	Day	Read	Use / Do
	1	Closure and Sets of Numbers Remainders and Divisibility
	2	Direct Arguments Proof by Cases	Exercises - Divisibility
	3	Indirect Argument (Proof by Contradiction) Secret Decoder Rings and the Caeser Cipher Simple Transposition Ciphers (English) Letter Frequencies Encryptor / Decryptor	Exercises - Indirect Arguments Exercises - The Pigeonhole Principle Read some fictional history... Crack the related "Strap Code"
	4	Summations and Sigma Notation Two Important Properties of Sums (Linearity) The Principle of Mathematical Induction	Exercises - Induction and Sums
	5	Variations on Induction Proof of the Division Algorithm	Exercises - Induction in Other Contexts
	6	Patterns and Conjectures Generating Pascal's Triangle An Odd Question About Pascal's Triangle Fibonacci's Rabbits Numbers in Different Bases A Curious Inequality	Exercises - Patterns and Conjectures Exercises - The Collatz Conjecture
	7	Pythagorean Triples	Exercises - Pythagorean Triples
	8	Permutation Puzzles (and Transposition Ciphers Revisited) Jug Problems	Exercises - Permutation Puzzles
	9	The Euclidean Algorithm Lame's Theorem	Exercises - The Euclidean Algorithm Gcd Finder
	10	Linear Combinations	Exercises - Linear Combinations Linear Combination Finder
	11	Congruence Solving Linear Congruences Affine Ciphers	Exercises - Linear Congruences Get an Encrypted Message
	12	Fundamental Theorem of Arithmetic	Exercises - The Fundamental Theorem of Arithmetic
	13	Vigenere's Cipher Vectors Dot Products, Norms, and Angles Between Vectors	Exercises - Vigenere's Cipher Vigenere Subsequence Analyzer
		Review
	14	Linear Transformations Inverses of Linear Transformations	Exercises - Linear Transformations
	15	The Hill Cipher	Exercises - The Hill Cipher
	16	Continued Fractions	Exercises - Continued Fractions
	17	Wilson's Theorem Converse of Wilson's Theorem	Exercises - Wilson's Theorem
	18	Fast Exponentiation Fermat's Little Theorem	Exercises - Fast Exponentiation and Fermat's Little Theorem
	19	Primality Testing and Carmichael Numbers Euler's Theorem	Exercises - Primality Testing and Carmichael Numbers
	20	Euler's Phi Function Table of Phi Values (0-224)	Exercises - Euler's Theorem
	21	Euler's Phi and the Chinese Remainder Theorem Solving a System of Congruences	Exercises - Chinese Remainder Theorem
	22	Cardinality and Infinite Sets Enumeration of the (Positive) Rationals Cantor's Diagonal Argument	Exercises - Cardinality and Infinite Sets
	23	The Cardinality of a Power Set
		Review	Exercises - Review Exercises (Set B)
	24	The Diffie-Hellman Key Exchange Protocol
	25	RSA and Public Key Codes	Exercises - RSA and Public Key Codes
	26	Finding Phi is Equivalent to Factoring Finding k^th Roots (mod n)
	27	Finding Square Roots (mod n)	Exercises - Finding Roots
	28	Finding Certain Roots is Equivalent to Factoring
	29	Flipping Coins over the Telephone
	30	The Order of an Integer Primitive Roots Index Arithmetic	Exercises - The Order of an Integer and Primitive Roots Exercises - Index Arithmetic
	31	Power Residues and Legendre's Symbol Properties of Legendre's Symbol	Exercises - Legendre's Symbol
	32	Gauss' Lemma A Consequence of Gauss' Lemma
	33	Quadratic Reciprocity
		Review	Exercises - Review Exercises (Set C)