# Math 414: Number Theory - Lectures

M 1/4 Prime factorization: 1 414-2010-01-04.pdf
W 1/6 Prime factorization: 2 414-2010-01-06.pdf
F 1/8 The Riemann Hypothesis: 1 414-2010-01-08.pdf; actual published worksheet from class; 414-2010-01-08-sage_worksheet.pdf; 414-2010-01-08-sage_worksheet.sws
M 1/11 The Riemann Hypothesis: 2 414-2010-01-11.pdf; sage worksheet (published)
W 1/13 The Riemann Hypothesis: 3 414-2010-01-13.pdf; sage worksheet (published)
F 1/15 Integers mod n (substitute, since I'll be in San Francisco)
M 1/18 No Class -- MLK Day
W 1/20 Euler, Wilson and the Chinese: 414-2010-01-20.pdf; sage worksheet (published); 414-2010-01-20.sws (non-published copy of worksheet)
F 1/22 Extended Euclidean Algorithm: 414-2010-01-22.pdf; sage worksheet (published); 414-2010-01-22.sws
M 1/25 Modular exponentiation; Testing primality: 414-2010-01-25.pdf;
sage worksheet (published); 414-2010-01-25.sws
W 1/27 Primitive roots and Artin's conjecture [follows section 2.5 of the course texbook exactly]
F 1/29 Diffie-Hellman [follows the section on Diffie-Hellman from chapter 3 of the textbook very closely]
sage worksheet (published); 414-2010-01-29.sws (local copy)
M 2/1 RSA (substitute, since I will be in Washington, DC at NSF)
W 2/3 Attacking RSA (substitute, since I will be in Washington, DC at NSF)
F 2/5 Quadratic reciprocity sagenb.org worksheet (or a local copy).
M 2/8 Proof of quadratic reciprocity: 1
W 2/10 Proof of quadratic reciprocity: 2
F 2/12 Computing square roots; Continued fractions: 1; (Midterm handed out); Sage worksheet [sagenb.org] (or a local copy)
M 2/15 No Class -- Presidents Day
W 2/17 Continued fractions: 2 (Midterm due!) Sage Worksheet [sagenb.org] (or a local copy) (notes will follow section 5.2 of book)
F 2/19 Continued fractions: 3
M 2/22 Infinite continued fractions
W 2/24 Applications of continued fractions
F 2/26 Diophantine equations
M 3/1 Elliptic curve group law: sage worksheet [sagenb.org] or local copy of sage worksheet
W 3/3 Lenstra's algorithm for factoring integers using elliptic curves: sage worksheet [sagenb.org] or a local copy.
F 3/5 Using elliptic curves for cryptography sage worksheet [sagenb.org] or a local copy.
M 3/8 The Birch and Swinnerton-Dyer Conjecture: congruent number problem sage worksheet [sagenb.org] or a local copy
W 3/10 The Birch and Swinnerton-Dyer Conjecture: statement and motivation; sage worksheet [sagenb.org] a local copy
F 3/12 The Birch and Swinnerton-Dyer Conjecture: sage worksheet [sagenb.org] a local copy