Dr. Sarah's Math 1010 Class Highlights

### Dr. Sarah's Math 1010 Class Highlights Spring 2003 Page The following is NOT HOMEWORK unless you miss part or all of the class. See the Main Class Web Page for ALL homework and due dates.

• Mon Apr 28 Review Lab

• Thur Apr 24 Selections cut from PBS Life by the Numbers Seeing is Believing Video:
The first special effects ever created in Renaissance paintings also owe their existence to mathematics and spurred on the industrial revolution. 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. (20 minutes)
PBS Life by the Numbers Shape of the World Video:
Hundreds of years before Columbus set sail, the Greeks used mathematics to determine the size and shape of the planet. Viewers see how mathematics has become a tool to explore the earth and the heavens as the world and the cosmos is charted. (45 minutes - stop at Jeff Weeks segment since we watched this part in lab.)

• Mon Apr 14 Give back lab 9 (2D Universes) and give groups a chance to review incorrect answers. Briefly go over problems 8-11. Shape of Our Universe Lab,   worksheet.

• Tues Apr 15 Oral quiz on questions 0-7 on the geometry of the earth.
Intro to hyperbolic geometry continued via sketchpad -
Sketchpad Sum of Angles       Sum of Angles Image
Sketchpad Pythagorean Theorem       Pythagorean Theorem Image
(and relate to Introduction to hyperbolic geometry from lab.)
Sketchpad Euclid's 5th Postulate       Euclid's 5th Postulate Image.
Highlight differences between Euclidean, hyperbolic and spherical geometry.
Worksheet on Escher. (solution to number 2)
Polygonal tiling models of the sphere, the plane and hyperbolic space.
Crochet model of hyperbolic space.

• Thur Apr 17 Review the shape of the universe material. Euclidean, hyperbolic and spherical geometries, the 4th physical dimension and its applications, the hypercube and the hypersphere via excerpts from Davide Cervone's Selected Course Notes why the universe is not thought to be a hypercube, and some of the shapes that might be the shape of the universe (10 Euclidean possibilities, a number of the infinite but known spherical possibilities via excerpts from Week's paper on Topological Lensing in Spherical Spaces page 1, page 12, and current mathematical attempts to classify the hyperbolic possibilities, including the Weeks example , which is the smallest known hyperbolic space), and current attempts to determine the shape of the universe. Brief intro to my own research and how it fits into these ideas, and my mathematical style.
• Mon Apr 7 Finish going over Ingrid Daubechies, Review the Homer questions, IDS Viewpoint Readings, 2D Universes, web research for the geometry report.

• Tues Apr 8 Review What is a Mathematician? segment via the segment themes as they relate to the entire group of mathematicians.

• Thur Apr 10 Collect geometry reports and go over problems 1-7.
• Mon Mar 31 Finish up RSA coding from Thursday. Presentations and worksheets on Georg Cantor and Srinivasa Ramanujan. Intro to hyperbolic geometry worksheet. In the time that remains, read the web readings for tomorrow and then complete the worksheets and give suggestions for improvement.

• Tues Apr 1 Presentation and worksheets on Paul Erdos and David Blackwell

• Thur Apr 3 Presentations and worksheets on Mary Ellen Rudin, Frank Morgan, and Ingrid Daubechies
• Mon Mar 24 Lab Directions (Perspective Drawing, Problem 0 of the geometry of the earth and universe, stock market update, web readings, and Are The Simpsons 2-D or 3-D?)

• Tues Mar 25 Presentations and Worksheets on Thomas Fuller and Maria Agnesi.

• Thur Mar 27 Collect Tuesday's worksheets. Presentations and Worksheets on Carl Friedrich Gauss and Sophie Germain. RSA Coding Continued Decode the Message RSA on the internet via Bank of America's website.

• Mon Mar 17Go over the logistics for the What is a Mathematician? segment, and discuss Microsoft PowerPoint features for your presentations. Each person practices putting a picture into powerpoint. Intro to The Pythagorean Theorem and Fermat's Last Theorem.   Andrew Wiles

• Tues Mar 18 Discuss the fact that in "The Proof" video, we saw very few women, and only heard about one woman working on the problem, and we saw no African Americans. Statistics on women and underrepresented minorities in mathematics. Worksheet on Andrew Wiles If time remains, then begin Dodge Ball

• Thur Mar 20 Collect preliminary writeup of answers to math questions. Collect any remaining Wiles' worksheets and then discuss the concept of proof and possible answers to those questions. Work on Dodge Ball. Intro to the geometry of the earth and universe.
Spring Break
• Mon Mar 3 Statistics Detective Review Lab.

• Tues Mar 4 Intro to the mathematician segment via powerpoint on Dr. Sarah, classroom worksheet on Carolyn Gordon. Pick groups for the mathematician segment. (Students decide how to choose). Questions on statistics segment.

• Thur Mar 6 Test 2 on statistics.
• Mon Feb 24 **Lab 5* * on regression (Part 1 and Part 2). When you have completed the Excel portions, then work on the "Worth More" parts or homework for the end of the week.

• Tues Feb 25 Do linear regression by hand via p. 208 number 11 and compare to Excel work. Discuss actual predictor value, estimated predictor values from a graph or via a line fit by eye, and related issues. Discuss Volume/High WORTH MORE from lab. Talk about Does SAT score predict college GPA? Discuss the fact that more than a dozen studies of large student groups and specific institutions such as MIT, Rutgers and Princeton conclude that young women typically earn the same or higher grades as their male counterparts in math and other college courses despite having SAT-Math scores 30-50 points lower, on average. Discuss gender and multicultural issues on test taking, and discuss stereotype vulnerability via students reading selections from FairTest Examiner Stereotypes Lower Test Scores, and Claude Steele has Scores to Settle. In groups of 2 or 3: Discuss situations where text anxiety or performance anxiety have hindered you. Discuss whether you or someone you know have ever experienced something similar to stereotype vulnerability as part of some kind of group (for example, gender, race, math phobic, "good" or "bad" student...) where external expectations from someone else (teacher, society, parents, friends... ) affected your performance. Groups share their experiences with the class. Relate to MRT test. Discuss things we would like to see to back up the articles. Look at decreasing pipeline for women in the sciences graph and discuss what it missing.

• Thur Feb 27 Collect hw, discuss how tv guide misrepresented stats for their advertising purposes, review literary digest poll on Roosevelt/Landon election from 1937. Discuss linear regressions of Buchanon votes in Palm Beach and the butterfly ballot. Review boxplot problems from the WebCT quizzes. Discuss HIV testing issues and unintended consequences of medical and educational testing and policy descisions such as raising airline prices via heart of math reading and stereotype vulnerability.
• Mon Feb 17 Snow Day - University Cancelled Classes Excel credit card checker, Mean, Median and Mode lab (stock update and graphs). Stock Update

• Tues Feb 18 Continue to use the class data to discuss bar charts (distance from home and height), and how you can tell whether the mean will be above or below the mean, standard deviation (distance from home, height, untimed MRT), review the timed and untimed MRT and stats from lab, histograms (distance from home with a class size of 50 and then 100), pie charts (class year), "bad" graphs. Intro to Boxplots via a boxplot of height separated by gender, and the meaning of boxplots.

• Thur Feb 20 Collect and then go over hw, boxplot of distance from home and of height separated by gender that includes outliers (ie how the boxplot changes when the outlier is removed). Music choices and compatibility issues (measuring "difference" in music tastes via looking at vertical distance between points) Begin linear regression via p. 209 # 11, does armspan predict height, and the worksheet on interpreting the results of regression.
• Mon Feb 10 Collecting Data

• Tues Feb 11 Collect hw. Go over How Do You Know homework problems, common sense for matching WebCT quiz 2 problem 6. Highlight the review sheet and the answers on the main web page. Go over credit card statement, payday lending offer, credit card offers, real-life rates and ways to build good credit.

• Thur Feb 13 Test 1 on Finance
• Mon Feb 3 Lab 3: Dr. Sarah's Condo Finish up to the designated point and then work on hw for Tues or WebCT quiz 2.

Tues Feb 4 Collect homework. Go over 1) If I can afford to save \$100 per month for a \$50,000 car, in an account compounding monthly at 8%, then how long will it take for me to save up? Set up the formula for the problem but do not solve. If I told you that the answer was approximately 18.38 years would that make sense? Show work to explain why. 2)What will my monthly payment be if I take out a car loan at 8% compounded monthly for \$50,000 for 18.38 years? 3) Use the Sept 2000 interest rate of 8.25% compounded monthly for the 105265 condo with a loan of 80%. What is the monthly payment? What is the 1st months interest? What is the total interest over the life of the loan? Compare to chart on condo lab. Review clarity and depth of lab answers by highlighting some student answers to the Ben lab (which are also on a WebCT posting). Finish Dr. Sarah's condo part 2. If finished before class ends, work on the finance review sheet.

Thur Feb 6 Look at summary of readings, review survey method guaranteeing complete anonymity from Heart of Math, use this method on an embarrasing but interesting survey question, and then we analyze the survey results. Perform the same survey method on a non-embarrasing question. Discuss the difference between a census and a survey. Then use the table of random digits to pick people from the class. Students work on the circle sampling problem. If time remains, then students work on homework.
• Mon Jan 27 Collect homework. Lab 2:   Stock Market Lab and Ben Franklin's Will - Part 1.

• Tues Jan 28 Go over \$37 problems. Go over Jane and Joan extra credit (excel sheet) by using goal seek to discuss what interest rate would result in equal savings for them both. Do problems by hand and/or on Excel. Picture of Excel work, Excel work file, Picture of Excel solutions, Excel solution file. Go over main class web page and Ben Franklin and Stock Market lab. Highlight the Dec 2002 \$315 Powerball winner in Hurricane, West Virginia who had a choice of 30 annual payments or one lump sum payment of \$170.5 million.

• Thur Jan 30 Loan payment formula. Student loan statements. Begin condo lab. If time remains, then examine credit card statement.
• Tues, Jan 21 Collect homework. Students begin working on: If \$100 is deposited into an account and left alone for 25 years, compounded monthly at 5%, how much will we end up with? How much will be interest (\$)? Review lump sum formula and the philosophy we used to come up with it. Discuss homework reading. Compare to \$100 deposited every month into an account and left alone for 25 years, compounded monthly at 5%. Work towards the periodic payment formula and compare the philosophy to the lump sum formula derivation philosophy. Transparencies from class \$100 is deposited each month for 12 years into an account compounding 5% monthly. How much do we end up with? We'll do an exercise to show that the number of digits we use does matter! 100 is deposited each month for 12 years into an account compounding 5% monthly. What do we have at the end? The interest rate is .05/12=.004166666... Each group of 3 used a different number of digits and rounding versus truncation methods (ie .004,.0041, .0042,.00416, .00417,.004166, .004167, .0041666, .0041667 ). The group helped each other with their calculators and made sure that they all came up with the same answer. We compared the final answers to show that we should never round until the final answer.

• Thur Jan 23 The University cancelled classes. Collect homework and go over. Hand out 3 handouts. Begin working on the problems on the back of the lump sum versus periodic payment handout. Go over Jane and Joan extra credit (excel sheet) by using goal seek to discuss what interest rate would result in equal savings for them both. Do problems by hand and/or on Excel. Picture of Excel work, Excel work file, Picture of Excel solutions, Excel solution file. In the time that remains, discuss lab on Monday and model stock market and Ben f work in Excel.

• Mon Jan 13 Intro to the course. Begin financial mathematics via How Do You Know? section 2.1. Web searches for history of interest:
+history   +"interest rates"         521,000 pages
+"history of interest rates"   -200*         649 pages
+"origins of banking"   +interest         308 pages
Origins of Banking
+"history of interest rates"   +babylonian         7 pages
Financing Civilization
+"cuneiform"   +babylonian   +interest         3160 pages
CUNEIFORM TABLET
+usury   +interest   +Babylonian   +money         1060 pages
Usury is Piracy
Fill out index sheet. Work on Wile E. Coyote. Come back together to discuss Wile E. Work on Homer tax homework. Read through the main class web page and Presenting Homework and Writing Assignments. Begin working on homework.

• Tues Jan 14 Collect homework. Review course web pages via volunteers from class. Have student enter WebCT, post a test message, read message, and look at quizzes. Show clip of Homer getting into trouble with the IRS. Turn back Homer homework. Homer's Taxes. If time remains then begin working on homework by reading the syllabus carefully, and then reading through Dr. Sarah's Sheet on the Main Web Page and WebCT Use, and the survey assignment.

• Thur Jan 16 Collect homework. Review big picture of Homer tax. Begin lump sum formula via compounding annually. Then compounding quarterly, and then the general lum sum formula. Compounding monthly. 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 if
-the bank will compound 8% each and every month (ie 96% per year!)
-the bank means that 8% is the annual rate.
Which did the bank really mean?
Use remaining time to review Presenting Homework and Writing Assignments and then work on homework.