MATH 5325: Structure of Number Concepts

Spring 2011

24 Jan

Warmup 1: Cher in six decades
Ancient mathematics
Real number system

HW: Research presentations and rubric
D: NCTM preface (pp. vii-xi) with
and Introduction (pp. 1-11) with worksheet

31 Jan

Warmup 2: Wicked maths quiz
Introduction to number theory
History of number theory
Interesting sets of numbers
Base 10 number system
Introduction to other number bases
Base 5 number system

HW #1: other number systems
READ: From Exploration to
(from the textbook CD)

7 Feb

Warmup 3: Number theory quiz
Goldbach conjecture
Sieve of Erastosthenes
100 cards POW
Prime & composite numbers
Fundamental Theorem of Arithmetic
Is one a prime number?

HW #2: primes
READ: NCTM Introduction (pp. 1-11) with worksheet

14 Feb

Warmup 4: For what bases does the number 1-2-1b represent a square number?
Babylonian number system
Egyptian number system
Simple proofs

HW #2a: simple proofs

21 Feb

Warmup 5: Division rule for 9
Mayan number system
Incan number system
& divisibility rules
Division by zero

HW #3: divisibility

28 Feb

Warmup 6: Busy Bee
Binary/Hex number systems
Wizard POW


READ: You can't get there from here!

7 Mar

Warmup 7: Hotel Infinity
Euclidean Algorithm

Cantor and infinity video (3:28 to 6:16)
Countable & uncountable sets

HW #4b: GCF/LCM and
HW #5: countable proofs

14 Mar
Spring Break
21 Mar

Warmup 8: St Ives problem
Sequence types
Series & more series

HW #6: series


28 Mar
Warmup 9: Coloring Pascal's Triangle
Chinese remainder theorem 
Modular arithmetic
Modular arithmetic quiz
Equivalence relations
Congruence & residue classes
HW #7: ants go marching
4 Apr

Warmup 10: Chickens & pigs
Golden ratio presentation
Diophantus & Diophantine equations
Constructible numbers
Transcendental numbers
Irrational numbers
Proof that sqrt(2) is irrational

HW #8: professional article & research article

11 Apr

Warmup 11: Palindrome numbers
Magic/Latin/Euler squares
Kaprekar numbers

18 Apr

Duodecimal number system
Fermat's last theorem presentation

READ: Calculator Cryptography (from the CD in the textbook)
25 Apr
RSA Cryptography presentation
Repeating decimals
Continued fractions & properties

HW #9: continued fractions

2 May
Imaginary numbers & complex numbers HW #10: imaginary numbers
All late work is due by tonight!
9 May

Number theory post-test