Schedule

A week-by-week breakdown of the material.

Week 1 (09/05-09/09)

• Day 1
  • Numbers: Rationals, Reals, Complex
  • Basic proof techniques: Direct
  • Assignment 1
• Day 2
  • Basic proof techniques: Indirect
  • Square root of 2 is irrational
  • Quantifiers
• Day 3
  • Principle of Mathematical Induction
  • Strong induction and Well-Ordering Principle
  • Fibonnaci Numbers
  • Assignment 2

Week 2 (09/12-09/16)

• Day 1
  • Divisibility
  • Prime and Composite Numbers
  • Assignment 3
• Day 2
  • Patterns in the Primes
  • Common Divisors
• Day 3
  • The Division Theorem

Week 3 (09/19-09/23)

• Day 1
  • A weird number system
  • The Division Theorem (cont)
  • Assignment 4
• Day 2
  • The Euclidean Algorithm
  • Diophantine Equations
• Day 3
  • Euclidean Division and Diophantine Equations
  • Finding all Solutions
  • Assignment 5

Week 4 (09/26-09/30)

• Day 1
  • Fundamental Theorem of Arithmetic
  • Consequences of Fundamental Theorem
• Day 2
  • Modular Arithmetic and Congruences
• Day 3
  • Arithmetic with Congruences

Week 5 (10/03-10/07)

• Day 1
  • Chinese Remainder Theorem
  • Assignment 6
• Day 2
  • Congruence Classes as a Number System
• Day 3
  • Multiplicative Inverses

Week 6 (10/10-10/14)

• Day 1
  • Basics of Encryption
  • Encryption via Multiplication
• Day 2
  • MIDTERM (Study guide)
• Day 3
  • Fermat's Little Theorem
  • Assignment 7

Week 7 (10/17-10/21)

• Day 1
  • Fall Break
• Day 2
  • Reduced Residues and phi
• Day 3
  • Reduced Residues and phi (cont)

Week 8 (10/24-10/28)

• Day 1
  • Reduced Residues and phi (cont)
  • Euler's Theorem
  • Assignment 8
• Day 2
  • Encryption via Exponentiation
• Day 3
  • Public Key Cryprography and RSA

Week 9 (10/31-11/04)

• Day 1
  • Public Key Cryprography and RSA (cont)
• Day 2
  • Order of Elements in Zn
• Day 3
  • Polynomials over Zn

Week 10 (11/07-11/11)

• Day 1
  • Primitive Roots
• Day 2
  • Primitive Roots (cont)
• Day 3
  • MIDTERM (Study guide)

Week 11 (11/14-11/18)

• Day 1
  • Applications of Primitive Roots: Diffie-Hellman protocol
• Day 2
  • Applications of Primitive Roots: Diffie-Hellman protocol (cont)
  • Quadratic Residues
  • Assignment 9
• Day 3
  • Quadratic Residues (cont)

Week 12 (11/21-11/25)

• Day 1
  • Law of Quadratic Reciprocity
• Day 2
  • Thanksgiving
• Day 3
  • Thanksgiving

Week 13 (11/28-12/02)

• Day 1
  • Gauss's Lemma
• Day 2
  • Proof of Quadratic Reciprocity
  • Assignment 10
• Day 3
  • Primality Tests

Week 14 (12/05-12/09)

• Day 1
  • Primality Tests (cont)
• Day 2
  • TBA
• Day 3
  • TBA