Class Highlights
Fri Jun 21 Final research presentations. Final evaluations.
Thur Jun 20 Share presentation topics and assign research
sessions. Pants.pdf research. Go to the computer lab and
work on the
research presentations.
In 205:
1. Work on and (and as I make my way around the room)
show me a list of any mathematical connections/mathematicians you
already have so that I can help you add to them.
2. Sell your stock
3. On ASULearn take the Anonymous Advice for Next Semester survey.
4. After I have met with you in lab and you have finished #2 and #3,
you may continue working on the
research presentations in the lab
(I am happy to continue helping!) or elsewhere.
Remember to bring printed copies of everything, including
your annotated bibliography, to tape up tomorrow.
Wed Jun 19 Discuss Project 4 as a review of the course.
Discuss mathematical
breakthroughs and revolutions: changing the world.
Look at the final research
presentations and discuss how to research mathematical connections for a
number of class interests.
Tues June 18
Discuss the homework
General Education and Mathematics in a General Education:
Liz Colman and Education
clicker questions #7-11.
Take any questions
In 205
1. Sell your stock
2. Read through
Meeting 21st Century Quantitative and Science Literacy
Needs of Appalachian Students and write down (to turn in)
3. You may work on project 4 or the research presentations
(I am happy to help!) in the lab or elsewhere
Mon Jun 17 Finish the
Andrew Wiles and The Proof video and
questions
Discuss.
clicker questions #1-6.
Discuss the What mathematics is
research and readings assignment.
Discuss Project 3 topics
Fri Jun 14 Test 2.
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
Mathematicians: David Blackwell and Andrew Wiles
David Blackwell
Andrew Wiles and The Proof video and
questions
Thur Jun 13
Take a look at homework.
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
Predicting height
and solving a crime
Clickers for regression lab
In 205:
1. Statistics Detective Review
2. Purchase your stock
3. If finished before we come back together, then review the
class highlights page and take notes for project
4.
Wed Jun 12
GE experiment
Discuss correlations versus
causations on why birds fly south during colder weather
Exposure to letters A through F
Discuss the
Bradford-Hill_criteria
In 205:
1. Can We Predict the Future?
Stocks, Class Data, and Raw Egg Regressions
Tues Jun 11
In 205:
1. Representations of Data lab
2. If finished before we come back together then work on
project 3
Back to the classroom:
Back to the classroom. 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 printed 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
Discuss the homework readings:
Golden mean and Fibonnaci
Mendel and genetics of peas, twin studies, GPA studies and SAT,
Visualizing, Vietnam draft
HIV testing, airplane safety, the price of life - asbestos, pap smears,
loss of life expectancy... [unintented consequenses]
Lady Tasting Tea
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
Mon Jun 10
Nielsen ratings.
Use your homework to decide 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
Boxplot and baseball.
Reminder of 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...
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.
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
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 readings
Discuss the homework readings in light of:
Collecting and Presenting Data
Boxplots
Predictors
Unintended Consequences
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.
Fri Jun 7
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 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.
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.
Armspan bar chart.
Height box plots.
Finish the statistics of nature.
doodling in math
class.
Discuss the hw readings and mention project 3.
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.
Thur Jun 6 Test 2. Meet in the lab.
In 205:
1. Work in groups of 2 or 3 people. On the front board, put up the
actively traded stock symbol that you wish to track [one stock per group - first come, first served]:
http://finance.yahoo.com/lookup for stocks with certain names
or www.google.com for
"stock symbol" "COMPANY NAME"
2. stock graph
3. ASULearn anonymous data collection.
4. statistics of nature
5. Work on hw for tomorrow if you are finished before we come back
together.
Wed Jun 5
Review the Condo lab questions:
1, 4, 7, 8 and 9-13
a) Option 1
b) Option 2
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:
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
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
In 205:
1. Find some stock symbols, as above
2. Stock Graph
Tues Jun 4 Collect the lab and the loan/debt research. Take
questions on the homework readings. Clicker questions:
1. In the derivation of the loan formula, we used:
a) x/(x-1) = 1/(1-1/x) = 1/(1-x-1)
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)
2. 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
3. If we pay an 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
4.
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
Second Student loan statement, credit
cards and finance charges
In 205:
1. Condo and Car
Purchases: Decisions, Decisions (Part 2)
2. Jane and Joan on ASULearn - saving for retirement
3. If finished early,
then go through the class highlights page and begin to collect items from
finance for Project 4
Mon Jun 3
Review lump sum and periodic payment.
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 May 31
lump sum clicker
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
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.
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 continue working on Project 2 (see the main calendar page)
Thur May 30 Collect hw and take questions.
Lump sum philosophy.
Revisit the clicker question from yesterday
(a) 1000(1+.08)8
(d) 1000(1+.08/12)8
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...
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.
In 205:
Benjamin Franklin's
Will - Part 1 (Lab)
Wed May 29 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 May 28
Review the lab.
Take questions on the quiz, project 4, or the study guide.
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 May 27 Questions or comments on the readings.
Maddie's video
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
In 205:
Universe Lab
Fri May 25
Use tape to make an equator. Begin going over the first 4 questions from
Project 1
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.
Review
http://www.youtube.com/watch?v=Uzd484Mvm2k
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
Thur May 24
In 205:
1. 2-D universe lab
2. If finished before we come back together, then work on project 1.
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
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).
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.
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).
Clicker question
Wed May 23
Register the i-clicker.
Go over the webpages and ASULearn messages and share from the syllabus or
yesterday's class.
Lab 1 Clicker questions
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)
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 21
Index sheet.
Overview
of the course including the attendance policy.
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 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.
Watch 10 minute video excerpts lifebynumbersintro.mov
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.
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, then work on homework for
tomorrow. Review the activities.
