Topology: Honours

Topologie: honours

3 EC

Semester 2, period 6

5122TOHO3Y

Owner Bachelor Wiskunde
Coordinator dr. Maximilian Engel
Part of Bachelor Mathematics, year 2
Links Visible Learning Trajectories

Course manual 2024/2025

Course content

The application of topological concepts (open sets, continuity, path liftings, compactness, counting measures, etc.) to dynamical systems with a focus on periodicity, chaos and topological entropy  (Sections 4, 7, 8 of Hasselblatt/Katok: A first course in dynamics).

Study materials

Literature

  • Hasselblatt/Katok: 'A first course in dynamics,' 2003,  Cambridge University Press

     

Objectives

  • The student can analyse rotations of the circle.
  • The student has an understanding of topological transitivity, the growth of periodic points and chaos.
  • The student can analyse if a dynamical system is chaotic, also using the theory of coding and symbolic dynamics.
  • The student understands the notion of topological entropy and can compute it for canonical example maps.
  • The student gains an overview and knwoledge of chaotic phenomena and can also give and create relevant examples themselves.

Teaching methods

  • Self-study
  • Working independently on e.g. a project or thesis

There is a question time at the beginning, with room for discussion and  overview of what will be covered.

For self-study, students should study Hasselblatt/Katok, 4,7,8,  themselves and do a number of selected exercises from this book.

 

Learning activities

Activiteit

Aantal uur

Hoorcollege

2

Zelfstudie

82

 

Attendance

Programme's requirements concerning attendance (OER-B):

  • Each student is expected to actively participate in the course for which he/she is registered.
  • If a student cannot be present due to personal circumstances with a compulsory part of the programme, he / she must report this as quickly as possible in writing to the relevant lecturer and study advisor.
  • It is not allowed to miss obligatory parts of the programme's component if there is no case of circumstances beyond one's control.
  • In case of participating qualitatively or quantitatively insufficiently, the examiner can expel a student from further participation in the programme's component or a part of that component. Conditions for sufficient participation are stated in advance in the course manual and on Canvas.
  • In the first and second year, a student should be present in at least 80% of the seminars and tutor groups. Moreover, participation to midterm tests and obligatory homework is required. If the student does not comply with these obligations, it can be decided to deny the positive effects of homework to be counted towards the final grade of the course. In case of personal circumstances, as described in OER-A Article A-6.4, a different arrangement will be proposed in consultation with the study advisor.

Assessment

Item and weight Details

Final grade

Het eindtentamen bestaat uit het mondeling overlopen van de geselecteerde sommen uit het boek die de student tijdens de zelfstudie heeft gemaakt.

Fraud and plagiarism

The 'Regulations governing fraud and plagiarism for UvA students' applies to this course. This will be monitored carefully. Upon suspicion of fraud or plagiarism the Examinations Board of the programme will be informed. For the 'Regulations governing fraud and plagiarism for UvA students' see: www.student.uva.nl

Course structure

De student verwerkt de leerstof op zijn eigen tempo.

Contact information

Coordinator

  • dr. Maximilian Engel