Fall 2009

Discrete and Foundational Mathematics I

Math 187, Section 001
MTWF   9:40 a.m. - 10:30 a.m. MG 120

Extra credit ASSIGNMENTS
 

XC Assignment 1:
 Write a one- to two- page biography on one (or more) of the following mathematicians. Be sure to describe their mathematical achievement and some details of their lives.

    a) Leonhard Euler                                          l)  Diophantus of Alexandria
    b) Pierre de Fermat                                       m) Appolonius of Perga
    c) Euclid of Alexandria                                   n)  Evariste Galois    
    d) Karl F. Gauss                                            o)  George Bernhard Riemann
    e) Marin Mersenne                                         p)  Leonardo Fibonacci
    f)  Srinivasa Ramanujan
    g) Joseph Lagrange
    h) Lejeune Dirichlet
    i) Archimedes of Syracuse
    j) Adrien-Marie Legendre
    k) Leonard Adleman
 
The essay should be your own work. Consulted works should be properly acknowledged and listed in your bibliography.
Due date: September 21 

XC Assignment 2:

Two players  ONE and TWO play a board game which has 15 numbered pieces. The board has 100 rows of 15 squares on which the pieces fit.
The rules are as follows:
 

• Player ONE starts the game by putting a piece on each square in the first row.

• Next is player TWO  who must take the pieces and put one in each square in the next row. The requirements are:
     a)  no two pieces that were in adjacent squares in any previous row can be adjacent again.
     b) no piece that was at a left or right edge in any previous row can be at the edge of any later row.

• After TWO played it is ONE's move again and he must follow the  adjacency rule as TWO  and put the pieces in the next row.

• The game continues in this way until the next player to play cannot satisfy the adjacency rule.
   

ONE wins the game if TWO cannot continue. Then TWO must pay to ONE  n dollars where n is the number of rows completed. Otherwise, when ONE looses, ONE must pay to TWO n dollars where n is the number of rows completed.

a) Who will win the game?
b) What is the amount of money that the winner receives?
c) How many different winning configurations are there?

Due date: October 2

Hint: First analyze this for numbers less than 15: 1, 2, 3, 4, 5, 6,... 

XC Assignment 3

Page 168,  21.4
 

Due date: October 30

XC Assignment 4:

Two players  ONE and TWO play a board game which has 8 numbered pieces. The board has 100 rows of 8 squares on which the pieces fit.
The rules are as follows:
 

• Player ONE starts the game by putting a piece on each square in the first row.

• Next is player TWO  who must take the pieces and put one in each square in the next row. The requirements are:
     a)  no two pieces that were in adjacent squares in any previous row can be adjacent again.
     b) no piece that was at a left or right edge in any previous row can be at the edge of any later row.

• After TWO played it is ONE's move again and he must follow the  adjacency rule as TWO  and put the pieces in the next row.

• The game continues in this way until the next player to play cannot satisfy the adjacency rule.
   

ONE wins the game if TWO cannot continue. Then TWO must pay to ONE  n dollars where n is the number of rows completed. Otherwise, when ONE looses, ONE must pay to TWO n dollars where n is the number of rows completed.

a)  Who will win the game?
b)  What is the amount of money that the winner receives?
c)  How many different winning configurations are there?

Due date: December 11