Main Goals for Chapter 4

• To become familiar with mathematical systems
• To understand different kinds of number systems: simple grouping (ex. Egyptian), multiplicative grouping (ex. Chinese), and positional (ex. our Hindu-Arabic decimal system)
• To understand positional systems with different bases, so converting between decimal and a different base, and doing addition and subtraction in other bases
• To become familiar with the symmetries of the square: the elements, operations and how to use the square
• To become familiar with different properties that mathematical systems can possess: identity, inverse, associative, commutative
• To become familiar with what a group is

Section 4.1 Historical Numeration Systems. Key Ideas: simple grouping (Egyptian), multiplicative grouping (Chinese), positional (Hindu-Arabic).  Not doing Egyptian algorithm. Sample exercises (pages 158-160): all odd except 35 and 37

Section 4.2  Arithmetic in the Hindu-Arabic System.  Key Ideas: exponential expressions, distributive property, expanded form. NOT doing lattice method or Napier's rods.  Sample exercises (pages 167-168): 1-13 (odd)

Section 4.3  Conversion Between Number Bases.  Key Ideas: converting numbers from decimal to a different base and vice versa, other systems like binary, octal and hexadecimal, addition and subtraction in different bases (not in the book).  Sample exercises (pages 176-179): 1-63 (odd), 83, 85

Section 4.4  Finite Mathematical Systems.  Key Ideas:  Main example: the symmetries of the square; closure property, commutative property, associative property, identity property, inverse property.  Sample exercises (pages 183-185):  1-9 (odd), 15-21 (odd)

Section 4.5 Groups.  Key Ideas: group.  Sample exercises (page 192): 1-37 (odd)

Chapter 4 Slides

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last updated November 7, 2011