This is an archived course. A more recent version may be available at ocw.mit.edu.

 

Lecture Notes

The lecture notes are courtesy of one of the students, Anna Marie Bohmann. Used with permission.

SES # TOPICS
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)