Topology

Vrije Universiteit Amsterdam

Course Description

  • Course Name

    Topology

  • Host University

    Vrije Universiteit Amsterdam

  • Location

    Amsterdam, The Netherlands

  • Area of Study

    Mathematics

  • Language Level

    Taught In English

  • Course Level Recommendations

    Upper

    ISA offers course level recommendations in an effort to facilitate the determination of course levels by credential evaluators.We advice each institution to have their own credentials evaluator make the final decision regrading course levels.

    Hours & Credits

  • ECTS Credits

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

    COURSE OBJECTIVE
    At the end of this course:
    -the student is familiar with the basic concepts, such as topology, openand closed sets, and continuous functions, and is able to use these toprove some fundamental results;
    -the student knows several ways to define a topology on a set and cancompare different topologies on the same set;
    -the student can determine if a given topological space satisfiescertain properties (such as compactness and connectedness);
    -the student understands the concept of topological manifold andfundamental group, and is aware of the importance of these concepts for
    more advanced subjects, such as algebraic topology and differential geometry.

    COURSE CONTENT
    This course is a first introduction to topology, that is, the
    mathematical study of the shape of space. The concepts that are
    introduced in this course are essential in understanding more advanced
    subjects, such as differential topology, functional analysis, and
    algebraic topology.

    The following topics will be covered during the course:
    -general topological spaces;
    -topology generated by a basis;
    -continuous maps and homeomorphisms;
    -connectedness, path-connectedness, local connectedness;
    -compactness, local compactness;
    -products and quotients;
    -topological manifolds;
    -separation axioms;
    -the fundamental group of a topological space.

    TEACHING METHODS
    Lectures and tutorials (2+2 hours per week)

    TYPE OF ASSESSMENT
    For this course there are 4 hand-in assignments (total: 20%), a midtermexamination (30%) and a final exam (50%). There will also be a resitexamination: the final grade will then be determined by the grade of the resit (80%) and the grade of the hand-in assignments (20%).

    RECOMMENDED BACKGROUND KNOWLEDGE
    Basic concepts of mathematics, Analysis 1 and 2, Group theory

Course Disclaimer

Courses and course hours of instruction are subject to change.

Some courses may require additional fees.