# 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
```