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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
Encode and decrypt messages using ciphers and cryptography.
- 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.
- 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.
- For any of the simple ciphers, input a text message to view its encrypted
output and numeric equivalent based on the specified cipher.
- To get started using RSA Public-Key Cryptography:
- Construct: Choose to Generate p and q and/or Generate e and d. If you
enter your own values, be sure to press Enter.
- Encrypt: Based on the key master /certificate generator values (n and
e), choose Encrypt to convert a text message to numbers.
- Decrypt: Based on the same key master /certificate generator values
(n and d), choose Decrypt to convert the numbers from the Encrypt stage
to the original text message.
Determine voting outcomes based on various ranked-choice voting
- Start by selecting a table from the dropdown menu.
- 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.
- Choose Vote Analysis to see the results of the six different voting methods
for the current table.
- 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.
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.
- Enter a quota—the number of votes needed to pass a proposal.
- Enter the number of voters.
- Enter voter weights by choosing "Go". Assign voter weights one-at-a-time
to each voter you specified in Step 2.
- 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.