  • Thur Apr 11
    Turn in the letters A or F reading homework and HDYK 3.4 #15, but answer the following question before you do so:

    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

    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 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
  • Tues Apr 9
    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.

  • Mon Apr 8 Representations of Data Lab

  • Thur Apr 4 Take questions on project 3. Review Review Vi Hart's doodling in math class and the statistics of nature.
    Anthropology study: width/length of 20 beaded rectangles used in Shoshani leather handicrafts and the relationship to 1/golden mean.

    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
  • Thur Mar 28
    Nielsen ratings.
    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

    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.

    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 reading
    Finish Height box plots.
    Mention 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...

    Worst graph intro, worst graphs cover.

    Discuss the homework readings in light of:
    Collecting and Presenting Data
    Boxplots
    Predictors
    Unintended Consequences
    statistics of nature. If time remains: doodling in math class.

  • Tues Mar 26
    Discuss the literature review/connection component of proj 3 as related to the themes of
    Collecting and Presenting Data
    Boxplots
    Predictors
    Unintended Consequences
    discuss the homework readings

    How many different items were you able to find (take note/highlight) in the homework readings that related to the themes?
    a) 0
    b) 1-4
    c) 5-9
    d) 10-14
    e) 15 or over

    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 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.

  • Mon Mar 25
    1. Show my your hw and begin working on below:
    2. Stock Graph and Data Collection
    3. ASULearn Anonymous Class Data Collection
    4. Work on upcoming hw if you are finished before we come back together
  • Thur Mar 21 Test 2 on finance
  • Tues Mar 19
    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
    Answer questions on the study guide, ASULearn activities and go over the homework.

    If we pay and 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
    statistics of nature. If time remains: doodling in math class.
  • Mon Mar 18 Condo and Car Purchases: Decisions, Decisions (Part 2)
  • Thur Mar 7
    1. 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


    2. If I pay extra each month on a loan, my total interest
    a) goes up
    b) goes down
    c) remains the same

    3. 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

    Review the lab questions: 1, 4, 7, 8 and 9-13
    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 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
    or www.google.com for
    "stock symbol" "COMPANY NAME"
    where COMPANY NAME is the name of the company that you are interested in.
    stock graph

  • Tues Mar 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)

    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 card and finance charges
    Discuss good credit
  • Mon Mar 4
    1. Take the Car Loan Practice Problem on ASULearn. Keep track of your formulas with the numbers plugged in and reasoning 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)
  • Thur Feb 28

    Philosophy of loans
    Student loan statement.
    If time remains, begin Condo and Car Purchases: Decisions, Decisions (Part 1)
  • Tues Feb 26 Take questions on project 2. Hand out rubric.
    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

    Jeff Weeks. 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.
  • Mon Feb 25 Jane and Joan on ASULearn - use your formula sheet and calculator to help you. You can ask me questions on project 2 before you leave if you have any.
  • Thur Feb 21
    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.
  • Tues Feb 19
    Lump sum philosophy.
    Review the lump sum equation via clicker questions

    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]. http://video.google.com/googleplayer.swf?docid=4537231419795681197 [DVD 4:11 - 5:48]
    Quotes on taxation. Local to global taxes.
  • Mon Feb 18 Benjamin Franklin's Will - Part 1 (Lab)
  • Thur Feb 14 Continue finance
    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?
    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:
    =1000*(1+B2/12)^(C2*12)
    Goal Seek: Data/What-If Analysis/Goal Seek/Set cell...
  • Tues Feb 12 Test 1
  • Mon Feb 11 Finish equations. Take questions on the study guide, ASULearn or any other questions.
    Begin finance.
    History and ethics of charging interest for the use of land, animals, money.
    Plimpton Cuneiform 322 and interpreting data
  • Thur Feb 7
    Maddie's video. Discuss the Jeff Weeks interview. Take questions on the activities on the class highlights page. Discuss the local to global theme in this segment.
    my own research as a part of the ways that people succeed and impact mathematics
    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. Review equations from the geometry segment.
  • Tues Feb 5
    Take questions or comments on the lab or readings. Begin going over the remaining universe Project 1 questions (local to global/universal) via:
    http://www.youtube.com/watch?v=5u7hFQy9Mt0&feature=relate
    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
    visualizing a hypersphere: Jeff Weeks worksheet [Einstein based his theory of relativity off of Riemann's work on this space]
  • Mon Feb 4 Universe Lab
  • Thur Feb 1 Make the material your own in ways that are satisfying to you. clicker question. Take questions or comments on the hw for Monday, the lab, or Tuesday class.
    Begin going over the first four questions from Project 1 - geometry of the earth.
    Review
    http://www.youtube.com/watch?v=Uzd484Mvm2k
    starting at about 4:11, including a 3-torus with only 96 stars
  • Tues Jan 29 Collect student responses from the 2D Universes Lab from Monday.
    Take any questions on the lab.
    Pull up the Klein bottle section of the lab with the pictures.
    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).

    [~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

    Turn in the notes before leaving.
  • Mon Jan 28 2D Universes Lab
  • Thur Jan 24 Take questions.
  • 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). Tic-tac-toe in PacMan's universe. Tic-Tac-Toe in the Klein bottle.
    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.
  • Tues Jan 22 Lab 1 Clicker Questions
    Where is North?

    Highlight some books from my office that are useful for research project 1.

    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

    First 3 questions on: Clicker review of Euclidean and Escher.

    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.

    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
  • Thur Jan 17 Fill out index sheet.
    Register the i-clicker 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?
    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?
    http://www.youtube.com/watch?v=TKQ8Ilr6PgU
    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.
  • Tues Jan 15 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). 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:
    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.
  • Mon Jan 14
    1. Perspective Lab Activities
    2. Take the ASULearn Mathematical Experiences reflection