Natural Numbers
Pigeonhole principle
	Heart of Math Chapter 2.1

Proof by Induction
	http://en.wikipedia.org/wiki/Mathematical_induction 

Fibonacci Numbers and Related Ideas
Fibonacci Numbers
	Heart of Math Chapter 2.2
	http://en.wikipedia.org/wiki/Fibonacci_sequence 

Continued Fractions		
	http://en.wikipedia.org/wiki/Continued_fraction 
	http://www.mathpath.org/concepts/cont.frac.htm 

Golden Ration (\phi)
	Heart of Math Chapter 2.2
       http://en.wikipedia.org/wiki/Golden_ratio 

(note that the golden ratio and the Euler function do not have any obvious connection even though they both are represented by the same Greek letter \phi). 

Prime Numbers, Multiplication and Division
Infinitude of Primes
	Heart of Math Chapter 2.3
	Magic of Numbers Chapter 10.5
	http://primes.utm.edu/notes/proofs/infinite/euclids.html 

Fundamental Theorem of Arithmetic
	Heart of Math Chapter 2.3
	Magic of Numbers Chapter 11.4
       http://en.wikipedia.org/wiki/Fundamental_theorem_of_arithmetic 

Division with Remainder
	Heart of Math Chapter 2.3
	http://en.wikipedia.org/wiki/Remainder 

Greatest Common Divisor
	Magic of Numbers Chapter 8.3
       http://en.wikipedia.org/wiki/Greatest_common_divisor 
       http://www.math.com/school/subject1/lessons/S1U3L2GL.html 

Sieve of Eratosthenes
	Magic of Numbers Chapter 10.3
       http://en.wikipedia.org/wiki/Sieve_of_Eratosthenes 
       http://www.faust.fr.bw.schule.de/mhb/eratosiv.htm 

Euclid's Algorithm
	Magic of Numbers Chapter 8.4, 8.5
       http://www.antilles.k12.vi.us/math/cryptotut/euclidean_algorithm.htm
	http://en.wikipedia.org/wiki/Euclidean_algorithm 

Extended Euclid's Algorithm (i.e. finding x, y such that ax + by = gcd(a,b))
	http://www.antilles.k12.vi.us/math/cryptotut/euclidean_algorithm.htm
	http://en.wikipedia.org/wiki/Extended_Euclidean_algorithm 

Modular (or Clock) Arithmetic
Equivalence Relations
	http://en.wikipedia.org/wiki/Equivalence_relation 

Calculation in Modular (or Clock) Arithmetic
	Heart of Math Chapter 2.4
	Magic of Numbers Chapter 15
	http://www.math.csusb.edu/faculty/susan/modular/modular.html 

Multiplicative Inverses
	Magic of Numbers Chapter 17.4
	http://en.wikipedia.org/wiki/Modular_multiplicative_inverse 

Check Digits on Bar Codes
	Heart of Math Chapter 2.4
	http://www.cs.queensu.ca/~bradbury/checkdigit/upccheck.htm 

Fermat's Little Theorem
	Heart of Math Chapter 2.5
	http://en.wikipedia.org/wiki/Fermat's_little_theorem 

Euler's Function 
	Magic of Numbers Chapter 13.2
	http://en.wikipedia.org/wiki/Euler%27s_totient_function 

Euler's Theorem
	Magic of Numbers Chapter 20.4
	http://en.wikipedia.org/wiki/Euler%27s_theorem 

Codes
Substitution Codes
	Magic of Numbers Chapter 21.1
       http://www.simonsingh.net/The_Black_Chamber/frequencypuzzle.htm 
	http://en.wikipedia.org/wiki/Substitution_cipher 
	http://www.otr.com/ciphers.shtml 

RSA or Public Key Cryptography
	Heart of Math Chapter 2.5
	Magic of Numbers Chapter 22
	http://en.wikipedia.org/wiki/RSA 
       http://en.wikipedia.org/wiki/Public-key_cryptography 

Prime Factorization
	Heart of Math Chapter 2.4
       http://en.wikipedia.org/wiki/Prime_factor 
	http://www.gomath.com/algebra/factor.php 
	http://www.amby.com/educate/math/2-1_fact.html 

Rational and Irrational Numbers
Rational Numbers (i.e. Fractions)
	Heart of Math Chapter 2.6
	http://en.wikipedia.org/wiki/Fraction_%28mathematics%29 
	http://en.wikipedia.org/wiki/In_lowest_terms 
	http://en.wikipedia.org/wiki/Rational_number 

Irrational Numbers
       Heart of Math Chapter 2.6
	Magic of Numbers Chapter 12.6
	http://en.wikipedia.org/wiki/Irrational_number 
	http://www.mathsisfun.com/irrational-numbers.html 

Square Roots and nth Roots
       Heart of Math Chapter 2.6
	http://en.wikipedia.org/wiki/Nth_root 

Real Line
       Heart of Math Chapter 2.7
	http://www.langara.bc.ca/mathstats/resource/onWeb/precalculus/reals/numline.htm 

Decimal Expansions of Real Numbers
       Heart of Math Chapter 2.7
	http://en.wikipedia.org/wiki/Recurring_decimal 
	http://en.wikipedia.org/wiki/Decimal_representation 

Turning Repeating Decimals into Fractions.
       Heart of Math Chapter 2.7
       http://www.webmath.com/dec2fract.html
	http://en.wikipedia.org/wiki/Fraction_(mathematics)