Math 44
Winter 2013 Home Page
Green Sheet

I've received a complaint about the late assignment of the problems in chapter 6 below. What seems fair is that if you want to turn it in, then I will count 4 of the 5 assignments for you. If you don't turn it in, I will count 3 of the 4 assignments you did turn in. There is thus a slight advantage to turning in chapter six. Plus it will re-familiarize you with some of the problems like on the final.

The problems on the final from the material in chapter six cover the following:
(1) 1- and 2-dimensional cellular automata.
(2) Calculate the dimension of a fractal - please bring your calculator!
(3) What does chaos mean (see section 6.5)

Here is a short handout on 1-dimensional cellular automata, like we did in class.

The last homework for chapter 6 will be checked during the exam on Friday.
If you've gotten full credit for each of the previous homeworks, you don't need to turn in this one.

Chapter 6.1: 1,2,3,5,7,8
Chapter 6.2: 3,5,13,23
Chapter 6.3: 1-5, 15, 16
Chapter 6.5: #10, 12-19

Class 22, Thu., Mar. 21, 2013
We had project presentations, went over take-home exam.
Here's a sample problem list from a previous quarter. Yours will be similar, but there are some things here we did not go over, or did not go over very much.
Here's another list of sample problems. Again, some similarities, some differences.

Class 21, Tue., Mar. 19, 2013
We worked on fractals, did the contra dance math!

Class 20, Thu., Mar. 14, 2013
We worked on fractals, also projects. Also had Pi day!

Class 19, Tue., Mar. 12, 2013
Thursday is Pi Day. Please bring something appropriate!

We taked about projects. Your project description is due on Thursday, and the project is due the last day of class, next Thursday.
Chapter 5 homework is due on Thursday. We will work more on fractals on Thursday also.

Class 18, Thu., Mar. 7, 2013
We learned about fractal dimension and worked on the fractal tree handout.
We also learned about frieze symmetries (straight line symmetries).
Paper is due Tuesday, be prepared to give a brief oral report - if you want, you can show graphics or diagrams on the overhead.

Here is the site with the "Royal Vacation" card trick.
Here is the site with the 4 rows of 5 trick that I did in class.
Chapter 5 homework is due next Thursday.

Chapter 5.5 homework (knots): #3,4,10,13,18,20,26,32,37
Chapter 5.6: #3,6,8,12

Here is your project description, for the project which is due the last week of class.

Class 17, Tue., Mar. 5, 2013

Class 16, Thu., Feb. 81, 2013
We went over material on knots and graphs.

For your third 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, submitted to Turnitin.com. 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, March 11.

Class 15, Tue., Feb. 26, 2013
Work on take-home exams, some material on knots, much of rest of Gardner video.

Class 14, Thu., Feb. 21, 2013

We saw part of the film about Martin Gardner and learned about Euler Circuits.

Class 13, Tue., Feb. 19, 2013
We learned about graphs and went over the section on scaling versus translation symmetry.

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.

Class 12, Thu., Feb. 14, 2013
We went over some take home test material, also began chapter 5.1 and 5.2.

We also built some polyhedra and cut out some mobius strips!

Here is the chapter 5 homework:
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

Chapter 4 homework due on Tuesday.

Class 11, Tue., Feb. 12, 2013
We learned about polyhedra, and worked on the handouts below. We are skipping the last two sections of chapter 4.
Chapter 4 homework will be due next Tuesday.

Class 10, Thu., Feb. 7, 2013
We heard the biographical reports. Work on homework from chapter 4 (see below).

Class 9, Tue., Feb. 5, 2013
Your second paper is due this Thursday, Feb. 7, at 1:30 PM, on Turnitin.com.

We went over chapter 4.3, and did a movement activity on symmetry. Here are the handouts we worked on at the end of class, which you should turn in next Tuesday:
Geoboard paths
Rotational Symmetry
Reflection symmetry

Begin working on chapter 4 homework.
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

Class 8, Thu., Jan. 31, 2013
We went over the exams, also chapters 4.1 and 4.2.
Your second paper is due by this Thursday, Feb. 7, at 1:30 PM, on Turnitin.com.

Please work on homework for chapter 4.1 and 4.2 (see list just below.)

Class 7, Tue., Jan. 29, 2013
We had exam 1, and went over the "billiard method" of solving water pouring problems.
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.

We also heard a bit of Sophie Germain's story. Here's a nicely written bio about Germain.

I've emailed many of you articles for your mathematician bio. Others will find articles in Mathematical People or More Mathematical People in the library.

Chapter 2 homework is due on Thursday of this week.

Homework for chapter 4:
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

Class 6, Thu., Jan. 24, 2013
We went over more about modular arithmetic, section 2.4 in the text. Please turn in the handout from the last part of class on Tuesday, Jan. 29. Chapter 2 homework will be due following the first exam on Tuesday, Jan. 29.

Here is a study guide for the first exam from a previous quarter. We have not gone over numbers 4(b), 4(c), and 10, that material is not on the test.
Here is another practice exam from a previous quarter, more like what you will have, since it's a multiple choice/Scantron exam. Please bring the half page long scantron for your exam 1.

Your mathematician biography is due a week from Thursday, Feb. 7. Here are the mathematician bios assigned.
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.

Here's an online article by Ivars Peterson on drivers license codes.
Here's Joseph Gallian's site on check digits in codes.

Here is a short handout on modular arithmetic; please print and birng to class Tuesday.

Here is the wikipedia article on UPC codes, with lots of detail. The reason it did not "work" in class the other day: we were looking at the bar code for the ISBN, not the UPC!

Class 5, Tue., Jan 22, 2013
We went over several chapter 1 problems, including the "dishonest politician" problem, which we solved by "working backwards." We went over material from chapter 2 on primes, least common multiple, greatest common divisor, and began section 2.4 on modular (clock) arithmetic. We also made rhythms out of our names, and saw how to put two rhythms together to make a star polygon. Here's a solution to the 12 coin problem written up by John Conway.

Here are the mathematician bios which were assigned in class. If you were absent, I assigned you someone also.

Here is the Fibonacci assignment, which is due this Thursday, Jan. 24.

We also looked at prime numbers. Here is a 2 minute slightly nutty but mathematically accurate music video (professionally produced by Nova) of SJSU's Dan Goldston's discoveries about the Twin Prime Conjecture.

Class 4, Thu., Jan. 17, 2013
We went over the pigeonhole principle, Fibonacci numbers, also prime numbers, and some other problems from chapter 1. Your chapter one homework is due next Tuesday, Jan. 22, but you should already be working on chapter 2 homework, which will be due one week later. The problems assigned in the text for chapters one and two are listed below.

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 #3,4,5,7,9,19,28,29,30,32,33

In the pigeonhole principle "magic trick," I asked you to choose seven numbers from the list 1,2,3,...,12. The properties each of your lists had were:
(1) A pair of your numbers had a sum of 13.
(2) A pair of your numbers had a difference of 6.
(3) A pair of your numbers had a difference of 3.
(4) A pair of your numbers had the property that their only common factor was 1.
(5) A pair of your numbers had the property that one divided the other equally.
We saw how the pigeonhole principle explained why properties 1,2, and 3 are true. For Thursday, can you use the pigeonhole principle to explain property 4? Remember, it's all in how you label to (six) pigeonholes!
Property 5 is more difficult to explain; in this case the six pigeonholes have different numbers of numbers assigned to them!

We learned how to find Fibonacci numbers on a pine cone.
Here is the Fibonacci assignment, which is due next Thursday, Jan. 24.

Here are Vi Hart's Fibonacci number videos.
A great site about Fibonacci numbers.
Fibonacci site with lots of pictures and interactive applets.
Interactive site that helps explain phyllotaxis, which is the pattern of spirals in many plants.
Pingala's possible use of the Fibonacci Numbers
Rachel Hall who credits Indian mathematician/musician with the Fibonacci numbers - see her article "Math for Poets and Drummers" listed at her site.

Class 3, Tue., Jan. 15, 2013
We went over chapter one problems, the pigeonhole principle, and the Fibonacci numbers.
We went over the comedians and officers problem (which used to be known as the "cannibals and missionaries" problem).

Class 2, Thu., Jan. 10, 2013
No class today.

Class 1, Tue., Jan. 8, 2013
We played the pattern game and played the take-away game.

Begin work on homework problems 1-15 from chapter 1, to be turned in next week.

Here's a list of all the problems from the 2nd edition of the text book; the numbers for the 3rd edition are extremely similar 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. 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

Some links from previous quarters:

Here is your final project form, for the project which is due the last week of class.

For your third 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, submitted to Turnitin.com. 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 Th., Nov. 6.

Here is an article published in the New York Times about Martin Gardner, in honor of his 95th birthday.

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!

Link on pentominos.
Here's a handout showing you how to find the symmetries in a tiling! Here are hundreds of links to some amazing tiling sites. 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.

Rotational symmetry handout.
4-Fold rotational symmetry handout.

Here's a list of "distributed" mathematical projects now being conducted throughout the internet.
Here's the "World Community Grid" site listing many online projects in which you (and your computer) can participate!
Here's another site for "Volunteer Computer Grids."

Patterns and Modular Arithmetic.
Modular Arithmetic Intro handout.

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.

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.

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.

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!