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Third-Cycle Courses

Faculty of Engineering | Lund University

Details for Course MATM15F Number Theory

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General
  • MATM15F
  • Temporary
Course Name
  • Number Theory
Course Extent
  • 7.5
Type of Instruction
  • Course given jointly for second and third cycle
  • MATM15
Administrative Information
  • 7151 (Centre of Mathematical Sciences / Mathematics)
  • MATM15
  • 2019-02-27
  • Professor Thomas Johansson

Current Established Course Syllabus

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

All Established Course Syllabi

1 course syllabus.

Valid from First hand in Second hand in Established
Autumn 2018 2019‑02‑01 15:38:28 2019‑02‑04 10:53:52 2019‑02‑27

Current or Upcoming Published Course Occasion

No matching course occasion was found.

All Published Course Occasions

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