Math 101 Assignments

Spring 2001

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All assignments should be completed before the next class meeting, unless otherwise indicated.

Day In Class Read Problems Computer Projects and Other Assignments

Jan. 11 Course Introduction and Overview;
Preference Voting

Chapter 1 None Explore the web page for your textbook.
Take a look at my Spiral Page and my Mandelbrot Set Page for a preview of some of the things we will be doing later in the course.
Use the ballots from our Fantasy Trip election (available on the web by 6:00 PM tonight) to construct a preference table; bring your table with you to class on Friday.

Jan. 12 Voting and Counting Appendix 1 and Appendix 2 to Chapter 1; Pp. 27-30: 1, 3-13, 25-27 Using your Preference Schedule from the class Fantasy Trip election, determine the winner using the Plurality Method, the Borda Count Method, the Plurality-With-Elimination Method, and the Method of Pairwise Comparisons. Bring your list of winners to class on Wednesday.

Jan. 17 Discuss Chapter 1 and Fantasy Trip election Chapter 1 (again) Pp. 31-32: 41-44, 51 Send me e-mail with your name and your e-mail address; tell me the last Math course you took and when you took it; put Math 101 in the subject line.

Jan. 19 Introduction to Weighted Voting Systems Pp. 41-53 Pp. 61-64: 1, 3, 5, 13, 17, 27 Go to the Math 101 Distribution List Page, where there is a list of e-mail addresses for all the students in this class, and for me. Copy and paste this list to make a class distribution list which you can use all semester to communicate with the rest of us. I have included instructions on how to do this using Gemini, but if you use some other system for e-mail you are on your own!
Now use your distribution list to send all of us a message introducing yourself. Put Introducing Myself in the Subject Line.
Get the list of coalitions and fill in the blanks.

Jan. 22 Weighted Voting Systems and Power Indices Pp. 53-60 Pp. 61-65: 7, 9, 11, 15, 17, 19, 21-25, 33, 35 There is a nice summary of Chapter 2 on the web at a page called Weighted Voting Systems. Check it out and write a short "review" of the site. Then use your class distribution list to send your "review" to your classmates and to me, with subject Review.

Jan. 24 Power Indices Chapters 1 and 2 (again) Any problems you couldn't work before. Take Quiz 1 via e-mail. This quiz is worth 10 points, and you may use your book and your notes, and you may ask me for help. However, you are on your honor not to assist anyone else or seek assistance from anyone other than me. You must submit your answers by NOON (class time) on Friday, Jan. 26. Put Quiz 1 in the Subject line.
We will have a Quiz on Chapters 1 and 2 in class on Monday, Jan. 29. It will NOT be open book or open notes.
Add the following to your Distribution List:
elm0736@tntech.edu
markwallace82@yahoo.com
ykd5392@tntech.edu

Jan. 26 Review of Chapters 1 and 2
Introduction to Fair Division
Pp. 73-78 Pp. 96-100: 1-3 Study for Monday's quiz.
"Surf" the Web for an interesting math-related web page. Here are some places you might start:
The TTU Math Department's Home Page
The Math Forum at Swarthmore College
UT's Mathematics Archives
Or try one of the search engines such as
Alta Vista (look under Science, then under Math), or
Yahoo (look under Science, then under Mathematics).
Now use your class distribution list to send the rest of us the URL for your site; tell us what it is about and why you like it. Put Math Site in the subject line.

Jan. 29 QUIZ 2 on Chapters 1 and 2
Fair Division
Pp. 78-81 Pp. 97-100: 4-13 Insert "1/3" between the words "least" and "of" on the last line of P. 81.
Visit the Web sites whose URL's were sent to you by your classmates (Click here for a list of the sites). Then use your Class Distribution List to tell us which one is your favorite, and why (subject: Favorite Site).

Jan. 31 Lone Divider Method Pp. 75-81 (again)
Pp. 81-84
Pp. 100-102: 14-19, 21 Take Quiz 3 via e-mail (Subject: Quiz 3). As for Quiz 1, you may use your book and your notes, and you may ask me for help. But you are on your honor not to assist anyone else or seek assistance from anyone other than me. You may take the quiz as many times as you like, and I will count only your last score. Thus, your best strategy is to take it early and try to improve your score by correcting your mistakes.
The quiz is due by NOON (class time) on Friday, Feb. 2.. Any quiz which I receive before 5:00 PM on Wednesday or Thursday will be graded and returned to you that evening. You may then re-take it if you are not satisfied with your score.

Feb.2 Lone Chooser Method Pp. 81-84 (again) pp. 100-106: 20, 40, 41 Go to Your Math Web Page to read the instructions for your web page. Begin to think about what you would like to use as a "theme" for your page. You might want to look ahead at Chapters 4-12 of your book for ideas about topics we will cover later in the semester.
This is a long-term project, due the last week of class, but you should begin to think about what you want to do. We will have some related projects to help you learn how to set up a basic web page, add graphics to it, make links, etc... these will be coming up in the next few weeks.
Add jlm0851@tntech.edu to your Distribution List
Delete pedaltone1@yahoo.com from your Distribution List.

Feb. 5 Last Diminisher Method Pp. 84-88 Pp. 102-107: 22-24, 43 Print out and read A Beginner's Guide to HTML. This is your first step in learning how to create your own web page.

Feb. 7 Sealed Bids Pp. 89-92 Pp. 103-107: 25-31, 42 Go to the TTU Home Page and choose"Web Publishing Info" (located under "About This Web Server" near thebottom of the page). Then choose "Student Personal Pages" to find out how to set up your own home web page on Gemini. Or, if you would prefer to use a private Internet Service Provider (ISP), find out how to set up a web page through it. Begin to build your home page by writing an html document which includes your name, your major, a list of some of your hobbies, and a link to the Math 101 Home Page. You may use the preformatted template provided by the Computer Center if you want. If you need help, see me or ask at the Computer Center Help Desk. Once you have your web page ready for viewing, use your Class Distribution List to send its URL to the rest of us. This project should be completed by Monday, Feb. 19.

Feb. 9 Markers Pp. 92-95 Pp. 104-110: 32-39, 52, 53 Keep working on your Web Page. Don't leave this until the last minute - it's not hard, but it may take you longer than you anticipate, and you may need to get some help from either me or the helpers in the Computer Center.

Feb. 12 Questions on Chapter 3 Chapters 1-3 (again) Rework a variety of problems from Chapters 1-3 Review for TEST on Chapters 1-3, which will be given in class on Friday, Feb. 16.
Keep working on your web page. You may put anything you like (within the bounds of decency and good taste) on it, and you may make links from it to other pages. Later on you will create another page which will be related to some mathematical topic. If you want to make a second page now, you may: Follow the same procedure, but name the file something other than index.html (that name is reserved for your home page).

Feb. 14 Review of Chapters 1-3 Study for test Study for test Study for test
Finish your home page

Feb. 16 Test on Chapters 1-3 Chapter 4, including the appendices No new problems to work. Take the Quiz on Chapter 4 via e-mail. The rules are the same as for Quiz 3, except that for this one you get only one try. Send me your answers, with subject Quiz 4, by Noon Monday, Feb. 19.

Feb. 19 Introduction to Graph Theory Pp. 149-158 Pp. 173-179: 1-13, 38 Think about how you might "jazz up" your web page; here is a page with some links to sites with graphics that you can download to use on your pages.

Feb. 21 Euler Circuits and Paths Pp. 158-167 Pp. 175-179: 14-22, 27-32 Take the Introductory Graph Theory Tutorial written by Chris Caldwell of UT-Martin. Then send me an e-mail message witih the answers to the 3 questions on the last quiz in the tutorial (subject tutorial).

Feb. 23 More on Euler Circuits and Paths Pp. 167-172 Pp. 176-181: 23-26, 39, 41-43, 46, 47 Read a biography of Leonhard Euler at the St Andrews University History of Math site. Then send me an e-mail message (subject: Euler) listing the titles of five of Euler's publications, including at least one on the theory of music.

Feb. 26 Review Chapter 5 Chapter 5 (again) Rework any problems you didn't understand the first time. Study for QUIZ on Chapter 5, which will be given in class on Wednesday, Feb. 28.
Take another of Chris Caldwell's tutorials, this one on Euler and Hamilton Circuits. The part on Euler circuits will be a review, and the part on Hamilton circuits will be a preview of the material we will study in Chapter 6.

Feb. 28 Quiz on Chapter 5
Hamilton Circuits and Paths
Pp. 185-191 Pp. 210-217: 1-10, 15, 16, 39, 42 Take another tutorial by Chris Caldwell, this one about Coloring Graphs. Then send me e-mail (subject: colors) with the answers to the following questions (the answers can be found in the tutorial):
1.What if we color our graph (map) on a sphere instead of a plane, then how many colors do we need?
2.What about on a mobius strip?
3.What about on a torus (doughnut)?
4.Suppose our map is on a sphere and we allow each country to have one colony (which must be colored the same color); then how many colors do we need?

Mar. 2 Traveling Salesman Problems Pp. 192-199 Pp. 212-218: 11-14, 17a, 17b, 19,47 Read "The Traveling Monkey". Then send me an e-mail message (subject: monkey) answering the following questions:

Who is the author of "The Traveling Monkey"?
This article reports on a paper published in the scientific journal Nature. What issue of that journal is cited?

Mar. 5 TSP Algorithms Pp. 199-209 Pp. 213-218: 17c, 17d, 18-37, 49, 50 Read about the History of the Traveling Salesman Problem . Note: a circuit is called a cycle on this page. Send me e-mail with answers to the following questions:

What company ran a contest in 1962 which involved solving a TSP for 33 cities?
In what year did four researchers solve the TSP problem for the 13,509 cities in the USA with population greater than 500?

Mar. 7 Trees and Spanning Trees
Kruskal's Algorithm
Pp. 225-232 Pp. 245-251: 1-16, 31 Go to a Kruskal's Algorithm page and practice building minimum spanning trees: first click on "New Problem" and then click on "Step Solve" to watch the computer build the tree one step at a time. Do this several times and try to predict which edge the computer will choose at each step. Send me an e-mail message (Subject: Kruskal) with the answer to the following two questions:
On this page the minimum spanning tree is called something else. What name is used here for the minimum spanning tree?
How does Kruskal's Algorithm compare with the Cheapest Link Algorithm for Hamilton Circuits?
Print out and work the problems on the 30-60-90 Triangle worksheet. Bring it with you to class on Friday.

Mar. 9 Steiner Points Pp. 232-245 Pp. 249-251: 17-25, 40-45 Go to a Steiner Point Web page. Be patient - it may take a little while to load. Eventually, you will see a red triangle ABC. On each side of the red triangle, an equilateral triangle has been built, and the third vertex of the new triangle has been connected to the third vertex of ABC by a line. Thus, the third vertex of the equilateral triangle built on side AB is connected to vertex C, etc. The Steiner point S is the intersection of those three lines. Use your mouse to move point A (or point B or point C) and watch how the Steiner point moves. Also, watch how the angles change (their measures are given in the upper left corner). Send me an e-mail message (subject: Steiner) with the answers to the following questions:

Fill in the blank: Either all three angles at S (ASB, ASC, and BSC) are 120 degrees, or else only one of them is 120 degrees and the other two are _____ degrees.
When only one of the three angles at S is 120 degrees, where is the point S in relation to triangle ABC? Is it still a Steiner point for triangle ABC?

Mar. 19 More on Trees and Steiner Points
Similar Triangles
Chapter 7 (again) Pp. 251-252, 32-36 Review Chapter 7
Print out and work the problems on the Worksheet on Similar Triangles; bring it and your answers to class on Wednesday.

Mar. 21 Questions on Chapter 7 Chapters 5-6 (again) Rework a variety of problems from Chapters 5, 6 and 7 No new project, but don't forget that you should be working on your Math Web Page.
Review for Test on Chapters 5-7 to be given in class on Monday, Mar. 26

Mar. 23 Review for Test
Introduction to Fibonacci Numbers
Chapters 5-7 (one more time!) Study for Test Work on your Web Page

Mar. 26 Test on Chapters 5-7 Pp. 301-308 Pp. 318-324: 1, 3-6, 8,9, 13-21 odd, 46 Read about Fibonacci's Rabbits and Dudeney's Cows. Send me an e-mail message (subject: cows) containing the title of the book in which Dudeney published his problem.

Mar. 28 Fibonacci Numbers;
Sequences and Limits
Similar Figures in Geometry
Same as Mar. 26 Same as Mar. 26 Find out how to Calculate the Next Fibonacci Number Directly. Note that on this page the Nth Fibonacci number is denoted by F(n), using a lower case n and putting it in parentheses instead of an upper case N used as a subscript like our book writes it. Don't let that confuse you. Also, the examples use "sqrt" to mean "square root of" because that is easier to type than the square root symbol.
Use the formula to calculate F(20), given that F(19) = 4181; write out all the steps to show your work, and bring this with you when you come to class Friday.
From here on, you are going to need a calculator which will take square roots and do exponentials, so try to get one if you don't already have one.

Mar. 30 The Golden Ratio;
Similarity and Gnomens Pp. 308-317 Pp. 320-322: 25-39 odd
Compute F(21) using the value of F(20) computed in class today and the formula from the web. Check your answer by computing
F(19) + F(20).
Read about The Fibonacci Rectangles and Shell Spirals. Watch as a sequence of Fibonacci rectangles is built. Explore the link given there to Logarithmic Spirals. Other names for the same thing are Geometric Spiral and Equiangular Spiral.

Apr. 2 Class Cancelled
Apr. 4 More on Gnomens;
Review Chapter 9 Chapter 9 (again) Pp. 323-324: 45, 51 Nothing new, but remember that you should be working on your Math Web Page.
Study for short Quiz on Chapter 9 to be given in class on April 9.

Apr. 6 Review Chapter 9 Work a variety of problems from Chapter 9 Keep working on your Math Web Page

Apr. 9 Short Quiz on Chapter 9
Population Growth
Pp. 329-337 Pp. 351-352: 1-15 By now, you should have decided on a topic or theme for your Math Web Page. Send me an e-mail telling me what that topic or theme is, and what ideas you have for carrying it out. (Subject: My web page)

Apr. 11 Exponential Growth Pp. 338-345 Pp. 352-354: 17-21, 30-33 Go to The Sciences Explorer Calculators and choose "Compound Periodic". Use this compound interest calculator to work Problems 22 and 24 P. 353. Note that this calculator requires a number to be entered in each of the five fields. For these problems, you are given the numbers for four of the fields, and the calculator will find the answer for the fifth (unknown) field. Enter the appropriate number in the four given fields, and any number in the unknown field,then click on the "Calc" button beside the unknown field and the answer will replace whatever number was there originally. Send me your answers by e-mail (Subject: Interest).

Apr. 16 More on Exponential Growth and Compound Interest Pp. 338-345 (again) Pp. 353-354: 23, 25-29 Go to the Radioactive Decay Page and work the problems there using the "Half-Life Decay Calculator" at The Sciences Explorer Calculators. Send me your answers by e-mail (Subject: Half-Life)

Apr. 18 Logistic Growth Pp. 345-350 Pp. 354-355: 34-37, 39, 41 Go to The Population Growth Page and read the discussion there. Then click on "Exponential Growth", and do the experiments listed there (you will need to click on "Run Applet" and wait a few seconds for it to load). Then click on "Logistic Growth" and do the experiments listed there. Now, run the Logistic Growth experiment with Birth rate 4 and Carrying Capacity 1000; here, the population eventually becomes 0 and the species is extinct. How many generations does it take to reach extinction? Send me an e-mail with the answer (Subject: Extinct).

Apr. 20 More on Logistic Growth;
Review Chapters 9 and 10
Chapters 9 and 10 (again) Work a variety of problems from Chapters 9 and 10 Study for Test on Chapters 9 and 10 to be given in class on Monday Apr. 23;
Keep working on your Web Page

Apr. 23 Test on Chapters 9 and 10 Pp. 393-402 P. 416: 1-4 Read about self-similarity and the Sierpinski Triangle (the same thing our book calls the Sierpinski Gasket). This should help you understand self-similarity in other figures.

Apr. 25 Fractal Geometry PP. 402-407 Pp. 416-418: 5-16 Play Leap Fractal at the University of Minnesota's Geometry Center. Be sure to try it at each of the four levels: Novice, Medium, Hard and Master. Send me an e-mail message (subject: Leap) explaining how this game relates to The Sierpinski Gasket

Apr. 27 More Fractals; The Chaos Game Pp. 407-413 Pp. 418-419: 17-20, 25-27 Play The Chaos Game as described in your book. Note that in the rules, what is called an edge should be called a vertex. Start with the version that says "Ive got plenty of time..." to roll the die one at a time, and get a good idea of what is going on. Then go to the other versions, which will do 10, 100, or 1000 rolls at once. Watch the Sierpinski Gasket appear before your eyes.

Apr. 30 More on Fractals;
Introduction to the Mandelbrot Set
Pp. 410-415 Pp.419-420: 28-30, 35,37 Take a look at some approximately self-similar figures.You don't need to do anything with this - it's just for fun. But you might want to create some of your own. There is a link to the site where I generated the pictures, so enjoy. If you want to know how this works, ask me and I will be happy to explain.

May 2 More on the Mandelbrot Set Review Chapters 1-3, 5-8, 9, 10 and 12 Pp. 419-420: 31-34, 37, 38-40 Explore the Mandelbrot Set at the Mandelbrot Explorer Site. Set a zoom factor and click on a point in the picture, then do it again, and again. Try different points and different zoom factors. When you get a picture you like, save it to a floppy, and then use FTP to upload it to your web site. You can name the file anything you want, but make sure it ends in .jpg (not.pic). Send us all an e-mail message with the URL for your picture.
Here are some pictures I created at the Mandelbrot Explorer Site.

May 4 Course Review Review the entire course Rework a variety of problems Finish your Math Web Page and use your distribution list to tell us where to find it and what it is about. This MUST be received by me BEFORE the Final Exam.

May 9
3:30 - 5:30 Final Exam

Day	In Class	Read	Problems	Computer Projects and Other Assignments
Jan. 11	Course Introduction and Overview; Preference Voting	Chapter 1	None	Explore the web page for your textbook. Take a look at my Spiral Page and my Mandelbrot Set Page for a preview of some of the things we will be doing later in the course. Use the ballots from our Fantasy Trip election (available on the web by 6:00 PM tonight) to construct a preference table; bring your table with you to class on Friday.
Jan. 12	Voting and Counting	Appendix 1 and Appendix 2 to Chapter 1;	Pp. 27-30: 1, 3-13, 25-27	Using your Preference Schedule from the class Fantasy Trip election, determine the winner using the Plurality Method, the Borda Count Method, the Plurality-With-Elimination Method, and the Method of Pairwise Comparisons. Bring your list of winners to class on Wednesday.
Jan. 17	Discuss Chapter 1 and Fantasy Trip election	Chapter 1 (again)	Pp. 31-32: 41-44, 51	Send me e-mail with your name and your e-mail address; tell me the last Math course you took and when you took it; put Math 101 in the subject line.
Jan. 19	Introduction to Weighted Voting Systems	Pp. 41-53	Pp. 61-64: 1, 3, 5, 13, 17, 27	Go to the Math 101 Distribution List Page, where there is a list of e-mail addresses for all the students in this class, and for me. Copy and paste this list to make a class distribution list which you can use all semester to communicate with the rest of us. I have included instructions on how to do this using Gemini, but if you use some other system for e-mail you are on your own! Now use your distribution list to send all of us a message introducing yourself. Put Introducing Myself in the Subject Line. Get the list of coalitions and fill in the blanks.
Jan. 22	Weighted Voting Systems and Power Indices	Pp. 53-60	Pp. 61-65: 7, 9, 11, 15, 17, 19, 21-25, 33, 35	There is a nice summary of Chapter 2 on the web at a page called Weighted Voting Systems. Check it out and write a short "review" of the site. Then use your class distribution list to send your "review" to your classmates and to me, with subject Review.
Jan. 24	Power Indices	Chapters 1 and 2 (again)	Any problems you couldn't work before.	Take Quiz 1 via e-mail. This quiz is worth 10 points, and you may use your book and your notes, and you may ask me for help. However, you are on your honor not to assist anyone else or seek assistance from anyone other than me. You must submit your answers by NOON (class time) on Friday, Jan. 26. Put Quiz 1 in the Subject line. We will have a Quiz on Chapters 1 and 2 in class on Monday, Jan. 29. It will NOT be open book or open notes. Add the following to your Distribution List: elm0736@tntech.edu markwallace82@yahoo.com ykd5392@tntech.edu
Jan. 26	Review of Chapters 1 and 2 Introduction to Fair Division	Pp. 73-78	Pp. 96-100: 1-3	Study for Monday's quiz. "Surf" the Web for an interesting math-related web page. Here are some places you might start: The TTU Math Department's Home Page The Math Forum at Swarthmore College UT's Mathematics Archives Or try one of the search engines such as Alta Vista (look under Science, then under Math), or Yahoo (look under Science, then under Mathematics). Now use your class distribution list to send the rest of us the URL for your site; tell us what it is about and why you like it. Put Math Site in the subject line.
Jan. 29	QUIZ 2 on Chapters 1 and 2 Fair Division	Pp. 78-81	Pp. 97-100: 4-13	Insert "1/3" between the words "least" and "of" on the last line of P. 81. Visit the Web sites whose URL's were sent to you by your classmates (Click here for a list of the sites). Then use your Class Distribution List to tell us which one is your favorite, and why (subject: Favorite Site).
Jan. 31	Lone Divider Method	Pp. 75-81 (again) Pp. 81-84	Pp. 100-102: 14-19, 21	Take Quiz 3 via e-mail (Subject: Quiz 3). As for Quiz 1, you may use your book and your notes, and you may ask me for help. But you are on your honor not to assist anyone else or seek assistance from anyone other than me. You may take the quiz as many times as you like, and I will count only your last score. Thus, your best strategy is to take it early and try to improve your score by correcting your mistakes. The quiz is due by NOON (class time) on Friday, Feb. 2.. Any quiz which I receive before 5:00 PM on Wednesday or Thursday will be graded and returned to you that evening. You may then re-take it if you are not satisfied with your score.
Feb.2	Lone Chooser Method	Pp. 81-84 (again)	pp. 100-106: 20, 40, 41	Go to Your Math Web Page to read the instructions for your web page. Begin to think about what you would like to use as a "theme" for your page. You might want to look ahead at Chapters 4-12 of your book for ideas about topics we will cover later in the semester. This is a long-term project, due the last week of class, but you should begin to think about what you want to do. We will have some related projects to help you learn how to set up a basic web page, add graphics to it, make links, etc... these will be coming up in the next few weeks. Add jlm0851@tntech.edu to your Distribution List Delete pedaltone1@yahoo.com from your Distribution List.
Feb. 5	Last Diminisher Method	Pp. 84-88	Pp. 102-107: 22-24, 43	Print out and read A Beginner's Guide to HTML. This is your first step in learning how to create your own web page.
Feb. 7	Sealed Bids	Pp. 89-92	Pp. 103-107: 25-31, 42	Go to the TTU Home Page and choose"Web Publishing Info" (located under "About This Web Server" near thebottom of the page). Then choose "Student Personal Pages" to find out how to set up your own home web page on Gemini. Or, if you would prefer to use a private Internet Service Provider (ISP), find out how to set up a web page through it. Begin to build your home page by writing an html document which includes your name, your major, a list of some of your hobbies, and a link to the Math 101 Home Page. You may use the preformatted template provided by the Computer Center if you want. If you need help, see me or ask at the Computer Center Help Desk. Once you have your web page ready for viewing, use your Class Distribution List to send its URL to the rest of us. This project should be completed by Monday, Feb. 19.
Feb. 9	Markers	Pp. 92-95	Pp. 104-110: 32-39, 52, 53	Keep working on your Web Page. Don't leave this until the last minute - it's not hard, but it may take you longer than you anticipate, and you may need to get some help from either me or the helpers in the Computer Center.
Feb. 12	Questions on Chapter 3	Chapters 1-3 (again)	Rework a variety of problems from Chapters 1-3	Review for TEST on Chapters 1-3, which will be given in class on Friday, Feb. 16. Keep working on your web page. You may put anything you like (within the bounds of decency and good taste) on it, and you may make links from it to other pages. Later on you will create another page which will be related to some mathematical topic. If you want to make a second page now, you may: Follow the same procedure, but name the file something other than index.html (that name is reserved for your home page).
Feb. 14	Review of Chapters 1-3	Study for test	Study for test	Study for test Finish your home page
Feb. 16	Test on Chapters 1-3	Chapter 4, including the appendices	No new problems to work.	Take the Quiz on Chapter 4 via e-mail. The rules are the same as for Quiz 3, except that for this one you get only one try. Send me your answers, with subject Quiz 4, by Noon Monday, Feb. 19.
Feb. 19	Introduction to Graph Theory	Pp. 149-158	Pp. 173-179: 1-13, 38	Think about how you might "jazz up" your web page; here is a page with some links to sites with graphics that you can download to use on your pages.
Feb. 21	Euler Circuits and Paths	Pp. 158-167	Pp. 175-179: 14-22, 27-32	Take the Introductory Graph Theory Tutorial written by Chris Caldwell of UT-Martin. Then send me an e-mail message witih the answers to the 3 questions on the last quiz in the tutorial (subject tutorial).
Feb. 23	More on Euler Circuits and Paths	Pp. 167-172	Pp. 176-181: 23-26, 39, 41-43, 46, 47	Read a biography of Leonhard Euler at the St Andrews University History of Math site. Then send me an e-mail message (subject: Euler) listing the titles of five of Euler's publications, including at least one on the theory of music.
Feb. 26	Review Chapter 5	Chapter 5 (again)	Rework any problems you didn't understand the first time.	Study for QUIZ on Chapter 5, which will be given in class on Wednesday, Feb. 28. Take another of Chris Caldwell's tutorials, this one on Euler and Hamilton Circuits. The part on Euler circuits will be a review, and the part on Hamilton circuits will be a preview of the material we will study in Chapter 6.
Feb. 28	Quiz on Chapter 5 Hamilton Circuits and Paths	Pp. 185-191	Pp. 210-217: 1-10, 15, 16, 39, 42	Take another tutorial by Chris Caldwell, this one about Coloring Graphs. Then send me e-mail (subject: colors) with the answers to the following questions (the answers can be found in the tutorial): 1.What if we color our graph (map) on a sphere instead of a plane, then how many colors do we need? 2.What about on a mobius strip? 3.What about on a torus (doughnut)? 4.Suppose our map is on a sphere and we allow each country to have one colony (which must be colored the same color); then how many colors do we need?
Mar. 2	Traveling Salesman Problems	Pp. 192-199	Pp. 212-218: 11-14, 17a, 17b, 19,47	Read "The Traveling Monkey". Then send me an e-mail message (subject: monkey) answering the following questions: Who is the author of "The Traveling Monkey"? This article reports on a paper published in the scientific journal Nature. What issue of that journal is cited?
Mar. 5	TSP Algorithms	Pp. 199-209	Pp. 213-218: 17c, 17d, 18-37, 49, 50	Read about the History of the Traveling Salesman Problem . Note: a circuit is called a cycle on this page. Send me e-mail with answers to the following questions: What company ran a contest in 1962 which involved solving a TSP for 33 cities? In what year did four researchers solve the TSP problem for the 13,509 cities in the USA with population greater than 500?
Mar. 7	Trees and Spanning Trees Kruskal's Algorithm	Pp. 225-232	Pp. 245-251: 1-16, 31	Go to a Kruskal's Algorithm page and practice building minimum spanning trees: first click on "New Problem" and then click on "Step Solve" to watch the computer build the tree one step at a time. Do this several times and try to predict which edge the computer will choose at each step. Send me an e-mail message (Subject: Kruskal) with the answer to the following two questions: On this page the minimum spanning tree is called something else. What name is used here for the minimum spanning tree? How does Kruskal's Algorithm compare with the Cheapest Link Algorithm for Hamilton Circuits? Print out and work the problems on the 30-60-90 Triangle worksheet. Bring it with you to class on Friday.
Mar. 9	Steiner Points	Pp. 232-245	Pp. 249-251: 17-25, 40-45	Go to a Steiner Point Web page. Be patient - it may take a little while to load. Eventually, you will see a red triangle ABC. On each side of the red triangle, an equilateral triangle has been built, and the third vertex of the new triangle has been connected to the third vertex of ABC by a line. Thus, the third vertex of the equilateral triangle built on side AB is connected to vertex C, etc. The Steiner point S is the intersection of those three lines. Use your mouse to move point A (or point B or point C) and watch how the Steiner point moves. Also, watch how the angles change (their measures are given in the upper left corner). Send me an e-mail message (subject: Steiner) with the answers to the following questions: Fill in the blank: Either all three angles at S (ASB, ASC, and BSC) are 120 degrees, or else only one of them is 120 degrees and the other two are _____ degrees. When only one of the three angles at S is 120 degrees, where is the point S in relation to triangle ABC? Is it still a Steiner point for triangle ABC?
Mar. 19	More on Trees and Steiner Points Similar Triangles	Chapter 7 (again)	Pp. 251-252, 32-36	Review Chapter 7 Print out and work the problems on the Worksheet on Similar Triangles; bring it and your answers to class on Wednesday.
Mar. 21	Questions on Chapter 7	Chapters 5-6 (again)	Rework a variety of problems from Chapters 5, 6 and 7	No new project, but don't forget that you should be working on your Math Web Page. Review for Test on Chapters 5-7 to be given in class on Monday, Mar. 26
Mar. 23	Review for Test Introduction to Fibonacci Numbers	Chapters 5-7 (one more time!)	Study for Test	Work on your Web Page
Mar. 26	Test on Chapters 5-7	Pp. 301-308	Pp. 318-324: 1, 3-6, 8,9, 13-21 odd, 46	Read about Fibonacci's Rabbits and Dudeney's Cows. Send me an e-mail message (subject: cows) containing the title of the book in which Dudeney published his problem.
Mar. 28	Fibonacci Numbers; Sequences and Limits Similar Figures in Geometry	Same as Mar. 26	Same as Mar. 26	Find out how to Calculate the Next Fibonacci Number Directly. Note that on this page the Nth Fibonacci number is denoted by F(n), using a lower case n and putting it in parentheses instead of an upper case N used as a subscript like our book writes it. Don't let that confuse you. Also, the examples use "sqrt" to mean "square root of" because that is easier to type than the square root symbol. Use the formula to calculate F(20), given that F(19) = 4181; write out all the steps to show your work, and bring this with you when you come to class Friday. From here on, you are going to need a calculator which will take square roots and do exponentials, so try to get one if you don't already have one.
Mar. 30	The Golden Ratio; Similarity and Gnomens	Pp. 308-317	Pp. 320-322: 25-39 odd Compute F(21) using the value of F(20) computed in class today and the formula from the web. Check your answer by computing F(19) + F(20).	Read about The Fibonacci Rectangles and Shell Spirals. Watch as a sequence of Fibonacci rectangles is built. Explore the link given there to Logarithmic Spirals. Other names for the same thing are Geometric Spiral and Equiangular Spiral.
Apr. 2	Class Cancelled
Apr. 4	More on Gnomens; Review Chapter 9	Chapter 9 (again)	Pp. 323-324: 45, 51	Nothing new, but remember that you should be working on your Math Web Page. Study for short Quiz on Chapter 9 to be given in class on April 9.
Apr. 6	Review Chapter 9		Work a variety of problems from Chapter 9	Keep working on your Math Web Page
Apr. 9	Short Quiz on Chapter 9 Population Growth	Pp. 329-337	Pp. 351-352: 1-15	By now, you should have decided on a topic or theme for your Math Web Page. Send me an e-mail telling me what that topic or theme is, and what ideas you have for carrying it out. (Subject: My web page)
Apr. 11	Exponential Growth	Pp. 338-345	Pp. 352-354: 17-21, 30-33	Go to The Sciences Explorer Calculators and choose "Compound Periodic". Use this compound interest calculator to work Problems 22 and 24 P. 353. Note that this calculator requires a number to be entered in each of the five fields. For these problems, you are given the numbers for four of the fields, and the calculator will find the answer for the fifth (unknown) field. Enter the appropriate number in the four given fields, and any number in the unknown field,then click on the "Calc" button beside the unknown field and the answer will replace whatever number was there originally. Send me your answers by e-mail (Subject: Interest).
Apr. 16	More on Exponential Growth and Compound Interest	Pp. 338-345 (again)	Pp. 353-354: 23, 25-29	Go to the Radioactive Decay Page and work the problems there using the "Half-Life Decay Calculator" at The Sciences Explorer Calculators. Send me your answers by e-mail (Subject: Half-Life)
Apr. 18	Logistic Growth	Pp. 345-350	Pp. 354-355: 34-37, 39, 41	Go to The Population Growth Page and read the discussion there. Then click on "Exponential Growth", and do the experiments listed there (you will need to click on "Run Applet" and wait a few seconds for it to load). Then click on "Logistic Growth" and do the experiments listed there. Now, run the Logistic Growth experiment with Birth rate 4 and Carrying Capacity 1000; here, the population eventually becomes 0 and the species is extinct. How many generations does it take to reach extinction? Send me an e-mail with the answer (Subject: Extinct).
Apr. 20	More on Logistic Growth; Review Chapters 9 and 10	Chapters 9 and 10 (again)	Work a variety of problems from Chapters 9 and 10	Study for Test on Chapters 9 and 10 to be given in class on Monday Apr. 23; Keep working on your Web Page
Apr. 23	Test on Chapters 9 and 10	Pp. 393-402	P. 416: 1-4	Read about self-similarity and the Sierpinski Triangle (the same thing our book calls the Sierpinski Gasket). This should help you understand self-similarity in other figures.
Apr. 25	Fractal Geometry	PP. 402-407	Pp. 416-418: 5-16	Play Leap Fractal at the University of Minnesota's Geometry Center. Be sure to try it at each of the four levels: Novice, Medium, Hard and Master. Send me an e-mail message (subject: Leap) explaining how this game relates to The Sierpinski Gasket
Apr. 27	More Fractals; The Chaos Game	Pp. 407-413	Pp. 418-419: 17-20, 25-27	Play The Chaos Game as described in your book. Note that in the rules, what is called an edge should be called a vertex. Start with the version that says "Ive got plenty of time..." to roll the die one at a time, and get a good idea of what is going on. Then go to the other versions, which will do 10, 100, or 1000 rolls at once. Watch the Sierpinski Gasket appear before your eyes.
Apr. 30	More on Fractals; Introduction to the Mandelbrot Set	Pp. 410-415	Pp.419-420: 28-30, 35,37	Take a look at some approximately self-similar figures.You don't need to do anything with this - it's just for fun. But you might want to create some of your own. There is a link to the site where I generated the pictures, so enjoy. If you want to know how this works, ask me and I will be happy to explain.
May 2	More on the Mandelbrot Set	Review Chapters 1-3, 5-8, 9, 10 and 12	Pp. 419-420: 31-34, 37, 38-40	Explore the Mandelbrot Set at the Mandelbrot Explorer Site. Set a zoom factor and click on a point in the picture, then do it again, and again. Try different points and different zoom factors. When you get a picture you like, save it to a floppy, and then use FTP to upload it to your web site. You can name the file anything you want, but make sure it ends in .jpg (not.pic). Send us all an e-mail message with the URL for your picture. Here are some pictures I created at the Mandelbrot Explorer Site.
May 4	Course Review	Review the entire course	Rework a variety of problems	Finish your Math Web Page and use your distribution list to tell us where to find it and what it is about. This MUST be received by me BEFORE the Final Exam.
May 9 3:30 - 5:30	Final Exam

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