NMAA05010U Topology (Top

Volume 2013/2014
Education
BSc programme in Mathematics
BSc programme in Science and IT
Content
This is a course on topological spaces and continuous maps. Main topics of this course are:
  • Topological Spaces
  • Subspace, Order, Product, Metric and Quotient Topologies
  • Continuous Functions
  • Connectedness and Compactness
  • Countability and Separation Axioms
  • Retractions and fixed points
Secondary topics are:
  • Tychonoff Theorem
  • Compactifications
  • The fundamental group and vistas of algebraic topology
Learning Outcome

This course will enable the participants to work with basic topological concepts and methods.  At the end of the course, the students are expected to have attained:


Knowledge:

  • understand and assimluate the concepts and methods of the main course topics including basic definitions and theorems 
  • understand secondary topics covered in the specific course

Skills:

  • determine properties of a topological space such as Hausdorffness, countability, (path) connectedness, (local) compactness
  • construct new spaces as subspaces, quotient spaces and product spaces of known ones
Competences:
  • analyze concrete topological spaces using acquired knowledge and skills
  • relate the theory of topological spaces and continuous maps to specific settings in past and future math courses

 

An2 or similar.
Lectures and single and/or group activities with consulting.
  • Category
  • Hours
  • Exam
  • 3
  • Lectures
  • 45
  • Practical exercises
  • 27
  • Preparation
  • 131
  • Total
  • 206
Credit
7,5 ECTS
Type of assessment
Continuous assessment
Written examination, 3 hour under invigilation
A complete evaluation of weekly work (weighted 50%) and a written 3 hour final exam with all aids (weighted 50%) constitute the basis for assessment.
Aid
All aids allowed
Marking scale
7-point grading scale
Censorship form
No external censorship
One internal examiner
Criteria for exam assesment

The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome.