Elementary Number Theory

Spring 2007

Math 480 at University of Washington

Instructor: William Stein


According to the UW academic calendar, Math 480 starts on Monday, March 26, 2007 and ends on Friday, June 1, 2007. There is exactly one holiday -- Memorial Day on May 28, 2007.

Please read as far ahead as possible before lectures. Also, do as many of the problems in the book as you can; there are usually solutions in the back of the book.

This directory contains a quick summary of each lecture along with relevant handouts.

Monday, March 26Introduction, Prime Factorization (part 1)Section 1.1
Wednesday, March 28Prime Factorization (part 2) Section 1.1
Friday, March 30The Sequence of Prime NumbersSection 1.2
Monday, April 2The Riemann HypothesisSection 1.2 and Mazur-Stein (tba)
Wednesday, April 4Integers Modulo nSection 2.1
Friday, April 6The Chinese Remainder TheoremSection 2.2
Monday, April 9Quickly Computing PowersSection 2.3
Wednesday, April 11Primality TestingSection 2.4
Friday, April 13Primitive RootsSection 2.5
Monday, April 16Diffie-Hellman CryptosystemSection 3.1
Wednesday, April 18RSA CryptosystemSection 3.2
Friday, April 20Attacks on RSASection 3.3
Monday, April 23Midterm Review Chapters 1-3
Wednesday, April 25In Class Midterm 
Friday, April 27Quadratic ReciprocitySection 4.1
Monday, April 30Proof of Quadratic ReciprocitySections 4.2-4.3
Wednesday, May 2Quadratic ReciprocitySection 4.5
Friday, May 4 (project draft 1 due) Finish QR proof; start continued fractions Section 5.1
Monday, May 7Infinite Continued Fractions Section 5.2
Wednesday, May 9Quadratic Irrationals Section 5.4
Friday, May 11Recognizing Rationals from their Decimal Expansion Section 5.5
Monday, May 14Sums of Two Squares Section 5.6
Wednesday, May 16Elliptic Curves Section 6.1
Friday, May 18(project draft 2 due) The Group Law Section 6.2
Monday, May 21Lenstra's Integer factorization algorithm (part 1) Section 6.3
Wednesday, May 23Lenstra's Integer factorization algorithm (part 2) Section 6.3
Friday, May 25An Elliptic Curve Cryptosystem Section 6.4
Monday, May 28no class -- Memorial Day  
Wednesday, May 30The Birch and Swinnerton Conjecture (part 1) Section 6.5
Friday, June 1(final projects due) The Birch and Swinnerton Conjecture (part 2)Section 6.5