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 |