- Course syllabus
- Lecture notes (course reader)
- Information on final presentations
- Online calculator for computing gcd's and writing gcd(a,b) as a linear combination of a and b
- Online modular arithmetic calculator
Tentative schedule of topics and problem sets:

Class Date **Topics****Problem Sets/Afternoon Activities**1 Tuesday July 13

Introduction to Number Theory Ch. 1: The Four Numbers Problem

Ch. 2: Primes and Divisibility

Ch. 1, 2 Problem Sets Supplemental Problem Set on elementary properties of divisibility (challenge problems)

2 Wednesday July 14

Ch. 3: Proof by Contradiction Ch. 4: Mathematical Induction

Ch. 5: The Greatest Common Divisor and the Euclidean Algorithm

Ch. 3, 4, 5 Problem Sets Supplemental Problem Set on proof by contradiction (review problems)

3 Thursday July 15

Ch. 6: Prime Factorization and the Fundamental Theorem of Arithmetic Ch. 34: Conway's Rational Tangles

Ch. 6, 34 Problem Sets (If time allows) Introduce modular arithmetic (Ch. 7) and prove the basic properties (1-3) in Theorem 7.1.

4 Friday July 16

Ch. 7: Introduction to Congruences and Modular Arithmetic Ch. 33: The 5 Card Trick of Fetch Cheney

Ch. 7 Problem Set Ch. 8 Problem Set 1

Ch. 22 Problem Set

Work on choosing a final presentation topic

5 Monday July 19

**Final Presentation Topic Due**Ch. 8: Applications of Modular Artithmetic

Problem-Solving with Congruences and Modular Arithmetic

Ch. 8 Problem Set 2 6 Tuesday July 20

Ch. 10: Fermat's Little Theorem Wilson's Theorem

Ch. 10 Problem Set 7 Wednesday July 21

Ch. 11: Euler's Phi Function and the Euler-Fermat Theorem Ch. 11 Problem Set 8 Thursday July 22

Ch. 13: Squares Modulo p and Quadratic Residues Ch. 28: Pick's Theorem

Ch. 13 Problem Set Ch. 28 Problem Set

9 Friday July 23

Ch. 14: Introduction to Quadratic Reciprocity Ch. 29: Farey Sequences and Ford Circles

Ch. 30: The Card Game SET

Ch. 14 Problem Set Ch. 29 Problem Set

Ch. 32: Mathematical Games

Movie: N is a Number

Ch. 30 Problem Set

10 Monday July 26

Ch. 15: Quadratic Reciprocity Ch. 29: Farey Sequences and Ford Circles

Ch. 26: Geometric Numbers

Ch. 15, 26, 29 Problem Sets 11 Tuesday July 27

Ch. 25: Continued Fractions Ch. 17: Fibonacci Numbers

Ch. 25, 17 Problem Sets 12 Wednesday July 28

Ch. 27: Square-Triangular Numbers and Pell's Equation Ch. 16: Diophantine Equations

Final Presentations

Ch. 27, 16 Problem Sets 13 Thursday July 29

Final Presentations Ch. 31: Magic Squares

Ch. 35: Problem-Solving Using Invariants and Monovariants

Ch. 35 Problem Set Ch. 36, 37 Problem Sets

14 Friday July 30

Final Presentations Number Theory Contest--The Dash

SET Tournament Movie: Hard Problems