• Tues 11/29
    Clicker questions on homework readings and discussion.
    Beauty of Mathematics, http://vimeo.com/77330591 [1:41]
    mathematical breakthroughs
    What is Mathematics slides, Final Exam Research Presentations, rubric. Come up front and share the topic (name, major(s), concentrations/minors, research project idea, and whether you prefer to go 1st, 2nd or have no preference).
    Formal evaluations.
  • Mon 11/28 Stocks, class stats, and research
  • Tues 11/22 This is a research day for the final project presentations. You may work with me in the classroom (bring in a phone, tablet or laptop), or you may work elsewhere. I will be in the classroom to collect Project 4 and lab from yesterday (if you didn't finish it) and to help you!
  • Mon 11/21 Stocks and what is mathematics and probability lab
  • Thur Nov 17
    Probability and Randomness in Games, Business, and Life I The Great Courses up until 4:00. [notice the connections to the first two sections]
    probability slides and birthday comic
    David Blackwell and controversy of Friend or Foe, Prisoner's Dilemna, Tragedy of the Commons
    TEDxBlackRockCity - Spencer Greenberg - Improve Your Life With Probability start with 1:42
    What is Mathematics slides. Project 4: What is Mathematics? (a Review), rubric. Final Exam Research Presentations, rubric.
    Real-World Problems Being Solved by Mathematicians
    Math It's Everywhere [1:04].
    Discuss how to research mathematical connections and people for a number of class interests, including equations, geometry, algebra, statistics, mathematicians, Mactutor, mathematicians research soccer
    Utility of Mathematics
    Mathematics and Religion (final project ideas: sacred geometry, spiritual numeracy)
  • Tues Nov 15 Test 3
  • Mon Nov 14 Statistics Detective Review and Stock Purchase lab
  • Thur Nov 10 Correlation vs causation continued
    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.
    Discuss the Bradford-Hill criteria 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.
    DNA evidence vs epidemological evidence
    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.
    Big Data and consensus via visualization! David McCandless: The beauty of data visualization [12:06] from 2010. data detective.

  • Tues Nov 8
    GE experiment
    Discuss correlations versus causations on why birds fly south during colder weather
    Case studies: College Success #6
    applications of statistics to our lives hw readings #5-8
    Clickers for regression lab
    November 11 is Veterans Day.
    Would you have been drafted for Vietnam in the 1969 draft?
    Is there anyone in the class with the same birthday?
    Begin the 1969 Vietnam draft [2:06-5:00] December 30, 003. Roger Mudd. data, scatterplot, line of best fit, and boxplots 195, boxplots via Starr
    Project 3, rubric, full criteria

  • Mon Nov 7
    1. Can We Predict the Future? Stocks, Class Data, and Raw Egg Regressions
    2. If finished before we come back together for the contest, work on homework for tomorrow, Project 3 or review.
  • Thur Nov 3
    Music choices and compatibility issues (measuring "difference" in music tastes via looking at vertical distance between points) music 1, music 2.
    Predicting the future! Put equation of line on the board, review the slides and show the ASULearn glossary entry.
    2000 election between Bush and Gore and Pat Buchanan's impact in Florida
    3.4 #11
    Does volume predict high? Discuss lab on Monday. jump, experiment, protect!. If there are any eggcidents, clean up and I need the mesh back.
    applications of statistics to our lives hw readings #1-4
    GE experiment

  • Tues Nov 1 Clicker questions on the hw readings
    Media Literacy Week.
    Review the Representations of Data Lab via clicker questions and by #20
    Clicker questions on elections, Project 3, Book connections to the articles
    Review box plots and begin inferences and regression.
    Predicting height and solving a crime
    price of a life: cost per injection x number of shots to save a life from the entire population.

  • Mon Oct 31 Representations of Data Lab
  • Thur Oct 27
    Nielsen ratings
    Clicker questions on the readings
    Boxplot and baseball. 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...
    Mauna Loa Observatory on the island of Hawaii has been measuring the concentration of carbon dioxide (CO2) in earth's atmosphere since the 1950's. The observatory is 3,400 meters, or 11,000 feet, above sea level. The undisturbed air, remote location, and minimal influences of vegetation and human activity are well-suited for monitoring atmosphere components, including those that may cause to climate change. The observatory is part of the National Oceanic and Atmospheric Administration (NOAA). http://www.esrl.noaa.gov/gmd/obop/mlo/
    Project 3, rubric
    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.
    Difficult to count, like stars in the universe. Sampling versus census.
    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.
    Last Week Tonight with John Oliver - Misleading Food Labeling [2:09]

  • Tues Oct 25
    Clicker questions on the hw readings Discuss the hw readings and mention project 3.
    Clicker questions on measures of center
    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.
    box plots
    Height box plots.
    Armspan bar chart.
    Nightingale, Gallup, Silver
    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. 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?).
    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.

  • Mon Oct 24
    1. Stock Graph and Data Collection
    2. ASULearn: Anonymous Class Data Collection
    3. Statistics of Nature
  • Thur Oct 20 Test 2
  • Tues Oct 18
    David deposits $500 at the end of each quarter into an account paying 6.5% interest compounded quarterly for 7 years. He then changes his deposit to $725 each quarter for 5 more years at the same rate. What will the amount on deposit be after the entire 12 years?
    Which formula(s) applies here.
    a) lump sum
    b) periodic payment
    c) loan payment
    d) combinations of lump sum and periodic payment
    e) other
    Mention hw for next week and lab. Stock Graph and Data Collection
    Berkshire Hathaway stock graph (BRKA versus BRK-A)
    themes, advice from previous students.
    Review responses to online problems. Take any questions. study guide

  • Mon Oct 17 Car Purchases: Decisions, Decisions (Part 2)
  • Tues Oct 11
    Collect hw. Review the condo and car lab 1, 4, 7, 8 and 9-13
    Which option would you choose?
    a) Option 1 Smaller Loan
    b) Option 2 Lower Rate
    Student loan statement: credit cards finance charges=monthly interest=interest paid that month
    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...
    Credit ratings, stores selling their credit cards by their employees, risk and interest rate, credit vs debit cards...
    Truth is in algebra and in details of the derivations, in lending practices, John Oliver exposing truth, in real-life issues like lottery winners ending up worse financially after 5 years. numerous conclusions made from the same measurements. risk in finance and lending.
    Discuss hw for Monday and Tuesday
    Connections between finance and geometry of the earth and universe:
    Plimpton Cuneiform 322 and interpreting data
    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.
    Truth in a picture/space versus algebraic derivations and equations.

  • Mon Oct 10 Condo and Car Purchases: Decisions, Decisions (Part 1) lab
  • Thur Oct 6 Go over the practice problem. Review
    loan payments and amortization
    Modify the Excel file 58.18, 4795, .08/12, 120 months in B3 and D3. Rounding so change B3 to 58.18 exact. Scroll down to month 120 to see the impact of rounding.
    Clicker loans
    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 clicker
    Introduce the theme of unintended consequences and pay attention to the appearance of North Carolina here: Stop at 15:28 (Rich Guy's Car): https://www.youtube.com/watch?v=PDylgzybWAw

  • Tues Oct 4
    Clicker review of lump and periodic combined
    loan payments and amortization
    Modify the Excel file 58.18, 4795, .08/12, 120 months in B3 and D3. Rounding so change B3 to 58.18 exact. Scroll down to month 120 to see the impact of rounding.

  • Mon Oct 3 Use lab time to work on Project 2 or review lump sum and periodic. I'll be in lab to help or you may work from home. Monday's hw
  • Thur Sep 29
    slides, Philosophy of derivation of periodic payment
    Jane - Traveled Early and then Saved. Joan - Saved Early and then Vacationed.
    pension decisions
    Take questions on Ben Franklin project sample beginning or the hw. Hand out the rubric. Monday's lab: I'll be there
    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 27 Write the derivation of lump sum. Clicker questions for lump sum #5-7
    Project 2, sample beginning
    What about $100 deposited every month into an account for 25 years, compounded monthly at 5%? slides Work towards periodic payment understanding and compare the philosophy to the lump sum formula derivation and to Jeff Weeks.
    Clicker questions for lump and periodic

  • Mon Sep 26 Benjamin Franklin's Will-Part 1 (Lab)
  • Thur Sep 22
    Clicker questions for lump sum #1-4
    Review the lump sum philosophy
    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
    Economic pearl harbor: snuck up, devastating, costly, motivated us to join the war-in this case a call to reform
    problems with Americans keeping their money under their mattress
    Lisa's Thrifty Savers savings account from Bart the Fink: Excel can't solve the resulting lump sum equation for number of times compounding per year. constructing a solution versus guess and check.
    Quotes on taxation. Local to global taxes.
    Discuss lab and project

  • Tues Sep 20 clickers on the history and ethics of charging interest #1-3. What kind of world are we making. What kind of world should we be making. What kind of world can we be making. books, tools, money, data itself
    equations and finance lab
    comic [actually Benjamin Franklin]
    Discuss 142 years compounding monthly versus annually.
    Lump Sum Philosophy
    clickers on the history and ethics of charging interest #4
    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:
    Start with B2=.08, C2=1
    Goal Seek: Data/What-If Analysis/Goal Seek/Set cell... a1, 2000, c2...

  • Mon Sep 19 (To turn in) equations and finance lab
  • Thur Sep 15 Test 1

  • Tues Sep 13
    Review the Universe Lab and clicker questions
    Take questions on the quiz, course themes, or the Test 1 study guide
    Discuss equations in this segment. equations in general [comparing infinite quantities, empirical versus platonic, down with fractions, beauty in equations]. prevalence of equations as a way to model. percentages, fractions and decimals.
    Historically multiples of 1/100 were common in taxation and computations. The decimal version came much later [.01, 1%]. Plimpton Cuneiform 322 and interpreting data

  • Mon Sep 12
    1. Geometry of our Universe Lab
    2. Read over the ASULearn Glossary/Wiki entry on truth and consequences in geometry
  • Thur Sep 8
    Clicker questions on the themes hw #1 and #2.
    Geometry of the Universe review slides
    Experiment: Discuss the density equation WMAP and Planck launches. Critiques: difficulty agreeing on the meaning of the data, neutrino mass, dark energy, speed of light?
    http://www.youtube.com/watch?v=5u7hFQy9Mt0&feature=relate From 47:46 onwards.
    Clicker questions on last part of project 1
    Clicker questions on the themes hw #3 onward. Discuss the themes review and Jeff Weeks interview hw. my scholarship
    Discuss equations in this segment.

  • Tues Sep 6
    Clicker questions on 4.6 Experiment 1: Gauss and Lobachevsky's measuring the angle sum. Critiques: Experimental error, light rays bend with gravity, triangles too small
    Review project 1
    Clicker question on 4.7
    Discuss the last 3 questions: Project 1.
    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. Sampling estimates and the role of chance and probability in creating a good sample and extrapolation.
    Geometry of the universe?
    A spherical universe: Visualizing a hypersphere-Jeff Weeks worksheet. hypersphere. algebraically and in statistics. shifting shadows [Einstein based his theory of relativity off of Riemann's work on this space]
    NASA and flat universe. finite? Portal trailer and Futurama: I, Roommate. Escher. Experiment: Looking for repeated star patterns-Critiques: light takes times to reach us and changes the view, recognize?
    Hyperbolic universes: Hyperbolic Icosahedral
    Experiment: Rob Kirschner's Supernovae results related to whether brightness=1/distance2. truth via reproducability and concensus and the role of chance and probability. Distant supernovae dimmer than expected in a coasting space Critiques: Experimental error, no perfect model, not necessarily exploding at the same brightness, convenience sample
  • Thur Sep 1 Collect and begin going over the first 4 questions from Project 1. Diverse perspective and local to global issues. The role of chance and probability in knowing the truth. 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? light rays, string theory

  • Tues Aug 30
    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
    Review research project 1 and books in my office for research project 1

  • Mon Aug 29 2D Universes Lab

  • Thur Aug 25
    Clicker questions for lab 1
    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 23
    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.
  • Pythagorean theorem and Image of Pythagorean theorem
    Difference of hyperbolic geometry and spherical geometry:
    Sphere with Angels and Devils, 1942.
    Sphere Surface with Fish. 1958
    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.
    Books in my office for research project 1.
    Where is North?

  • Mon Aug 22 Perspective Lab Activities and ASULearn Mathematical Experiences reflection survey

  • Thur Aug 18 Clicker question on round earth. Press the On/Off (power) button on their iClicker remote until the blue Power light begins flashing (about 2 seconds). Press the new two-letter code AA.
    Take questions or comments on the syllabus or on project 1.
    Discuss the lab (and reading) for Monday via Perspective Drawing and Projective Geometry. Discuss Excel.
    Review geometry segment themes: What does a space look like, how do we know and how do we represent it?
    clicker cartoon question, cartoons and dimensions
    Are The Simpsons 2D or 3D?
    Dutch graphic artist M.C. Escher and the mathematical clues he left in his work:
    Sun and Moon.  
    Worksheet on Escher.   (number 2).
    Folding a Euclidean angle sum

  • Tues Aug 16 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.mov 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 led to the 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:
    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.