Class Highlights

  • Fri Jun 27 Final research presentations, peer review and self-evaluation
  • Thur Jun 26 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).
    Pants.pdf research and reflection.
    Lab work in 205.

  • Wed Jun 25 Discuss Project 4: What is Mathematics: A Class Review as a review of the course.
    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.

    Mathematics and Religion (final project ideas: sacred geometry, spiritual numeracy)
    Discuss mathematical breakthroughs and revolutions: changing the world.
    Math It's Everywhere:
    Beauty of Mathematics:
    Smarter Math Builds Equations for a Smarter Planet
    Real-World Problems Being Solved by Mathematicians
    Look at the final research presentations and discuss how to research mathematical connections for a number of class interests.
    Survey clicker questions
    Time to work on the final research presentations

  • Tues Jun 24 Discuss what you found on David Blackwell and Andrew Wiles.
    Finish discussing Andrew Wiles and The Proof video and questions
    Why make Liberal Arts Majors take Math in College? 3:23
    Liberal arts
    General Education and Mathematics in a General Education: Liz Colman and Education.
    Clicker questions on what is mathematics #7-11

    In 205
    1. Sell your stock (using the original purchase price)
    2. Meeting Quantitative Needs
    3. You may work on project 4 or the research presentations in the lab or elsewhere (I am happy to help!)

  • Mon Jun 23
    Continue What is Mathematics. Take questions on the last 2 assignments.
    Share from Project 3 (Critical Analysis of Recent Media)
    Share your favorite quote about what mathematics is and the person it is attributed to. Clicker questions on what is mathematics #1-6 and discuss the what mathematics is research and readings hw.
    Andrew Wiles and The Proof video and questions
  • Fri Jun 20 Test 3.

    In 205 1. Sell your stock

    Come back together in the classroom.
    What is Mathematics during the last week.
    Mathematicians: Jeff Weeks, myself, David Blackwell and Andrew Wiles

  • Thur June 19

    Predicting height and solving a crime

    In 205:
    1. Can We Predict the Future? Stocks, Class Data, and Raw Egg Regressions
    2. If finished before we come back together, then review the class highlights page and take notes for project 4 related to statistics.

    Come back together.
    Clickers for regression lab
    Take questions on test 3 study guide, ASULearn review or anything else.

  • Wed June 18 Lab clicker questions
    GE experiment
    Discuss correlations versus causations on why birds fly south during colder weather
    Discuss the Bradford-Hill criteria
    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

    In 205:
    1. Statistics Detective Review
    2. Purchase your stock

  • Tues June 17
  • Discuss the rest of the homework readings in light of:
    Collecting and Presenting Data, Boxplots, Predictors, Unintended Consequences:
    Clicker questions on the hw readings.
    Clicker questions on applications of statistics to our lives hw readings

    In 205:
    1. Representations of Data lab
    2. Ask me any questions about project 3 before you leave

  • Mon June 16 doodling in math class.
  • Anthropology study: width/length of 20 beaded rectangles used in Shoshani leather handicrafts and the relationship to 1/golden mean.
  • 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...
  • 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
  • Elections
    Clicker questions on elections
    2000 election between Bush and Gore and Pat Buchanan's impact in Florida
    3.4 #11.
  • Fri June 13
    Clicker questions on the hw readings Discuss the hw readings and mention project 3.
    Clicker questions on measures of center
    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.
    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.

    In 205:
    Finish the statistics of nature.
    Mention part of the hw on the articles on the impact of young voters

  • Thur June 12 Test 2. Meet in the lab.
    In 205:
    1. ASULearn anonymous data collection.
    2. statistics of nature
    3. Read through Project 3 and take note of the literature review/connection component as related to the themes of
    a) Collecting and Presenting Data
    b) Boxplots
    c) Predictors
    d) Unintended Consequences
    So, as you are completing hw for tomorrow, take notes on anything you see related to the above 4 themes and the page numbers they are on...
    4. Ask me any questions and make sure that I have looked through your lab responses to the statistics of nature before you leave.

  • Wed June 11
    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 10 Turn in hw. Take questions on the homework readings.
    Clicker questions on loans
    Review the Condo lab questions: 1, 4, 7, 8 and 9-13
    a) Option 1
    b) Option 2
    Second Student loan statement, credit cards and finance charges

    In 205:
    1. Condo and Car Purchases: Decisions, Decisions (Part 2)

  • Mon Jun 9 Mon Jun 3 Review lump sum and periodic payment via Jane and Joan extra credit. 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 Jun 6 Collect hw.
    Clicker questions for lump sum #3-6
    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

    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 ask me any questions you have on Project 2 before you go

  • Thur Jun 5 Collect hw and take questions.
    Clicker questions for lump sum #1 and 2 Review the lump sum philosophy.
    Intro to Goal Seek via using today's rate and seeing how long it will take to double money using her rate of 8% compounded monthly, and then today's rate: =1000*(1+B2/12)^(C2*12)
    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.

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

  • Wed Jun 4 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 Jun 3
    Review the lab. Take questions on the quiz, project 4, or the study guide.
    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 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 Jun 2 Discuss the last 3 questions from Project 1:
    Google search how many stars in the universe
    Geometry of the Universe slides
    Review starting at about 4:11, including a 3-torus with only 96 stars
    Portal and Futurama: I, Roommate.
    Gauss and Lobachevsky's measuring the angle sum
    Rob Kirschner's Supernovae results related to whether brightness=1/distance2.
    Discuss the density equation WMAP and Planck launches. From 47:46 onwards.
    Questions or comments on the readings.

    In 205:
    Universe Lab

  • Fri May 30 Lab 2 clicker question
    Use tape to make an equator. Begin going over the first 4 questions from Project 1
    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
    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.
  • Thur May 29
  • 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 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.

    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
    Davide Cervone's Cube Projections.
    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.

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

  • Wed May 28 Register the i-clicker. Go over the webpages and ASULearn messages
    Prepare to share your name, major(s)/minors/concentrations, and something you learned from hw or class yesterday or had a question on. yesterday's class.

    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)

    Lab 1 Clicker questions
    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 27 Overview of the course including the attendance policy, 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, and the 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. Truth: what a space looks like, how can we know, how we represent it.
    Watch 10 minute video excerpts notes
    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 to review the activities, then work on homework for tomorrow.
    What kind of world are we making. What kind of world should we be making. What kind of world can we be making.