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: https://www.youtube.com/watch?v=gAvIR3vFu8c
Beauty of Mathematics: http://vimeo.com/77330591
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?
https://www.youtube.com/watch?v=bvO1yAzQq9E
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:
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 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
Dimensions
Shape
Geometry of the Universe slides
Review http://www.youtube.com/watch?v=Uzd484Mvm2k 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.
http://www.youtube.com/watch?v=5u7hFQy9Mt0&feature=relate
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 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
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.
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 lifebynumbersintro.mov
notes
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 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.