Dr. Sarah's Math 1010 Class Highlights

Dr. Sarah's Math 1010 Overnight Assignments and Class Highlights Spring 2001 Page
See Main Class Web Page or WebCT calendar for longterm project due dates. See WebCT calendar for quiz retake due dates.

Geometry of our Earth and Universe

  • Mon, April 30
    Finish up Geometry of the Earth and Universe via Dr. Sarah's Geometry of the Universe.
    Look at Syllabus and Summarize the Course
    Course Evaluations
    Hand out Final Exam Review Sheet
    Stock Market Update
    New Scientist Planet Science: Ghosts in the sky Homework Think about what kind of mathematcial style that we've seen/used works best for you.
  • Tues, May 1 Review for Final Exam - Last Day of Class!
  • Mon, April 23WebCT quiz 8, Web readings on 2d, 3d and 4d, and 3-d into 4-d Homer.
  • Tues, April 24 Seeing is Believing video from the Life by the numbers series.
  • Thur, April 26 Shape of the World video from the Life by the numbers series. Talk about how to construct a cylinder from a strip in the plane by identifying the edges, and how we could explain this to 2d Marge.
  • Thur, April 19Finish Geometry of our Earth and Universe presentations.
  • Mon, April 9 WebCt quiz on first 3 days of the presentations, 2-d into 3-d homer.
  • Tues, April 10 Presentations on Daubechies and Morgan. Review Gender and Multicultural Issues and the diverse styles of all the mathematicians that we saw.
  • Thur, April 12 Collect Geometry of our Earth and Universe reports and references. Begin presentations.

    What is a Mathematician?

  • Mon, April 2 Icosahedron sheet, WebCT quiz, begin Geometry of our Earth and Universe.homework Work on classroom worksheet from presentations, What is a Mathematician? Geometry of our Earth and Universe, and WebCT quiz retakes.
  • Tue, April 3 Presentations on Gauss, Ramanujan and Erdos. Homework See WebCT calendar
  • Thur, April 5 Presentations on Blackwell, Rudin and Gordon. Homework See WebCT calendar and study for WebCT quiz on the first 3 days of presentations on mathematicians (Muhammed up to Gordon).
  • Mon Mar 26 Dr. Sarah goes over PowerPoint, and then student groups work on What is a Mathematician?
  • Tues Mar 27 Begin Dr. Sarah's mathematics and mathematical style (and contrast with Andrew Wiles) Discuss diameter of spaces, the diameters of a sphere, a football made from a sphere, and a three-cornered pillow shaped object made from a sphere by using an icosahedron.
  • Thur March 29 Presentations on Muhammad ibn Muhammad al-Fullani al-Kishnawi (-1741) Magic Squares, Maria Agnesi (1718-1799) Witch of Agnesi, and Sophie Germain (1776-1831) Modular Arithmetic, Sophie Germain Primes and Coding Theory. Dr. Sarah goes over ideas and mathematics involved after each presentation. Homework Do classroom worksheets from presentations, work on What is a Mathematician?, test revisions, and study for WebCT quiz on Dr. Sarah's and Wiles' mathematics.
  • Mon March 19 Hand out remainder of Mathematician Folders, Statistics Test Homework for Tues grades assignment.
  • Tues Mar 20
    The first few minutes of The Royale - Star Trek Next Generation's 1989 episode from Stardate 42625.4
    Picard
    Fermat's Last Theorem. Familiar With it?
    Riker
    Vaguely. I spent too many math classes daydreaming about being on a starship.
    Picard
    When Fermat died, they found this equation scrawled in the margin of his notes-
    X to the Nth plus Y to the Nth equals Z to the Nth where N is greater than two, which he said had no solution in whole numbeers but he also added the phrase "REMARKABLE PROOF."
    Riker
    But no proof was included.
    Picard
    And for 800 years people have tried to solve it.
    Riker
    Including you.
    Picard
    I find it stimulating. It puts thing in perspective. In our arrogance, we feel we are so advanced yet we still can't unravel a simple knot tied by a pert-time French mathmatician working alone without a computer.
    Discuss Pythagorean Thm, why a computer can't check all the cases, and the mathematical style of Pierre de Fermat. begin The Proof - A Nova video about Princeton University Professor Andrew Wiles and his solution of Fermat's Last Theorem.
  • Thur Mar 22 Finish The Proof Video Discuss Then we discuss the mathematical style of Andrew Wiles Fermat's Last Theorem, how a mathematical proof will demonstrate that there are no solutions without checking all the cases, Taniyama-Shimura conjecture and the Epsilon conjecture. By looking at the example If I get a speeding ticket, then I was driving too fast, we demonstrate how If A then B is logically equivalent to If not B then not A, but that these are different statements then If B then A. Then, We apply this to the Epsilon conjecture to see that the conjecture is logically equivalent to If Taniyama-Shimura is true then Fermat is true. Dr. Sarah's Worksheet on Andrew Wiles

    Statistics

    Over spring break - study for test 2 on statistics, do WebCT quiz 5 retakes (due Mon at 2pm), and start working on What is a Mathematician?
  • Mon, Mar 5 Go over linear regression on excel via p. 209 number 11, and how to use the equation of the line to make predictions, and highlight situations where the prediction makes sense versus those that don't (stocks, p. 209 number 11 prediction for 15 hours, 30 hours and 100 hours). Measure some students armspan and height, discuss why it makes sense that there should be a correlation between them and then linear regression. Students give data to Dr. Sarah for input into Excel. Egg bungee jump lab, then WebCT quiz. Homework for Tues Need Internet Explorer for Problem 3.5, Problem 4.1, Problem 4.2, Problem 4.3, Problem 4.4, also do p. 209 number 12 parts b) and c) using the line and p. 186 #15 (given Thur).
  • Tues, Mar 6 Go over p. 185 #16, and p. 209 number 12 b) and c). Do linear regression by hand via p. 208 number 11 and compare to Excel work. Have students do p. 209 number 12 part a) by hand. Go over this and discuss actual predictor value, estimated predictor values from a graph or via a line fit by eye, and related issues such as the fact that if someone had 10 absences in our class then they wouldn't even be taking the midterm! Hand out Does Armspan predict Height? regression graph from Excel based on data taken in lab yesterday. Go over WebCT quiz 5 problem on SAT score boxplot, 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 HomeworkWebCT quiz 4 retake due Tues night. Work on stock lab (you may pick up your draft after 1pm on Wed on my door). For Thur, bring stock draft to class, bring WebCT quiz 5 handout to class. WebCT quiz 5 retake due before class on Mon after spring break, and test on stats is during that lab.
  • Thur Mar 8 Go over stock lab, go over WebCT quiz 5, Hand out What is a Mathematician projects, review for Statistics Test.Homework See Tues HW, read this website on linear regressions of Buchanan votes in Palm Beach, read Hispanics Draw Even With Blacks In New Census (washingtonpost.com)
  • Mon, Feb 26 Stock Statistics lab
  • Tues, Feb 27 Students called on to go over HW from Tues, Feb 20, discuss examples of data for p. 185 number 6. For class data, do a pie chart and then a boxplot. Compare to histogram for the class data. Review NITE graphs Homework for ThurSee WebCT calendar for other HW, Need to use Internet Explorer for web based problems, Problem 3.2 , Problem 3.3, Problem 3.4, p. 186 number 14.
  • Thur 3/1 Students put homework on the board. Discuss standard deviation for the class data, discuss standard deviation of Web Based Problem 3.1 from last HW, continue analyzing what kind of info one can read from different statistical representations, begin linear regression. Homework for Mon Work on stock lab which is due on Monday, Study for WebCT quiz - notes on stock graphs and statistics, histogram, pie chart, boxplots, mean, median, standard deviation, linear regressions.Homework for Tues p. 186 #15
  • Mon, Feb 19 WebCT quiz 4, stock intro, web polls. Homework See WebCT calendar (Feb and March)
  • Tues, Feb 20 Survey: How far away (in miles) is each student's hometown? Discussed biases in the data. Order the data. Find the mean and median. Do one histogram at a bin width of 100. Discuss the difference between the book and the computer on histograms. Each group does a different bin width. Discuss measures of center and related ideas. Homework for Thur See WebCT Calendar, p. 151 You try it 2.1, p. 160 You try it 2.5, (answers are in the back of the book), p. 168 number 12, p. 185 number 6, Use Internet Explorer for this Web based problem (bras should be bias!) Problem 1.1, Problem 3.1 (see my WebCT posting on the errors in here!).
  • Thur, Feb 22Go over HW, Dr. Sarah models stock lab process for NITE, and discusses related issues.

    Financial Math

  • Mon, Feb 12 Homer Tax lab, finish up Dr. Sarah's condo lab from 2 weeks ago.
  • Tues, Feb 13 Review major ideas from Homer Tax lab, including 28% bracket. Review major ideas from end of the condo lab. Discuss Real life rates. Analyze credit card statement. Analyze Payday Lender info. Analyze credit card offers. Homework for Thur Where did 449.67 balance subject to finance charge come from (extra credit if you find the correct calculation before we go over it on Thursday)? Review Payday Lender and Credit Card calculations.
  • Thur, Feb 15Finish up credit card calculation, discuss benefits and negatives of credit cards versus debit card, wrap up financial math and give overview of that style of doing mathematics. Transition into statistics by looking at MSFT stock price on the web and modeling what the students will do at the begining of lab on Monday (Each student will choose a different stock to track). Begin statistics via samples, polls and census, explain how the Random Digit Table is used in sampling.Homework for next week Study for WebCT quiz, look up stocks that you might be interested in via stock intro, work on test 1 revs,...
  • Mon, Feb 5 WebCT quiz 3, car lab
  • Tues, Feb 6 review
  • Thur, Feb 8 Test 1 on Finance
  • Mon, Jan 29 WebCT quiz 2, Dr. Sarah's condo
  • Tues, Jan 30 Go over homework, web pages, Jane and Joan extra credit (excel sheet) - using goal seek to discuss what interest rate would result in equal savings for them both. condo lab (excel sheet) - go over amortization table, and discuss when the loan would be paid off if we pay an extra $20 each month, and how much interest we would pay. Discuss payment formula for Look at Dr. Sarah's Condo (costs $105,265, putting 20% down, at 6.75% compounded monthly) with the payment formula and compare to Excel. With a loan of 84,212, what is the monthly payment and total interest? What if buy down the rate to 6.25%, which is the monthly payment and total interest? Hand out test 1 review sheet, and car lab hw. Homework for Thursday (3 web based problems, and 3 by-hand problems)
  • Web based problems need to use Internet Explorer , Problem 2.3 #1, Problem 2.3 #2, Problem 2.3 #3.
    Set up formula and solve on your calculator:
  • what is the monthly payment for Dr. Sarah's condo if we keep the rate at 6.75%, but instead take out a smaller loan of 82,212? How much would she pay total? What is the 30 year interest?
  • What would have happened if I had waited until today to buy the condo? Assume that the price of the condo had remained the same (which it wouldn't have!). What is the monthly payment if we use today's mortage rate of approximately 7.5%. How much would I pay in total? How much of that would be interest? (I obtained this rate at Bank of America Page by choosing Conventinal Fixed and looking at the 30 year rate.)
  • If I can afford to save $100 per month for a $50000 car, in an account compounding monthly at 8%, then how long will it take for me to save up?
  • Either go to a bank sometime in the next week or search on the web to find real rates on savings, checking & money market accounts, cds, & student, house and car loans. Write up or print out your findings.
  • Thur Feb 1 Go over homework, look at the third 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? Compare this to the $100 savings per month above and discuss. Analyze Dr. Sarah's student loan statements, analyze past student Mark's student loan statement. Homework See WebCT calendar. For WebCT quiz 3, study webct quiz 2 and know loan payment formula setup and common sense.
  • Mon, Jan 22 Work on Ben F. lab due next Wed.
  • Tues, Jan 23 Continue log problems. 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 car if we put in $200 a month into a 6% compounded monthly account if we need $22,000? Students work on problems, and then we go over them as a class. Homework for ThurSee HW from Tues the 16th (below), and also Internet Explorer Problem 2.2 #12 (be prepared to present hw problems), work on Jane and Joan due Fri, work on Ben F.
  • Thur, Jan 25 Students called on randomly to present hw, Math Whiz Contest. Homework for Mon See Tues hw, study for WebCT quiz (know how to match formula to problem, and common sense), and for Tues p. 91 #17 and 20 and redo all the web based problems as a review.
  • Tues, Jan 16 Review formulas, go over homework, hand out Ben Franklin Lab, Jane and Joan sheet. How much do we need to invest now for Dr. Sarah to give her niece 100,000 at her niece's retirement? Assume that she has found an account that will pay 6.5% interest, compounded monthly. We used algebra. How about if Dr. Sarah will deposit a certain amount per month? How much must she put in? The problem with this scheme is that Dr. Sarah will be making payment for the next 60ish years! Instead, let's say she 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 Dr. Sarah to save 100,000 for her niece if she puts 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. Homework for this and next week Wile E. Final Version due by Friday by 5pm on to my door 326 along with draft. You may turn it in early. For Mon, read text of Ben Franklin lab and do quiz 1 retakes. Also, p. 90, 8 and 10 -13, You Try It 2.8, 2.9 and 2.10 (solutions are on page 306), Internet Explorer web based problems Problem 2.2 #7 Problem 2.2 #8 Problem 2.2 #9, Problem 2.2 #10, Problem 2.2 #11. Work on Joan and Jane sheet.
  • Mon January 8 - Section 2.1, and Web based problems on % need to use Internet Explorer , problem 1.1 (Click on the word PROBLEM and use the down arrow key to view the 2nd line), problem 1.2, and problem 1.3 (.91 is the correct answer - notice that the problem incorrectly identifies .2, .3, .4, ... as correct answers also). Intro to course via the syllabus and policies. Follow Lab 1 Directions HOMEWORK for Tues p. 69-71 # 1, 17, 20, review syllabus and class notes. Bring the textbook and a scientific calculator (with y^x, x^y, or ^) to classes.
  • Tues Jan 9 Go over homework problems, via randomly picking on students to present them. Fill out index sheets. Begin lump sum formula via $20 in an interest bearing acount for 5 years, compounding annually at 2%. How about compounding monthly? If you win a lottery, is it better to take 10,000 now, or wait 12 years and get 30,000 then (assume that if we take the 10,000 now, then we won't spend any of the money and instead will compound monthly at an interest rate of r%). Each group of 2 does this for a different r ranging from 6% to 11.5%. HW for Thur Web based problems on % need to use Internet Explorer problem 1.4, and problem 1.5 and Web based problems on savings accounts, problem 2.2 #1 and problem 2.2 #2, read pages 72-76, do page 90 numbers 1 and 2.
  • Thur 1/11 Review lump sum formula. Students present hw. Real Life Bank formula. 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.
    The bank means 8% is the annual rate! Discuss periodic payment formula. If 100 is deposited into an account and left alone for 25 years, compounded monthly at 5%, how much do we have? Compare to 100 deposited every month into an account and left alone for 25 years, compounded monthly at 5%. Discuss solutions and calc keys. We'll do an exercise to show that the number of digits we use does matter! 100 is deposited each month for 25 years into an account compounding 5% monthly. What do we have at the end? The interest rate is .05/12=.004166666... Each group used a different number of digits (ie 0, .004,.0041,.00416,...) and we compared the final answers to show that we should never round. HW for Tues Problem 2.2 #3, Problem 2.2 #4 Problem 2.2 #5 Problem 2.2 #6 (the answer to the last question is wrong - 9% we would choose 1500 a month and 8% 30,000 later, Put in $37 each month for 2 years, at 12.99% compounded monthly. Compare this with putting in $37 and leaving it there for 2 years, at 12.99% compounded monthly. Read pages 77-79.