Tues 11/29
Clicker questions on homework readings and discussion.
Mathcuffed
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.
questions
Big Data and consensus via visualization!
David McCandless: The beauty of data visualization [12:06]
from 2010. data detective.
Tues Nov 8
GE experiment
regression
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...
CO2
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.
http://www.huffingtonpost.com/mike-branch-cfp/should-you-say-yes-to-you_b_5889992.html
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:
=1000*(1+B2/12)^(C2*12)
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:
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.