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