Dr. Sarah's Math 1010 Class Highlights

### Review

• Mon May 6 Review Lab

• Tues May 7 We will complete course evaluations and I will give you study suggestions for the in-class part of the final as we continue reviewing for the final. If you must miss class, you must see me in office hours before the final exam.

### Geometry of the Earth and Universe

• Mon Apr 29 Briefly go over problems 8-11. If you are waiting for the video, do stock update number 3 and look at the main web page for assignments. The Shape of Our Universe, worksheet

• Tues Apr 20 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. (stop at Jeff Weeks segment since we watched this part in lab.)
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.

• Thur May 2 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. Exit survey.
• Mon Apr 22 Conclude the What is a Mathematician Segment via an IDS Viewpoint,     2D Universes, work on WebCT quiz 5, 6 and/or the geometry report.

• Tues Apr 23 Review Homer questions, collect geometry reports, go over questions 1-7.

• Thur Apr 25 2D Universes continued... Oral quiz on questions 0-7 to finish geometry of the earth. Intro to hyperbolic geometry via sketchpad -       Sketchpad Playfair's       Playfair's Image,       Sketchpad Sum of Angles       Sum of Angles Image       Sketchpad Euclid's 5th Postulate       Euclid's 5th Postulate Image       Sketchpad Pythagorean Theorem       Pythagorean Theorem Image and Escher. Highlight differences between Euclidean, hyperbolic and spherical geometry. Polygonal tiling models of the sphere, the plane and hyperbolic space. Crochet model of hyperbolic space. If time remains, Review gluing spaces - torus, klein bottle (learn to visualize this), and a 2-holed torus.

### What is a Mathematician?

• Mon Apr 15 Readings and Activities on Perspective Drawing and Projective Geometry,     perspective worksheet,     Homer 1. If you are finished early, then work on WebCT quiz 5 retakes, review of Mathematician ideas via web references, or homework or projects.

• Tues Apr 16 Paul Erdos and David Blackwell Presentations. Dr. Sarah reinforces the material.

• Thur Apr 18 Mary Ellen Rudin, Frank Morgan and Ingrid Daubechies Presentations. Dr. Sarah reinforces the material.
• Mon Apr 8 Work on a MathSciNet search for authors (only works from school) for modern mathematicians (Erdos up until recent times) and other searches for papers by your mathematician. Do a stock market update. Winning strategy for "Dodge Ball" Begin geometry of the earth and universe segment. If time remains then WebCT quiz 5. Otherwise take this outside of lab. Lab Directions

• Tues Apr 9 Gauss and Germain presentations. Discuss the fact that mathematics research is often completed for its own sake and not for its usefulness, but that it often ends up being useful and applicable, sometimes immediately, and at other times hundreds of years later (as in the case of research that formed the basis for modern computers, Sophie Germain primes that are used in RSA coding, Dr. Sarah's research, ...). Relate statistics to the 55 reasons article. Go over RSA coding via link from mathematician reference page. Go over Gauss' mathematics.

Thur Apr 11 Cantor and Ramanunjan presentations. Dr. Sarah reinforces the material.
• Thur Apr 4 Thomas Fuller and Maria Agnesi Mathematician Presentation and Classroom Worksheet. Dr. Sarah reviews the material after each presentation. If time remains then begin "Dodge Ball".
• Mon Mar 25 Go over logistics for the What is a Mathematician segment, and discuss Microsoft PowerPoint features for your presentations. Each person practices putting a picture into powerpoint. Andrew Wiles lab

• Tue Mar 26 Andrew Wiles worksheet Work on What is a mathematician segment.

• Thur Mar 28 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. Briefly talk about Carolyn Gordon and Can you Hear the Shape of a Drum? Carolyn Gordon worksheet

### Statistics

• Mon Mar 18 Choose mathematician in groups of 2 (additional directions will be given out on Thursday). Interactive linear regression plot via heart of math activity. Statistics Detective Lab due at the end of lab.

• Tues Mar 19 Review by calling on students to answer questions based on WebCT quizzes and review sheet.

• Thur Mar 21 Test 2 on Statistics
Spring Break March 11-15
• Mon Mar 4 Collect hw, go over linear regression on excel via How Do You Know p. 209 number 11, how to use the equation of the line to make predictions, and highlight situations where the prediction makes sense versus those that don't (armspan as a predictor of height, p. 209 number 11 prediction for 15 hours and 100 hours, and stocks), and Does Smoking Predict Breath Held? graph. Lab Directions, Linear Regression Lab, Egg Bungee Jump Regression

• Tues Mar 5 Discuss music choices from class survey and compatibility issues via Music graph 1 and Music graph 2. 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 via WebCT quiz 4 question 11. 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 Groups discuss the article and then discuss whether they have ever experienced something similar as part of some kind of group (for example, gender, race, math phobic, ...) that wasn't expected to do well on a test or in another situation.

• Tues Mar 7 Collect hw, discuss HIV testing issues, and discuss unintented consequences of medical and educational testing and policy decisions such as raising airline prices via heart of math reading and stereotype vulnerability. Discuss literary digest poll on Roosevelt/Landon election from 1937. Discuss linear regressions of Buchanan votes in Palm Beach.
• Mon Feb 25 Mean, Median and Mode, Modular Arithmetic and Check Digits, Excel credit card checker
• Tues Feb 26 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 (smokers, class year), and then talk about "bad" graphs.
• Thur Feb 28 Collect and then go over hw, boxplot of female versus male height, boxplot of female versus male untimed MRT, boxplot of distance from home, begin linear regression via does armspan predict height, and the worksheet on interpreting the results of regression.
• Mon Feb 18 Lab directions, Class data collection sheet, Quantitative literacy, pinecones

• Tues Feb 19 Collect real life rates. Go over credit card statement, payday lending offer, credit card offers, real-life rates. Discuss biases related to the census of class data. Begin sampling. Review pineapple material. students look at golden mean poster and pinecones.

• Thur Feb 21 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. Review 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 from How Do You Know.

### Financial Mathematics

• Mon Feb 11 Stock Market and Homer Tax

• Tues Feb 12 Students work on p. 90-92 9 and 14 and p. 1010 number 8, go over the answers, review parts of the condo lab, and common sense for matching WebCT quiz 2 questions to the number answers. In remaining time, students review for Thursday's test or work on the lab.

• Thur Feb 14 Test 1 on Finance
• Mon Feb 4 Dr. Sarah's condo continued - at least finish up to and including the car table. WebCT quiz 2 (take this outside of class if you didn't have a chance to take it in class). If you finish both of these work on homework.

• Tues Feb 5 Review condo today problem. Go over 2nd by-hand problem from the hw (and how much is the total interest) by calling on students using the index cards. Also do that to look at the second by hand homework problem as a loan payment problem - instead of saving up for the \$50000 car, assume that we found a car loan for 18.38 years at 8% compounded monthly. Then what will our monthly payment be? How much is the total interest? Compare this to the \$100 savings per month option and discuss. Finish Dr. Sarah's condo part 2 in class. If finished before class ends, work on the finance review sheet or other hw.

• Thur Feb 7 Analyze Dr. Sarah's student loan statements, analyze past student Mark's student loan statement. p.90-92 problems 19, 21, 22, 23, 24, and 25 - students worked in groups (counted off and then formed groups via the whole # remainder of their # divided by 6) and presented their solutions to the class.
• Mon Jan 28 Lab 2, Ben Franklin Part 1

• Tues Jan 29 Go over web pages - main, class highlights, syllabus, web based problems, WebCT (bulletin board, quizzes and retakes, and grades). Use index cards to call on people to answer questions on Ben F and Jane and Joan. Go over Jane and Joan extra credit (excel sheet) - using goal seek to discuss what interest rate would result in equal savings for them both.

• How long does it take to tripple a lump sum of \$1000 at 6% compounded yearly?
• How long does it take to tripple a lump sum of \$1000 at 6% compounded monthly?
• When can we get our \$22,000 car if we can't get a car loan but are forced to save up \$200 a month into a 6% compounded monthly?
• Dr. Sarah read about the 2001 Powerball lottery from usatoday.com. It said "For the jackpot worth 295 million, if there is one winner, then they will have a choice between 25 annual payments of 11.8 million each (25*11.8)=295 or a single lump sum payment of 170 million". How can we compare the logical benefits of each choice? Let's cut off the "million" to make it easier to work with (if you look at the formulas for lump sum and periodic payment, this is ok to do, since it is multiplication outside the parenthesis). Let's assume that if we took the lump sum then we would leave the 170 in an account at 5% compounded annually for the 25 years. Let's assume that if we took the annual payment then we would deposit each 11.8 annual payment into the same type of account. Which yields more money? Which would you choose? Why? What rate would yield the same amount of money?

• Thur Jan 31 Dr. Sarah's condo
• Mon Jan 21 MLKJ Holiday

• Tues, Jan 22 Review lump sum formula and the philosophy we used to come up with it. 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 (\$)? 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. \$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. If we have a baby, how much we we need to put in per month in order to have \$100,000 for college (18 years from now) assuming 6% compounding monthly. How much do we put in total? How much is interest(\$)?

• Thur, Jan 24 Review formulas via sheet, go over questions, How much do we need to invest now to have 100,000 in 63 years at 6.5% compounded monthly? What if we will deposit a certain amount per month? How much must we put in per month? The problem with this scheme is that we will be making payments for the next 63 years! Instead, let's say we can affort a monthly payment of \$20. How long will it take for the money to grow to 100,000? We set up the problem and then did Guess and check. Intro to Logs. Solve 5^time=25. Then solve: How long will it take to save 100,000 if we put in \$20/month at 6.5% interest, compounded monthly. We set up the problem and then reduced to number^power=number, and then solved for the exact answer using logs.
• Mon Jan 14 Intro to the course. Begin financial mathematics via How Do You Know? section 2.1. Fill out index sheet. Work on Lab 1, Wile E. Coyote, and complete the survey. As time allows, follow the directions at the end of lab 1 to read the Dr. Sarah's Office Hours and Syllabus and Grading Policies links.

• Tues Jan 15 Collect homework. Each group does a problem 2.1 5,6,7,9,10 to turn in and present to the rest of the class. Attitude Survey. Review course web pages. Web searches to find the history of interest rates and related issues.
+history   +"interest rates"         371,000 pages
+"history of interest rates"         693 pages
+"history of interest rates"   +loan   +credit
FT.Com - FT Guide to the New Millenium
+"history of interest rates"   +babylonian
Financing Civilization
Usury is Piracy

• Thur, Jan 17 Review and continue with the history of interest. 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?