Dr. Sarah's Math 1010 Class Highlights

### Review

• Mon Dec 9 Dr. Sarah, Review lab

• Tues Dec 10 Review continued.

### Geometry of the Earth and Universe

• Mon Dec 2 Shape of Our Universe lab, Shape of the Universe Worksheet. Stock Market update #3, WebCT quizzes.

• Tues Dec 3 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.)
Selections cut from PBS Life by the Numbers Seeing is Believing Video (20 minutes) 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 Dec 5 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 Nov 25 Collect geometry reports, go over problems 1 - 7. Briefly go over problems 8-11. Introduction to hyperbolic geometry Work on homework from main web page (review problems 0-7, WebCT quizzes, heart of math reading on WebCT)

• Tues Nov 26 2D Universes continued... Oral quiz on questions 0-7 to finish 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.
Worksheet on Escher. (solution to number 2)
Highlight differences between Euclidean, hyperbolic and spherical geometry.
Polygonal tiling models of the sphere, the plane and hyperbolic space.
Crochet model of hyperbolic space.

• Thanksgiving

### What is a Mathematician?

• Mon Nov 18 Review the Homer questions, IDS Viewpoint Readings, 2D Universes. If you are finished early, then work on homework for Tues or Thursday.

• Tues Nov 19 Rudin, Morgan and Daubechies presentations and worksheets.

• Thur Nov 21 Review What is a Mathematician? segment via the segment themes as they relate to the entire group of mathematicians.

• Mon Nov 11 Readings and Activities on Perspective Drawing and Projective Geometry,   Perspective Worksheet,   Homer 1. Complete the web readings for this week. If you are finished early, then work on WebCT quiz 6 retakes or projects (mathematician or geometry).

• Tues Nov 12 Presentations and Worksheets on Georg Cantor and Srinivasa Ramanujan

• Thur Nov 14 Presentations and Worksheets on Paul Erdos and David Blackwell
• Mon Nov 4 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 after Dr. Sarah models this by searching for herself. Finish "Dodge Ball" Begin the geometry of the earth and universe segment. Do a stock market update. If time remains then WebCT quiz 6. Otherwise take this outside of lab. Work on hw. Lab Directions

• Tues Nov 5 Presentations and Worksheets on Thomas Fuller and Maria Agnesi

• Thur Nov 7 Presentations and Worksheets on Sophie Germain and Carl Friedrich Gauss RSA Coding Continued
• Mon Oct 28 Go 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. Andrew Wiles lab

• Tues Oct 29 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. Andrew Wiles worksheet.

• Thur Oct 31 Discuss Carolyn Gordon and Can you Hear the Shape of a Drum? Carolyn Gordon Worksheet. Begin Dodge Ball via the first side. Class time to work on What is a Mathematician Segment.

### Statistics

• Mon Oct 21 Collect homework. Choose groups and presentation dates for What is a Mathematician? project (additional info will be given out by Thursday). Work on Statistics Detective Lab which is due at the end of lab. If time remains, take WebCT quiz retakes or review for Thur test.

• Tues Oct 22 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.

• Thur Oct 24 Test 2 on Statistics. Hand out Mathematician guidelines, references and the Carolyn Gordon Worksheet as a model.
• Mon Oct 14 Collect hw (HDYK and worksheet), 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 (height as a predictor of armspan, p. 209 number 11 prediction for 15 hours and 100 hours, and stocks), and Does Smoking Predict Breath Held? graph. Linear Regression Lab, Egg Bungee Jump Regression

• Tues Oct 15 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 question. 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 your 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.
• Mon Oct 7 Excel credit card checker, Mean, Median and Mode lab (stock update and graphs). Stock Update

• Tues Oct 8 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 28 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 does armspan predict height, and the worksheet on interpreting the results of regression.
• Mon Sep 30 Lab Directions (class data collection and pinecones)

• Tues Oct 1 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 and table of random digits.

• Thur Oct 3 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 and (if time remains) the Modular Arithmetic and Check Digits homework.

### Financial Mathematics

• Mon Sep 23 Stock Market and Homer Tax Lab

Tues Sep 24 Students work on p. 90-92 9 and 14 and p. 101 number 8, go over the answers, review parts of the condo lab, and common sense for matching WebCT quiz 2 problem 3. In remaining time, students review for Thursday's test, work on Homer lab, Ben writing assignment, class data collection sheet, and/or read the instructions for test 1.

Thur Sep 26 Test 1 on Finance
• Mon Sep 16 Condo Lab continued.

• Tue Sep 17 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? Setup 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. Finish Dr. Sarah's condo part 2. If finished before class ends, work on the finance review sheet.

• Thur Sep 19 Analyze Dr. Sarah's student loan statements, analyze past student Mark's student loan statement. How do you know 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. If waiting for to come back together as a class, then work on 24.
• Mon Sep 9 Lab 2 Directions (Ben Franklin lab and WebCT quiz 1).

• Tues Sep 10 Collect homework and go over. Hand out lump sum versus periodic payment sheet and problems. Begin working on the problems. Go over web pages - main, WebCT. Go over Ben F. 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

• Thur Sep 12 Begin condo lab.
• Tues, Sept 3 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. 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.

• Tues Aug 27 Intro to the course. Begin financial mathematics via How Do You Know? section 2.1. Fill out index sheet. Work on Wile E. Coyote. As time allows, read the handouts and begin lump sum.

• Thur Aug 29 Collect homework. 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 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?