Dr. Sarah's Math 1010 Class Highlights

### Dr. Sarah's Math 1010 Class Highlights The following is NOT HOMEWORK unless you miss part or all of the class. See the Main Class Calendar for ALL homework and due dates.

• Fri Apr 29 Final project research presentations and peer review 12-2:30.
• Tues Apr 26 Oral abstracts. Finish up What is Mathematics theme. Evaluations.
• Mon Apr 25 Class Statistics
• Thur Apr 21 Finish Review. Discuss mathematical breakthroughs and revolutions. Pants activity. Discuss the final project.
• Tues Apr 19 Review Test 3 and Stock Market. Begin Review.
• Mon Apr 18 Stock and What is Mathematics lab activities
• Thur Apr 14 Test 3
• Tues Apr 12 Review the lab from Monday. Finish statistics of nature. Case Studies: College Success. Take questions on the test. If time remains, Predicting height and solving a crime.
• Mon Apr 11 Statistics Detective Review Lab
• Thur Apr 7 Media representations: Review elections including Landon and Roosevelt, Bush and Obama, and Buchanan and Gore. Analyze and critique and discuss what we would like to back them up. Relate to project 4. Read and discuss the succeeding in mathematics handout. Discuss the homework reading - article exposure to A or F. Here's Good News... SAT scores are declining at a slower rate. Discuss the SAT and whether the SAT should predict college scores. Review the biased MRT instructions and relate to stereotype vulnerability. Statistics of nature. Discuss questions on the ASULearn review and project 4 including the Lower Level of the Library.
• Tues Apr 5 Go over the lab and do the egg bungee contest. Mention the quality of the responses to #10, 16 and 22 for the representations of data lab. Review 3.4 #11. Review 3.4 #15 parts b) and c). Discuss the interactive regression. Review median, mean and boxplots via the average of Nielsen ratings.
• Mon Apr 4 Can We Predict the Future? Stocks, Class Data, and Raw Egg Regressions
• Thur Mar 31 Clicker questions. Discuss the contradictory perspectives in the youth vote, how to "lie" with statistis and relevant page numbers in How Do You Know and Heart of Mathematics, as well as project 3. Continue the 1969 Vietnam draft data, introduction to scatterplot, line of best fit, and boxplots via Starr [relate to the theme of breaking it up into smaller pieces, like Jeff Weeks, and shifting viewpoints, like Andrew Wiles]. Does Volume predict high from stock graph. Discuss linear regression and r2 value. Do How Do You Know p. 185# 11. Discuss the actual predictor value, the estimated predictor values from a graph or via a line fit by eye, and related issues. If time remains then Predicting height and solving a crime.
• Tues Mar 29 Go over the lab. Discuss the Heart of Mathematics Readings. Begin the 1969 Vietnam draft data, introduction to scatterplot, line of best fit, and boxplots via Starr [relate to the theme of breaking it up into smaller pieces, like Jeff Weeks, and shifting viewpoints, like Andrew Wiles].
• Mon Mar 28 Representations of Data
• Thur Mar 24 Worst graph intro, worst graphs, cover. Random number sequence generator Discuss the measures of centers homework and share from How Do You Know. Nielsen Ratings and advertising spins. Music choices and compatibility issues (measuring "difference" in music tastes via looking at vertical distance between points) music 1, music 2.
• Tues Mar 22 Discuss homework readings on the stock market. Distance from home bar chart. Armspan bar chart. Height box plots. Review 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. Histogram of the ASULearn random number from 1 to 10. experiment and Excel analyses, including expected value of 5.2 from SUM(B2:B11)/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 whether the human mind can provide a random number. Discuss sampling versus census. Discuss mathematical proof versus statistical significance. GE experiment as a clicker question.
• Mon Mar 21 Stock Graph and ASULearn anonymous data collection.
• Thur Mar 17 Test 2
• Tues Mar 15 Review from the homework problems due on Tuesday, the lab, the ASULearn questions, and the study guide. If time remains discuss the lab on Monday.
• Mon Mar 14 Happy π-Day. Condo lab.
• Thur Mar 3 Student loan statement continued. Payday lender. Credit cards and finance charge. Kelly blue book. Begin Condo.
• Tues Mar 1 Collect debt info. 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. philosophy of loans Student loan statement.
• Mon Feb 28 Discuss Project 2.
• Thur Feb 24 Solutions to the \$37 problems. Go over the Jane and Joan extra credit by using goal seek to discuss what interest rate would result in equal savings for them both. Search google news for lottery winner lump. Lottery Picture of Excel work, Excel work file. Picture of Excel solutions, Excel solution file.
• Tues Feb 22 Intro to Goal Seek and Solver in Excel via Lisa's Thrifty Savers savings account from Bart the Fink. Review the Lump sum philisophy. 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 Andrew Wiles and Fermat's Last Theorem (philosophy slides). Transparencies from class. If time remains then begin the lottery questions .
• Mon Feb 21 Benjamin Franklin's Will - Part 1
• Thur Feb 17 Finish equations. Begin finance: Quotes on taxation. Local to global taxes. Search for history of taxation. 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. Each student comes up with their own formula. Lump sum philisophy. 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? Discuss other possibilities for unknowns - the time length, the rate, or the number of times compounding per year.
• Tues Feb 15 David Blackwell and Friend or Foe, my research and a reflection on equations.
• Mon Feb 14 Finish Andrew Wiles' work. If time remains before we come back together, search for information about David Blackwell.
Review themes from mathematicians:
Viewing objects that are impossible to see by managing small pieces at a time (Jeff Week's research).
Impossibility of checking all the cases, but finding a solution by shifting our viewpoint or finding a non-constructivist approach (Andrew Wiles' research). If time remains, then begin David Blackwell.
• Thur Feb 10 Share quotations about what mathematics is. Go over questions from lab on Monday. Andrew Wiles' work.
• Tues Feb 8 Test 1
• Mon Feb 7 Andrew Wiles and The Proof video and questions.
• Thur Feb 3 Finish project 1 questions. Discuss Jeff Weeks interview. Review using the Jeff Weeks worksheet. Portal. Futurama: I, Roommate. Discuss test 1 and the study guide. Discuss lab on Monday.
• Tues Feb 1 Collect and discuss the lab. Rob Kirschner's Supernovae results related to whether brightness=1/distance2. Discuss Gauss' experiment, WMAP data. Discuss the Heart of Mathematics readings. Continue going over project 1 questions.
• Mon Jan 31 Universe lab
• Thur Jan 27 Use tape to make an equator. Begin going over project 1 questions. In the last 15 minutes, motivate the lab on Monday via: The Shape of Space Video - this 11-minute animated video produced by The Geometry Center introduces the two-dimensional space of flatland, looks at possible shapes for flatland from the perspective of three dimensions, and represents those shapes of space in two dimensions. Then the animation uses the same kind of representation to look at possible shapes for three-dimensional space. Viewers are taken on a ride across the boundless three-dimensional surface of a three-torus and a four-dimensional Klein bottle. As viewers see these imaginary universes from inside the spaceship, they experience the illusion of seeing copies of the universes.
• Tues Jan 25 Go over the lab and the homework reading from Monday. Watch an excerpt from Flatland: The Movie. clicker questions
Highlight some books from my office that are useful for the project.
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
• Mon Jan 24 2D Universes Lab
• Thur Jan 20 Clicker questions. 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). What does our universe look like, how do we know, and how do we represent it? 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. 2-D creature movements of the caterpillar turning into a 3-D movement butterfly. Davide Cervone's Cube Projections.
• Tues Jan 18 Where is North? Register the i-clickers. Review Euclidean geometry including angle sum and the Pythagorean theorem.
Escher's space and Poincare's disk model of hyperbolic geometry.
Escher drawing
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.
Hyperbolic worksheet.
• Angle sum and Image of Angle sum
• Pythagorean theorem and Image of Pythagorean theorem
In the weeks to come, we will see that there are many real-life applications of hyperbolic geometry, such as models of the internet that hope to reduce the load on routers, building crystal structures to store more hydrogen or absorb more toxic metals, mapping the brain, mapping the universe, and modeling Mercury's orbit.
Discuss physical models of small pieces of hyperbolic space. Crochet model of hyperbolic geometry Reef Crochet reef. If time remains, discuss homework for Thursday and project 1.
• Thur Jan 13 Share something from the readings on perspective drawing or class on Tuesday. Class Activities on Perspective Drawing and Projective Geometry
• Tues Jan 11 Fill out index sheet. Share from the syllabus or Monday's lab. What does a space look like? How do we know? How do we represent it? Are The Simpsons 2D or 3D? http://www.youtube.com/watch?v=TKQ8Ilr6PgU M.C. Escher and the mathematical clues he left in his work: Sun and Moon.   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. Advice from last semester. Go over the webpages and ASULearn messages.
• Mon Jan 10 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 and prepare to share something to discuss: Life By the Numbers Shape of the World (maps of the earth) and Seeing is Believing (perspective). Write down something you found interesting, disagreed with, or that you wish had been shown. 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. 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.