Study Guide for Test 2
Friday, November 12th, 2004
I recommend that you study the following

Readings in the course packet:

Class notes and handouts.

Homework assignments 2 and 3.

Past quizzes (October 11thNovember 8th)
Essay questions: you must do at least 2

Discuss the role of sona designs in Chokwe culture.

We have found in class that sona drawings involve mathematical rules.
Give examples from your readings and class notes of how mathematics is
involved in sona construction.

Religion has played an important part in the early study of number theory.
Pick two of the following concepts, explain the concept, and give a crosscultural
analysis of the topic. You may use examples from the readings or
outside sources.

Powers

Multiples

Modular equivalence

Religion has also hindered the development of mathematics in some cultures.
Discuss.
Here are the topics covered

Multiplication algorithms

Gelosia multiplication

Vedic multiplication

Egyptian multiplication

The distributive law and the role it plays in multiplication

Number theory

Multiples, divisors, and powers

Greatest common divisor (GCD) and least common multiple (LCM)

Relatively prime, prime, even, and odd numbers

Modular arithmetic

Definition of equivalence (mod b), where b stands for a counting
number

Use of modular arithmetic in calculating time, zodiac symbols, etc.

Applications of modular arithmetic to number theory

Modular multiplication

Use of casting out 9s in checking multiplication

Proofs

Understand why you can't use examples to show a statement is true about
all numbers, but you can use one example to show a statement about all
numbers is false.

Make basic arguments like ``the product of two odd numbers is an odd number.''

Sona drawings

Cultural context

How to calculate the number of lines in a sona

How to choose dimensions for a plaitedmat sona that ensure the drawing
can be traced in one line.

Construction of mirror designs

Identifying similar designs (i.e. variations of the chasedchicken design)

Celtic knots

Making a Celtic knot out of a sona design.