Discrete Diversions

Sequences and Series

• Basic Sequences
• Generating Formulas for Sums
• Arithmetic Sequences
• Partial Sums of an Arithmetic Sequence
• Geometric Sequences
• Sums of Geometric Sequences
• Recognizing More Patterns
• Fibonacci Sequences
• A Proof of Binet's Formula
• Logistic Sequences
• Recursion and Cobweb Diagrams


• Simple Recursive Sequences (webMathematica):  input a parameter value and see the graph of an arithmetic, a geometric, or a logistic sequence
• Fibonacci and Related Sequences (webMathematica): input parameter values and see the graph of a generalized Fibonacci sequence

Combinatorics

• Basic Counting
• Playing Card Frequencies

Fractals

• Mandelbrot Scenes and Animations (GIF animation):  view zooms at three points in the Mandelbrot set

Linear Algebra

• 2D Matrix Transformations (webMathematica):  input a matrix and see it iteratively transform a simple geometric object
• 2D Homogeneous Transformations (webMathematica):  input a matrix and see it iteratively transform a simple geometric object

Social Choice

• Power on the Nassau County Board of Supervisors
• Power on the United Nations Security Council
• Voting and Power Indices (webMathematica):  input the quota and a set of player weights to see the Banzhaf and Shapley-Shubik power indices
• Apportionment Methods (webMathematica):  input the legislature size and a set of state populations to see the apportionments of Hamilton, Jefferson, Adams, Webster, and Huntington-Hill.