| 1 | Divisibility (PDF) |
| 2 | Greatest Common Divisor (PDF) |
| 3 | More on Greatest Common Divisor and Division Algorithm (PDF) |
| 4 | Prime Factorization and Binomial (PDF) |
| 5 | Binomial Theorem and Congruences (PDF) |
| 6 | Congruences (PDF) |
| 7 | Residue Systems, Fermat's Little Theorem, Euler's Theorem, and Wilson's Theorem (PDF) |
| 8 | Review for Midterm |
| 9 | Midterm 1 |
| 10 | More on Factorization (PDF) |
| 11 | Chinese Remainder Theorem (PDF) |
| 12 | RSA Cryptography (PDF) |
| 13 | Hensel's Lemma (PDF) |
| 14 | Solving Equations Modulo Primes (PDF) |
| 15 | More on Solving Equations Modulo Primes (PDF) |
| 16 | Quadratic Residue Symbol (PDF) |
| 17 | More on Quadratic Residues (PDF) |
| 18 | More on Quadratic Residues (cont.) (PDF) |
| 19 | Quadratic Reciprocity (PDF) |
| 20 | More on Quadratic Reciprocity (PDF) |
| 21 | Continued Fractions (PDF) |
| 22 | More on Continued Fractions (PDF) |
| 23 | More on Continued Fractions (cont.) (PDF) |
| 24 | More on Continued Fractions (cont.) (PDF) |
| 25 | More on Continued Fractions (cont.) (PDF) |
| 26 | More on Continued Fractions (cont.) (PDF) |
| 27 | More on Continued Fractions (cont.) and Solving Equations (PDF) |
| 28 | Midterm 2 |
| 29 | Curves in Projective Space (PDF) |
| 30 | More on Curves in Projective Space and Statement of Falting's Theorem (Mordell Conjecture) (PDF) |
| 31 | Singular Points and Smoothness (PDF) |
| 32 | Elliptic Curves (PDF) |
| 33 | More on Elliptic Curves (PDF) |
| 34 | Abelian Groops, Torsion Points and Finite Generation of Group of Torsion Points (PDF) |
| 35 | Mazur's Theorem and Calculating the Torsion Subgroup (PDF) |
| 36 | More Calculations (PDF) |
| 37 | Advanced Topics (PDF) |