Notes, Assignments and Study Guides

Notes

• Numbers: Rationals, Reals, Complex
• Basic proof techniques: Direct
• Square root of 2 is irrational
• Quantifiers
• Principle of Mathematical Induction
• Strong induction and Well-Ordering Principle
• Fibonnaci Numbers
• Divisibility
• Prime and Composite Numbers
• Patterns in the Primes
• Common Divisors
• The Division Theorem
• A weird number system
• The Division Theorem (cont)
• The Euclidean Algorithm
• Diophantine Equations
• Euclidean Division and Diophantine Equations
• Finding all Solutions
• Finding all Solutions (cont)
• Fundamental Theorem of Arithmetic
• Consequences of Fundamental Theorem
• Modular Arithmetic and Congruences
• Arithmetic with Congruences
• Chinese Remainder Theorem
• Congruence Classes as a Number System
• Multiplicative Inverses
• Basics of Encryption
• Encryption via Multiplication
• Fermat's Little Theorem
• Reduced Residues and phi
• Euler's Theorem
• Encryption via Exponentiation
• Public Key Cryprography and RSA
• Order of Elements in Zn
• Polynomials over Zn
• Primitive Roots
• Applications of Primitive Roots: Diffie-Hellman protocol
• Quadratic Residues
• Law of Quadratic Reciprocity, Gauss's Lemma
• Proof of Quadratic Reciprocity
• Primality Tests

Assignments

• Assignment 1
• Assignment 2
• Assignment 3
• Assignment 4
• Assignment 5
• Assignment 6
• Assignment 7
• Assignment 8
• Assignment 9
• Assignment 10

Study Guides

• Midterm 1 Study Guide
• Midterm 2 Study Guide
• Midterm 3 Study Guide