| 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) |