Math 497 Winter 2002, Meeting #2

Discussion of Homework and last Week's Topics

What Comes Next?

This class is based on Chapter 3 of the The Book of Numbers.

Factorial Numbers

What do they count?

How big do they get?

Arrangement Numbers

Formula

What do they count?

Choice Numbers

Formula

What do they count?

Pascal's Triangle

What is it?

Why do choice numbers appear?

Where are the triangular numbers and tetrahedral numbers in the triangle.

Binomial Coefficients

Binomial expansion.

Powers of 2 can be written as binomial expansions.

Visualize the quadratic and cubic expansion with a square and a cube.

How Many Regions?

Lines divide the plane into how many regions?

Chords divide the disk into how many regions?

Difference Tables

Make difference tables from data.

Turn tables into polynomials.