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.

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.

Discuss the homework

General Education and Mathematics in a General Education:

Liz Colman and Education

clicker questions #7-11.

Take any questions

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

Discuss.

clicker questions #1-6. Discuss the What mathematics is research and readings assignment.

Discuss Project 3 topics

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

Take a look at homework.

Look at succeeding in mathematics (Circle lots of As):

Case studies: College Success #6

Predicting height and solving a crime

Clickers for regression lab

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.

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

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

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 r

a) There is a typo in the book - the actual r

b) The mathematics of the r

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

a) 0

b) 1-4

c) 5-9

d) 10-14

e) 15 or over

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.

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.

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.

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:

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

1. In the derivation of the loan formula, we used:

a) x/(x-1) = 1/(1-1/x) = 1/(1-x

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

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)

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)

Lump sum philosophy. Revisit the clicker question from yesterday

(a) 1000(1+.08)

(d) 1000(1+.08/12)

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)

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)

(b) 1000(1+.08/8)

(c) 1000(1+.08/12)

(d) 1000(1+.08/12)

(e) none of the above

What did the bank really mean?

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.

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/distance

Gauss and Lobachevsky's measuring the angle sum

In 205:

Universe Lab

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

In 205:

1. 2-D universe lab

2. If finished before we come back together, then work on project 1.

discuss local (close to Euclidean geometry) to global (geometry is very different) perspectives

Crochet model of hyperbolic geometry

PacMan sequence from

Watch an excerpt from

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

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

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.

discuss local (close to Euclidean geometry) to global (geometry is very different) perspectives

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

Advice from last semester.

Julian Beever's pavement drawings:

Butterfly

Globe wrong view

Globe correct view

Accident

Perspective Drawing and Projective Geometry

Lab work in 205:

1) ASULearn Mathematical Experiences Reflection

2) Perspective lab Activities

3) Are

If time remains before we come back together, then work on homework for tomorrow. Review the activities.