Vrije Universiteit Amsterdam
Amsterdam, The Netherlands
Area of Study
Taught In English
Course Level Recommendations
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.
Recommended U.S. Semester Credits3
Recommended U.S. Quarter Units4
Hours & Credits
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.
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
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;
-the fundamental group of a topological space.
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
Courses and course hours of instruction are subject to change.
Some courses may require additional fees.