Main Goals for Chapter 5

• To become familiar with various concepts from number theory
• To understand what it means for a number to be divisible by another number
• To understand what it means for a number to be prime or composite
• To be familiar with some divisibility tests
• To learn the Fundamental Theorem of Arithmetic
• To become familiar with a proof that there are infinitely many primes
• To understand clock arithmetic as an example of a modular system
• To become familiar with modular systems in general, what it means for two numbers to be congruent with respect to a certain modulus
• To review the Fibonacci sequence and see its connection to the Golden Ratio
• To explore some interesting features of the Golden Ratio

Section 5.1 Prime and Composite Numbers. Key Ideas: divisibility and divisibility tests, prime and composite, Fundamental Theorem of Arithmetic, Infinitude of primes. Sample exercises (pages 203-206): odd 1-7, 31-35, 47-53

Section 5.4  Clock Arithmetic and Modular Systems.  Key Ideas: addition and subtraction on a clock, congruence mod m, word problems with congruences.  Sample exercises (pages 228-231): 1-21 (odd), 33-51 (odd), 57, 59, 61

Section 5.5  The Fibonacci Sequence and Golden Ratio.  Key Ideas: Fibonacci Sequence, golden ratio (golden rectangle, connection to Fibonacci).  Sample exercises (pages 237-239): 1-15 (odd), 31

 Chapter 5 Slides

Golden Ratio Slides

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last updated November 29, 2011