MAS320, Number Theory


A course in some of the more elementary aspects of algebraic number theory, from a classical perspective. The main strands are continued fractions, binary quadratic forms and modular arithmetic. The theory of continued fractions serves as a unifying theme as well as a source of algorithms. Applications include the representation of primes as sums of squares and the solution of Pell's equation.


Unit value 1 cu
Level 2/3
Semester 6
Timetable C 21,23,32 (17)
Prerequisites Disc Maths
Assessment 10% cwk+90% final exam
Lecturer Dr F Vivaldi


  1. Continued fractions: finite and infinite continued fractions, approximation by rationals, order of approximation.
  2. Continued fractions of quadratic surds: applications to the solution of Pell's equation and the sum of two squares.
  3. Binary quadratic forms: equivalence, unimodular transformations, reduced form, class number. Use of continued fractions in the indefinite case.
  4. Modular arithmetic: primitive roots, quadratic residues, Legendre symbol, quadratic reciprocity. Applications to quadratic forms.


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Author: Dr J. Radcliffe
Last updated 3 November 1999