Math 44
Spring 2010 Home Page
Green Sheet

Class 16, Thursday, June 3, 2010
We did more work on fractals, including on dimension and web diagrams. Please complete the web diagrams handout for next Thursday.

Here is your final project form, for the project which is due the last week of class. Fill out the form and turn in Tuesday, June 8. (Note: disregard the "turn-in date" on the form, it's due for your class next Tuesday!)

Next Thursday is the field trip to Dale Seymour's house. Your next paper is due Tuesday. Here is a description with some suggested references: For your next written report, you are to report on a mathematical subject connected to this course, that has caught your interest. I suggest that you read a chapter or two from one of Martin Gardner's books on mathematics, he covers a wide variety of topics. Here is a list of a few of the 70 books by Martin Gardner.  Choose a chapter (or two) that is of interest to you and report on it:
The Colossal Book of Mathematics
Mathematical Circus
Mathematical Magic Show
The Magic Numbers of Dr. Matrix
Mathematical Carnival
Knotted Doughnuts and Other Mathematical Entertainments
Wheels, Life, and other Mathematical Amusements
Time Travel and Other Mathematical Bewilderments

You might also want to look at books by Ian Stewart, Keith Devlin, or Ivars Peterson.

Please check out one of the books and sign up to do a report on one chapter. You can email me which chapter you want to do a report on, if you have any question. This will be a 600 word paper, as before. The main criteria for how you select which chapter to report on is that it should be of interest to you. You will also give a brief 2-3 minute oral report on what you learned to the class, if we have time, on Tuesday, June 8.

Class 15, Thursday, May 27, 2010
Take home exams turned in. More work on fractals.

Class 14, Tuesday, May 25, 2010

Class 13, Thursday, May 20, 2010
We began chapter 6, learning about cellular automota, especially Conway's Game of Life. We also went over section 5.4 on fixed point theorems, which we saw might be likened to "magic tricks."

You will have the take home exam emailed to you. If you did not receive it let me know right away.

Class 12, Tue., May 18, 2010
We learned about numbers of graphs.
We also looked at the "Small World Phenomenon," and "six degrees of separation,"
Here are some more links:
Six degrees of Kevin Bacon.
Oracle of Bacon, where you can look up actor's links to other actors.
Kevin Bacon's charitable SixDegrees.org.
The Erdos-Bacon number site.
The Facebook Six Degrees site.
The Erdos Number project.

I'll post the slides on African Mathematics shortly...

Class 11, Thu., May 13, 2010
We went over more from chapter 5, including knot theory.

Class 10, Tue., May 11, 2010
We heard reports.

Upcoming: We will soon look at the symmetries of frieze patterns; are frieze symmetry slides we will discuss and here is a handout on patterns from Benin in which you will find which of the 7 symmetries is shown in each pattern (some appear more than once, some do not appear.)

Class 9, Th., May 6, 2010
We went over tilings (tesselations), introduced the graph alphabet and also the chapter on topology (surfaces such as the Moebius strip.)

For those of you wanting more info on pentominoes, here is a standard intro, with pictures of all 12 pentominoes. Your homework from two classes ago was to "Choose one of the pentominoes, make a tiling of the plane, find the symmetries, and bring to class! " Pentominoes each have five identical unit squares, linked complete edge to edge. For example, we might try to solve the same problem for the "hexomino:" there are 34 hexominoes, each having six squares. Here is a diagram indicating briefly how all 34 hexominoes tile the plane. These are not shown in complete detail; your penomino tiling should extend further than these, and indicate how the pattern you found really could extend in all directions throughout the plane.

We have gone over a variety of graph theory concepts, including Euler Circuits (these are not in your text). An assigned reading is this site which has excellent explanations of such graph concepts, with links to good diagrams.

Due Tuesday: Math Bios (Danny Troung, I don't have your email address, please contact me for bio material!). Also due Tuesday: Chapter 2 homework (leave out section 2.5!)

Do these homework problems also on Mobius strips.

Class 8, Tue., May. 4
We went over homework problems, and worked on tessellations. Please complete your pentomino tessellation and bring to class on Thursday. Use this handout showing you how to find the symmetries in your tiling to understand how to complete it. We also learned about 4 symmetries (see below.) Please turn in chapter 2 homework on Thursday (we have not covered section 2.5, so you don't need to complete that section.)

We did a "body" symmetry activity in which we constructed the table of "compositions" of four planar symmetries:
T for Translation (or slide),
G for Glide (also called glide reflection),
M for Mirror (or reflection), and
R for Rotation (180 degree turn).
Here's the table we constructed:

Class 7, Th., Apr. 29
We went over exam and built polyhedra. Turn in symmetry handouts on Tuesday.

The reference books, Mathematical People and More Mathematical People are on reserve in the campus library. The report will be 600 words, and will also involve a short 2 to 3 minute oral report. Include in your paper some response by yourself to the person - is this someone you might like to have a conversation with, or is it someone who does not seem very interesting to you? Your main reference must be a printed source, not a web site, and you must cite any sources you use. Your mathematician bio is due next Tuesday, May 11 (not the coming week!). Here is the list showing who is assigned which bio.

Please visit Scott Kim's homepage and look at the many examples of Inversions, some from his book by the same name, some animated. Recently other artists have produced these letterform images that exhibit symmetry, for example here is a site for ambigram tattoos by Mark Palmer. The artist John Langdon has also been creating Ambigrams for many years, and produced those used by Dan Brown in his book Angels and Demons. See Langdon's site for examples of his work, or look for his book Wordplay. Here's a site by the mathematician and artist Burkard Polster with lots of playful examples.

Symmetry leads us to the field of "tilings" or "tessellations." There is an enormous amount of recent mathematics and art  on this subject. Take a look at David Eppstein's enormous collection of links on tilings. He calls his collection of such links the Geometry Junkyard; it's very entertaining, in a mathematical and arts sort of way!

Class 6, Tue., Apr. 27
We wen over chapter 4.2 and 4.3, and began working on symmetry.

Class 5, Th., Apr. 22, 2010
We had exam 1 and went over more material from chapter 2 on modular arithmetic, also the "art gallery theorem." Do homework through section 2.4. Turn in modular arithmetic handout.

Class 4, Tue., Apr. 20, 2010
We went over modular arithmetic, also prime numbers, logic problems, and some other problems from chapter 1, the pigeonhole principle.
First exam is Thursday, Apr. 22, bring a scantron.

Class 3, Tue., April 13, 2010
We went over modular arithmetic and the Fibonacci numbers. Chapter 1 and the Fibonacci assignment de Tuesday.

Class 2, Thu., April 8, 2010
We went over the "cannibals and missionaries" problem and saw an unsual method of solving it that used "arrow diagrams."
We also played the "take-away" game, and saw an analysis of it that introduced modular arithmetic. And we learned a little about the history of modular arithmetic.
We went over several of the chapter 1 problems (the most difficult is number 15).
Due Tuesday: Math autobiography
Please also complete homework for chapter 1 and the problems in Patterns and Modular Arithmetic (the latter due next Thursday.)

Class 1, Tue., April 6, 2010
We played the pattern game, saw the "billiards table" analysis of the water pouring problem, and started to work on the "missionaries and cannibals" water crossing problem.

Begin work on homework problems 1-15 from chapter 1, to be turned in next week.
Please print out this handout, begin working on it, and bring them to class on Thursday:
Patterns and Modular Arithmetic.

Here's a site where you can get free software for implementing the billiard ball approach to the water pouring problem. You have to download the "Mathematica Player" (also free) first.

Here's a list of all the problems from the text book for the quarter. There might be some revisions, and there will be other additions.
Ch. 1 #1-15, pg 28-32.
Ch. 2.1 I: 4,6,9,10-12,14-18,21
Ch. 2.2: 1-7,16,18,21,24,26
Ch. 2.3: 1-3,6,7,13,14,19,20,22,37,39
Ch. 2.4 #3,4,5,7,9,19,28,29,30,32
Ch. 2.5: 3,6,7,8,11,15 
Ch. 4.1 #2,11,12,13,15,18,19
Ch. 4.2 #5,7,9,11,21
Ch. 4.3 # 1-8
Ch. 4.4 # 1-5
Ch. 4.5: 11,12,15,16,21
Ch. 5.1: 4-6, 12,14,16,22,25,26,36
Ch. 5.2: Do any three of 8,9,10,13,14. Also do 18,19,22, any one of 26-28, 37
Ch. 5.3: 2,4,5,7-10
Ch. 5.4: 1-5,13,16,19,20
Ch. 6.1 1,2,3,5,7,8
Ch. 6.2 3,12-23
Ch. 6.3 #1,2,4,5,9,13,21,23
Ch. 6.4 #2,3,6,8,12-15
Ch. 6.5 1-10, 26-28,38-40
Ch. 6.6 #1-6,10-12,15