January 17, 2006
- I gave everyone a printout of the 'syllabus' which is exactly a copy of the web page for the class (http://garsia.math.yorku.ca/~zabrocki/math1590w06/) as of Tuesday, January 17th.
- We talked about the first chapter of the book TM. One of the questions in the discussion of the first chapter includes a question about a 20% discount on a sweater and 15% sales tax. The question is what do you want to do take the discount and then the tax, or the reverse? Read the discussion in the book and it doesn't mention the points that were brought up in class, namely which method benefits the store?
- Next we talked a little about the homework and figured out (somewhat) how to solve the problem 'Arithmagons' for triangles. Please follow the method described in the first few chapters of TM when you do this assignment. You will get full credit for the homework problems from the book only if you do the 'extend' part of the problem.
- I asked the question: "Consider an infinite plane. If I have no lines on it there is one region. If there is is one line on the plane it divides the plane into into two different regions. If there are two lines on the plane the maximum number of regions those two lines can make is 4. For three lines we can make at most 7 regions. How many regions can be made with 10 lines on the plane? How many regions can be made with 1000 lines on the plane?" We managed to arrive at a formula that worked for any number of lines.
- We look a little more at the mathematics of Sudoku. We figured out that it is possible to count the number of 2^2x2^2 Sudoku puzzles by hand. We came up with an answer of 384 and then we looked at the web (I googled "mathematics of Sudoku") and found that the real answer is 288 and so we had made a mistake. Homework (besides what is due for next week) is to find where we went wrong.
- Wikipedia article on Sudoku (http://en.wikipedia.org/wiki/Sudoku)
- Wikipedia article on the mathematics of Sudoku (http://en.wikipedia.org/wiki/Mathematics_of_Sudoku) including the number of 2^2x2^2 Sudoku puzzles
- The sequence of number of Sudoku grids (http://www.research.att.com/~njas/sequences/A107739)
- The sequence of different Sudoku grids (http://www.research.att.com/~njas/sequences/A109741) we mentioned it depends on what you mean by puzzles being distinct.
- I then did a search on Google news for 'the largest prime'
- An article from the Arizona republic (http://garsia.math.yorku.ca/~zabrocki/math1590w06/articles/AZrepubprime.pdf)
- An article from the associated press from CNN (http://garsia.math.yorku.ca/~zabrocki/math1590w06/articles/cnnprime.pdf)
- An article from the Guardian (http://garsia.math.yorku.ca/~zabrocki/math1590w06/articles/guardianprime.pdf)
- Wikipedia article on prime numbers (http://en.wikipedia.org/wiki/Prime_number)
- The radio program on the largest prime (http://www.bbc.co.uk/radio4/science/another5.shtml)
- GIMPS (http://www.mersenne.org/) the organization that found the largest prime using distributed computing
- Finally I asked everyone to write down a prediction about the election and I placed them in an envelope. We will discuss the mathematics of elections and polls next week.
Previous class : January 10, 2006
Next class : January 24, 2006
Main class page : Mathematics 1590 Nature of Mathematics II