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Discrete Mathematics Custom Apps

The Discrete Custom Apps include tools for exploring topics such as encryption and voting methods. Click on the name of a tool for a description and additional help topics:

Codes
Ranked-Choice Voting
Weighted Voting

Codes

Encode and decrypt messages using ciphers and cryptography.

Instructions:

  1. Use the Text menu to specify what to accept as input. Options include: Numbers (0-9), Letters (A-Z), Letters and Space, Alphanumeric, and Ascii.
    Note: Only the specified text will be encrypted; all other text characters will be ignored.
  2. Choose a simple cipher from the Security / Cryptograph menu to vary the model y=mx+b with parameter sliders for m and b. The corresponding graphical and character assignment representations will be updated automatically based on the Simple Cipher that is selected.
  3. For any of the simple ciphers, input a text message to view its encrypted output and numeric equivalent based on the specified cipher.
  4. To get started using RSA Public-Key Cryptography:

 

Ranked-Choice Voting

Determine voting outcomes based on various ranked-choice voting methods.

Instructions:

  1. Start by selecting a table from the dropdown menu.
  2. For existing tables in the dropdown menu, the candidates and rankings will be displayed automatically. If you want to create your own table, select (blank table), Add Candidates / Add Rankings as needed, then fill in the table cells. If you add too many rows or columns, you can Reset the table and start again.
  3. Choose Vote Analysis to see the results of the six different voting methods for the current table.
  4. Select Details for a detailed analysis of each vote analysis method including: Plurality Method, Majority Method, Runoff Method, Pairwise-Comparison Method, Points-for-Preferences Method, and Instant Runoff Voting (IRV) Method.

 

Weighted Voting

Investigate a voting situation using the Banzhaf Power Index (BPI) to measure the power of a person's vote and determine whether their vote is critical or not.

Instructions:

  1. Enter a quota—the number of votes needed to pass a proposal.
  2. Enter the number of voters.
  3. Enter voter weights by choosing "Go". Assign voter weights one-at-a-time to each voter you specified in Step 2.
  4. Once the weights are entered, the weighted voting situation is displayed along with tables showing the result of the winning coalition and critical voter analyses as well as the calculation of the Banzhaf Power Index (BPI) for each voter.