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 11th-November 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 cross-cultural 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 plaited-mat sona that ensure the drawing can be traced in one line.
• Construction of mirror designs
• Identifying similar designs (i.e. variations of the chased-chicken design)
• Celtic knots
• Making a Celtic knot out of a sona design.