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Third-Cycle Courses

Faculty of Engineering | Lund University

Details for the Course Syllabus for Course MATM15F valid from Autumn 2018

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General
Aim
  • That the postgraduate student should learn the basic concepts of Number Theory. This is an important research field within Mathematics, but also has applications in Cryptography, Coding Theory and Computer Science.
Contents
  • Classical theory of modulo arithmetic, quadratic reciprocity, quadratic forms and Diophantine approximation.
Knowledge and Understanding
  • For a passing grade the doctoral student must
  • be able to state and prove the Quadratic Reciprocity Law

    be able to state and prove some results about when it is possible to express an integer as a sum of squares
    be able to account for the basic theory of Diophantine approximation of real numbers.
Competences and Skills
  • For a passing grade the doctoral student must
  • be able to solve systems of linear congruences.
Judgement and Approach
  • For a passing grade the doctoral student must
Types of Instruction
  • Lectures
  • Seminars
Examination Formats
  • Written exam
  • Oral exam
  • Failed, pass
Admission Requirements
Assumed Prior Knowledge
  • Calculus in one and several variables. Linear Algebra.
Selection Criteria
Literature
  • Burton, David M.: Elementary Number Theory. 2010. ISBN 9780071289191.
Further Information
Course code
  • MATM15F
Administrative Information
  • 2019-02-27
  • Professor Thomas Johansson

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