Number Theory 2013-2014

Notes and handouts

• Problem sheet 1
• Problem sheet 2
• Problem sheet 3
• Problem sheet 4
• The extended Euclidean algorithm (written 2005)
• Primitive roots
• Three proofs of Wilson's theorem (written 2005)
• The binary powering algorithm (written 2003)
• Algorithms in MAPLE (written 2003)
• Pythagorean triples and sums of squares (written 2004)
• The two-square and four-square formulas
• Quadratic reciprocity (written 2003)
• Quadratic reciprocity: a lattice point proof
• Quadratic reciprocity: Eisenstein's proof
• The Legendre and Jacobi symbols
• Peralta's algorithm
• Square roots modulo a prime (written 2003, not as slick as Peralta's algorithm)
• Exam (1997-1998)
• Exam (1998-1999)
• Exam (1999-2000)
• Exam (2000-2001)
• Exam (2001-2002)
• Exam (2002-2003)
• Exam (2003-2004)
• Exam (2004-2005)
• Exam (2005-2006)
• Exam (2006-2007)
• Exam (2012-2013)
• Outline solutions to 2013 exam
• Outline notes for the course
• notes compiled by Oliver Bond

Coursework schedule

• Assignment 1: due in 4th November 2012
• Assignment 2: due in 15th November 2013
• Assignment 3: due in 29th November 2013
• Assignment 4: due in 10th January 2014

Other links

• William Chen's lecture notes on Elementary Number Theory
• Online number theory lecture notes from The Number Theory Web.
• Verification of Goldbach's conjecture up to 4×10^18 by Tomás Oliveira e Silva
• The Prime Pages by Chris Caldwell
  
• A Guide to Arithmetic (some old lecture notes by me)

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