| 1 | Introduction, Diophantine Equations, Divisibility, GCD (PDF) |
| 2 | Euclidean Algorithm, Primes (PDF) |
| 3 | Binomial Coefficients, Congruences (PDF) |
| 4 | FFermat, Euler, Wilson, Linear Congruences (PDF) |
| 5 | Linear Congruences, Chinese Remainder Theorem, Algorithms (PDF) |
| 6 | Primality, Factoring, RSA, Hensel's Lemma (PDF) |
| 7 | Congruences mod Primes, Order, Primitive Roots (PDF) |
| 8 | Primitive Roots (Prime Powers), Index Calculus (PDF) |
| 9 | Midterm 1 |
| 10 | Quadratic Residues, Quadratic Reciprocity (PDF) |
| 11 | Jacobi Symbol, Computation, Zolotareff's Definition (PDF) |
| 12 | Square Roots, Tonelli's Algorithm, Number of Consecutive Pairs of Squares mod p (PDF) |
| 13 | Cyclotomic Polynomials, Primes Congruent to 1 mod n (PDF) |
| 14 | Arithmetic Functions (PDF) |
| 15 | Mobius Inversion Formula, Zeta Functions (PDF) |
| 16 | Linear Recurrences (PDF) |
| 17 | Generating Functions (PDF) |
| 18 | Midterm 2 |
| 19 | More on Generating Functions, Two Squares Theorem (PDF) |
| 20 | Continued Fractions I (PDF) |
| 21 | Continued Fractions II: Inequalities (PDF) |
| 22 | Periodic Continued Fractions, Quadratic Irrationalities (PDF) |
| 23 | Brahmagupta-Pell Equation (PDF) |
| 24 | Four Squares Theorem (PDF) |
| 25 | Pythagorean Triples, Fermat Descent (PDF) |
| 26 | Rational Points on Conics (PDF) |
