Class Highlights

  • Thur Dec 4
    Clicker questions # 3-5.
    Data 1 [1:16] start at :15
    Data [2:04]
    Math It's Everywhere [1:04].
    Smarter Math Builds Equations for a Smarter Planet. [:32]
    Mathematics and Religion (final project ideas: sacred geometry, spiritual numeracy)
    Beauty of Mathematics
    http://vimeo.com/77330591 [1:41]
    Survey clicker questions
    Pants research and reflection.
    Discuss mathematical breakthroughs and revolutions: changing the world.
    Share the final research presentations topic (name, major(s), concentrations/minors, research project idea, and whether you prefer to go 1st, 2nd or have no preference).
    Discuss how to research mathematical connections and people for a number of class interests. final research presentations
    Formal evaluations.

  • Tues Dec 2 Discuss what you found on David Blackwell and Andrew Wiles and The Proof video and questions.
    Real-World Problems Being Solved by Mathematicians.
    Clicker questions # 1 and 2
    Why make Liberal Arts Majors take Math in College? video. Liberal arts.
    Ted talk: Liz Coleman on General Education.
    Discuss the final research presentations.

  • Mon Dec 1 Turn in hw. Class Stats
  • Tues Nov 25
    What good is math? Why are we taking it in schools?
    Math Cuffed: Is math binding or freeing?.
    Share a quote from the hw along with the person (try to share something different than what came before). Questions on the last 2 major assignments? Clicker questions on homework readings and discussion.
    Our species needs, and deserves, a citizenry with minds wide awake and a basic understanding of how the world works--Carl Sagan
    What kind of world are we making? What kind of world should we be making? What kind of world can we be making?
    Utility of Mathematics and connections to Thomas Banchoff from the beginning of the semester
    Andrew Wiles and The Proof video and questions (to turn in). We watched the Nova version, but here is the BBC version as well as a text transcript

  • Mon Nov 24 Begin the What is Mathematics segment, which we'llcontinue tomorrow and next week!
    1. Review the slides about the What is Mathematics segment, including the 2 projects, and ask me any questions.
    2. Sell your stock (using the original purchase price)
    3. Meeting Quantitative Needs (to turn in)
    4. You may work on hw for tomorrow (or either of the last 2 projects) here or elsewhere (I am happy to help!).
  • Thur Nov 20 Test 3
  • Tues Nov 18 Review histograms, bar charts, box plots and regression. Critical analysis and connections.
    Take questions on test 3 study guide, ASULearn review or anything else.
    What is Mathematics segment.
    David Blackwell and controversy of Friend or Foe http://vimeo.com/59756719
    David McCandless: The beauty of data visualization [12:06] [started but didn't finish]
    Case studies: College Success #6 Consquences by Linda Gorman

  • Mon Nov 17
    1. Statistics Detective Review Lab
    2. Purchase your stock
    3. Ask me any statistics questions

  • Thur Nov 13
    Discuss the Bradford-Hill criteria
    a) yes and I strongly feel so
    b) yes
    c) no
    d) no and I strongly feel so
    The Cigarette Controversy The tobacco companies knew and for most part accepted the evidence that cigarette smoking was a cause of cancer by the late 1950s. The documents also reveal that the tobacco companies helped manufacture the smoking controversy by funding scientific research that was intended to obfuscate and prolong the debate about smoking and health. Today, the tobacco companies acknowledge that smoking is a cause of disease, but they have not materially altered the way they do business.
    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.
    Predicting height and solving a crime
    David Blackwell and controversy of Friend or Foe http://vimeo.com/59756719
    David McCandless: The beauty of data visualization [12:05]
    Case studies: College Success #6
    What is Mathematics during the last week

  • Tues Nov 11
    applications of statistics to our lives hw readings#1, 2 and 7
    Clickers for regression lab
    Project 3
    Begin the 1969 Vietnam draft data, scatterplot, line of best fit, and boxplots via Starr
    GE experiment
    Discuss correlations versus causations on why birds fly south during colder weather

  • Mon Nov 10
    1. Can We Predict the Future? Stocks, Class Data, and Raw Egg Regressions
    2. If finished before we come back together, work on project 3
  • Thur Nov 6
    Project 3
    2008 Obama and McCain election
    Put equation of line on the board.
    Music choices and compatibility issues (measuring "difference" in music tastes via looking at vertical distance between points) music 1, music 2.
    2000 election between Bush and Gore and Pat Buchanan's impact in Florida
    3.4 #11
    Does volume predict high.
    applications of statistics to our lives hw readings #3-6
  • Tues Nov 4 Election day! Clicker questions on the hw readings
    Review the Representations of Data Lab via clicker questions and by #22
    Clicker questions on elections Book connections to the articles
    John Oliver and food labels: John Oliver on Misleading Labeling of Food Products [5:12]
  • Mon Nov 3 Representations of Data Lab
  • Thur Oct 30
  • Clicker questions on the readings
  • Nielsen ratings
  • Boxplot and baseball. Reminder of google news for "box plot" or boxplot, google scholar [any time since 2014], including connections to the social sciences, medicine and sports and google images including cell phone usage and the Michelson-Morley experiment in 1887 that led to the acceptance of special relativity...
    Project 3
    Review doodling in math class.
    Golden mean analysis
  • 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.
    Mathematical model for Ebola---predicting the future

  • Tues Oct 28
    Clicker questions on the hw readings Discuss the hw readings and mention project 3.
    Clicker questions on measures of center
    Psychic experiment. Histogram of the ASULearn random number from 1 to 10. Truth and Consequences: Random number experiment. The expected value if equally distributed from adding the people in the class and dividing by 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...
    Identity theft, fraudulent election in Iran faked economic data, cooked accounting books.

    Distance from home bar chart.
    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.
    Armspan bar chart.
    Height box plots.
  • Mon Oct 27
    1. Stock Graph and Data Collection
    2. ASULearn Anonymous Class Data Collection
    3. Statistics of Nature
  • Thur Oct 23 Test 2
  • Tues Oct 21 Review 9, 14, and 21. Review 24:
    a) lump sum
    b) periodic payment
    c) loan payment
    d) combination of lump sum and periodic payment
    e) other

    and 10. Take any questions on test 2.

    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
    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

    Connection between Escher and tiling in the geometry segment and the statistics of nature: the golden mean/phi and plants, flowers and pinecones:
    Doodling in Math Class: Spirals, Fibonacci, and Being a Plant [2 of 3]
  • Anthropology study: width/length of 20 beaded rectangles used in Shoshani leather handicrafts and the relationship to 1/golden mean.
  • Mon Oct 20
    1. Condo and Car Purchases: Decisions, Decisions (Part 2)
    2. Review the lump sum, periodic payment and loan payment formulas, as well as how to calculate total interest in all three cases and the first month's interest in the case of a loan, and ask me any questions before you leave. Note the hw for tomorrow.
  • Tues Oct 14
    Review the Condo lab questions: 1, 4, 7, 8 and 9-13
    a) Option 1
    b) Option 2
    Student loan statement: credit cards finance charges=monthly interest=interest paid that month
    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.
    Review prohibitions against charging interest on money to members of the community (usury), but was ok for strangers - lending was considered philanthropy and part of a giving back to the community...
    Introduce the theme of unintended consequences
    Discuss project 4. The people mentioned in the finance segment... Equations in this segment.

    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
    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

  • Mon Oct 13
    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) lab.
  • Thur Oct 9 Review loan and amortization table:
    Answer question 2 on the Condo and Car Purchases: Decisions, Decisions (Part 1) lab: Excel formulas in B3, D2, D3, C6, D6, and E6.
    Modify the Excel amortization table - 58.18, 4795, .08/12, 120 months in B3 and D3. Rounding so change B3 to 58.18 exact, but the interest is still $2,186.60 rather than the $2,185.97 on the Student loan statement.
    Scroll down to month 120
    month # End of Month Payment Interest Paid that Month Principal Paid that Month Loan Balance
    120 $58.18 $0.38 $57.80 ($0.63)
    120*58.18-.63 [total paid - overbalance last month]
    Clicker questions on loans #2 and 3
    Second Student loan statement
    Review prohibitions against charging interest on money to members of the community (usury), but was ok for strangers - lending was considered philanthropy and part of a giving back to the community...
    Payday lender in Boone
    Introduce the theme of unintended consequences:
    Stop at 15:28 (Rich Guy's Car): https://www.youtube.com/watch?v=PDylgzybWAw

  • Tues Oct 7
    Review lump, total interest, periodic payment, total interest formulas for 3.2% compounded monthly for 20 years, with principal and total savings left as unknown variables.
    http://www.huffingtonpost.com/mike-branch-cfp/should-you-say-yes-to-you_b_5889992.html
    pension decisions
    Philosophy and derivation of loans
    Clicker questions on loans #1
    Student loan statement.

  • Mon Oct 6 Use lab time to work on Project 2.
  • Thur Oct 2
    Philosophy of derivation of periodic payment
    Take questions on Ben Franklin project or the hw. Hand out the rubric.
    Jane - Traveled Early and then Saved. Joan - Saved Early and then Vacationed.
    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.
  • Tues Sep 30
    Clicker questions for lump sum #4-5
    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
    Clicker questions for lump and periodic

  • Mon Sep 29 Benjamin Franklin's Will - Part 1 (Lab)
  • Thur Sep 25 Collect hw and take questions.
    Clicker questions for lump sum #1 and 2
    Review the lump sum philosophy.
    Goal Seek: Data/What-If Analysis/Goal Seek/Set cell...
    Discuss other possibilities for unknowns in lump sum - the amount put in, the rate, or the number of times compounding per year. 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]
    Youtube first 1:27
    Quotes on taxation. Local to global taxes.
    Plimpton Cuneiform 322 and interpreting data
    Clicker questions for lump sum #3 and #6
    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
    Clicker questions for lump and periodic

  • Tues Sep 23
    Begin finance.
    History and ethics of charging interest for the use of land, animals, money, even betrothal.
    Historically multiples of 1/100 were common in taxation and computations. The decimal version came much later.
    Usury is Piracy [Responsibilities of Community Membership]
    Historically, animals, land and other property was lent out, and a part of the growth of the living animals, crop, etc, where given back to the lender. We have evidence of stone tablets that charging interest for the use of money dates back to at least the ancient Babylonian times. In numerous religions over time, including Christianity, Judaism and Islam, there were prohibitions against charging interest on money to members of the community (usury), but was ok for strangers - lending was considered philanthropy and part of a giving back to the community... In 1304, interest rates in Nuremberg were 220%. Interest rates have also been capped in history.
    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 (ie is the monthly rate). 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...

  • Mon Sep 22
    Continue equations in the context of "what is mathematics" and the prevalence of equations in and outside of mathematics. Highlight percentages, fractions and decimals.
    History and ethics of charging interest for the use of land, animals, money.
    1. Research the web to find out how old the idea of charging interest is
    2. Research the web to find one reason it makes sense to charge interest (for land, animals, money)
    3. Research the web to find one reason it doesn't make sense to charge interest
    4. Share what you found with your neighbors.
    If you are finished before we come back together, work on hw for tomorrow.
  • Thur Sep 18 Test 1
  • Tues Sep 16
    Review the Universe Lab
    Geometry of the Universe slides
    Discuss equations in this segment.
    Take questions on the quiz, course themes, or the study guide.
    Test 1 study guide
    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.
    Scholarship of Teaching
    Plimpton Cuneiform 322 and interpreting data
    Usury is Piracy
  • Mon Sep 15 Universe Lab
  • Thur Sep 11
    Clicker question on heart of mathematics
    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]
    http://vimeo.com/73243719
    https://www.youtube.com/watch?v=kNva9WpQXvM
    Rob Kirschner's Supernovae results related to whether brightness=1/distance2.
    Discuss the density equation WMAP and Planck launches.
    http://www.youtube.com/watch?v=5u7hFQy9Mt0&feature=relate From 47:46 onwards.
    Discuss the local to global theme in this segment (part d of the homework). and the connection to project 4
    My own research as a part of the ways that people succeed and impact mathematics

  • Tues Sep 9 Revisit lab 2 and the final exam time. Klein bottle tic tac toe or 2nd site for it
    Lab 2 clicker question
    How many stars in the universe?
    Review http://www.youtube.com/watch?v=Uzd484Mvm2k starting at about 4:11, including a 3-torus with only 96 stars
    Shape and geometry of the universe?
    Portal and Futurama: I, Roommate.
    Gauss and Lobachevsky's measuring the angle sum

  • Mon Sep 8 2D Universes Lab. Discuss the final exam day (ie the final research presentations).

  • Thur Sep 4 Collect and begin going over the first 4 questions from Project 1. Diverse perspective and local to global issues. Begin to discuss the last 3 questions, which we will continue to go over.
    Dimensions of our universe. Experiment: Is the Universe a 2D Hologram?
  • Tues Sep 2
    Clicker questions on dimensions and 2-D universes
    [~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
    Davide Cervone's Cube Projections
    Where is North?
    Review research project 1 and books in my office for research project 1
  • Thur Aug 28
  • Pythagorean theorem and Image of Pythagorean theorem
    discuss local (close to Euclidean geometry) to global (geometry is very different) perspectives
    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.
    Another 2-D universe: 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).
    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
    Introduce 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).
    Watch an excerpt from Flatland: The Movie. What do you think spherius would say to the idea of a 4th dimension?

  • Tues Aug 26 Clicker questions and other activities: Euclidean, Escher (hyperbolic) and perspective drawing. Angle sum: Walking and folding a Euclidean angle sum, what goes wrong on a crochet model of hyperbolic geometry, local (close to Euclidean geometry) to global (geometry is very different) perspectives in Sketchpad. Parallels in various geometry and models. Pythagorean theorem water demo.
    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.
    Clicker questions for lab 1
    Where is North?
    Difference of hyperbolic geometry and spherical geometry:
    Sphere with Angels and Devils, 1942.
    Sphere Surface with Fish. 1958
    Books in my office for research project 1.

  • Mon Aug 25 Lab work in 205:
    1. Lab on perspective
    2. Take the ASULearn Mathematical Experiences reflection survey
  • Thur Aug 21 Register the i-clicker Clicker question on round earth. Take questions or comments on the syllabus or on project 1.
    Discuss the lab (and hw reading) for Monday via Perspective Drawing and Projective Geometry
    Review geometery segment themes: What does a space look like, how do we know and how do we represent it?
    Think of your favorite cartoon. What dimension is it?
    a) 2-D
    b) 3-D
    c) both
    d) neither
    e) unsure

    Are The Simpsons 2D or 3D?
    http://www.youtube.com/watch?v=TKQ8Ilr6PgU
    Dutch graphic artist 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.
    Clicker review of Euclidean and Escher
  • Tues Aug 19 Overview of the course including the attendance policy. What kind of world are we making. What kind of world should we be making. What kind of world can we be making.
    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)
    lifebynumbersintro.mow 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.