· Crisler, Fisher, & Froelich. Discrete Mathematics Through Applications. W H Freeman. 2000.

· Tannenbaum & Arnold. Excursions in Modern Mathematics. Prentice-Hall. 2001.

· Scheinerman. Mathematics: A Discrete Introduction. Thompson Learning. 2000.

1. Demonstrate the use of various methods for determining the outcome of an election.
   
   1. Compute election winners by:
      
      1. plurality method.
         
      2. runoff method.
         
      3. sequential runoff method.
         
      4. Borda method.
         
      5. Condorcet method.
         
   2. State and discuss the issue of fairness using Arrow’s theorem.
      
      
2. Describe weighted voting systems.
   
   1. Determine winning coalitions.
      
   2. Compute the power index (Banzhaf).
      
      
3. Use organizational procedures for fair division.
   
   1. Apply continuous case division for two or more participants.
      
   2. Apply discrete case division for two or more participants.
      
      
4. Describe relationships involving apportionment.
   
   1. Compare and contrast the historical apportionment methods:
      
      1. Hamilton
         
      2. Jefferson
         
      3. Hill-Huntington
         
      4. Webster
         
   2. Apply apportionment methods to nongovernmental situations.
      
      1. scheduling
         
      2. sports salary caps
         
         
5. Apply game theory strategies to situations involving conflict and cooperation. (Optional)
   
   1. Create a game matrix.
      
   2. Determine the value of the game matrix.
      
   3. Identify zero-sum and nonzero-sum games.
   4. Demonstrate the strategies behind:
      
      1. the prisoner’s dilemma.
         
      2. the game of chicken.
         
      3. inspection games.
         
      4. duel games.
         
      5. equilibrium.
         
   5. e. Discuss the definition of fairness as related to game theory.

1. Identify and define terms relating to matrices.
   
   
2. Create a matrix on paper, graphing calculator, and computer.
   
   
3. Perform matrix operations of addition, subtraction, and multiplication on paper, graphing calculator, and computer.
   
   
4. Find the inverse of a matrix and state its application.
   
   
5. Apply the Leslie matrix model to population models.
   
   
6. Apply the Leontief model to economic situations.
   
   
7. Apply the Markov chain to probability models.

1. Define recursion.
   
   
2. Model and describe classic recursion problems such as:
   
   1. hand shake
      
   2. Tower of Hanoi
      
   3. Pascal’s triangle
      
   4. Von Kock snowflake
      
   5. Sierpinski’s triangle or gasket
      
      
3. Investigate difference equations.
   
   1. Write first- and second-degree difference equations.
      
   2. Use the process of finite differences to convert difference equations into explicit equations.
      
   3. Use mathematical modeling to prove difference equations (optional).
      
      
4. Demonstrate cobwebbing (graphical iteration) manually and with a graphing calculator.