Number Theory

Vrije Universiteit Amsterdam

Course Description

  • Course Name

    Number Theory

  • Host University

    Vrije Universiteit Amsterdam

  • Location

    Amsterdam, The Netherlands

  • Area of Study

    Mathematics

  • Language Level

    Taught In English

    Hours & Credits

  • ECTS Credits

    6
  • Recommended U.S. Semester Credits
    3
  • Recommended U.S. Quarter Units
    4

  • Overview

    COURSE OBJECTIVE

    • Knowing elementary concepts and techniques from number theory and being able to apply these to concrete problems.
    • Being acquainted with a number of modern developments and open problems within number theory en being able to explain their importance.
    • Knowing certain number theoretic algorithms and being able to perform and analyse them (e.g. by using the mathematics software system "SageMath").

    COURSE CONTENT
    The following subjects will be treated:

    • integers, primes, prime distribution
    • congruences, primitive roots
    • primality tests, factorization
    • public key cryptography
    • quadratic reciprocity
    • Diophantine equations, abc-conjecture
    • algebraic numbers, algebraic integers
    • continued fractions (if time permits) Next to a theoretical approach, practical/algorithmic aspects will also be covered. In particular, the mathematics software system "SageMath" will be used to perform explicit number theoretic calculations.

    TEACHING METHODS
    Lectures and exercise sessions (‘werkcolleges’), both 2 hours per week.

    TYPE OF ASSESSMENT
    Homework assignments (25%) and a final written exam (75%). Extra rule: the grade for the final exam must be at least 5.0 in order to pass

    RECOMMENDED BACKGROUND KNOWLEDGE
    Basic knowledge of groups, rings, and fields is essential.

Course Disclaimer

Faculty of Behavioural and Movement Sciences 

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