Number Theory, 6 credits

Main field of study

Course level

Advancement level

Course offered for

• Mathematics
• Computer Science and Engineering, M Sc in Engineering
• Applied Physics and Electrical Engineering, M Sc in Engineering
• Computer Science, Master's programme
• Information Technology, M Sc in Engineering
• Applied Physics and Electrical Engineering - International, M Sc in Engineering
• Computer Science and Software Engineering, M Sc in Engineering

Entry requirements

Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshold requirements for progression within the programme, or corresponding.

Prerequisites

Intended learning outcomes

The course should give insight into elementary number theoretic concepts and advance ability in their use. After completing the course the student should

• know how integers are constructed from the prime numbers and how the prime numbers are distributed among the integers
• be able to do calculations with congruences and solve certain diophantine equations
• know of certain important number theoretic functions, e.g. the Euler phi-function, and their use
• know the Möbius inversion formula and how to apply it
• have knowledge of some simple primality tests
• know the law of quadratic reciprocity
• be able to calculate with continued fractions and to use these in order to solve Pell's equation
• be able to handle the Gaussian integers and know how they are used to write integers as sums of two squares

Course content

Prime numbers, arithmetic modulo n, little Fermat, primitive roots, chinese remainder theorem, quadratic residues, reciprocity, sums of squares. Continued fractions.

Teaching and working methods

Lectures.

Examination

Grades

Department

Director of Studies or equivalent

Examiner

Education components

Course literature