LEARNING OUTCOMES
* developing the logical reasoning skills to write rigorous proofs in mathematics
* ability to describe fundamental topological concepts such as continuity, convergence, and compactness
* applying basic definitions and results in topology to evaluate the properties of various topological spaces
* building a solid foundation in set theory and its operations
Credits: 5
Schedule: 25.02.2025 - 04.04.2025
Teacher in charge (valid for whole curriculum period):
Teacher in charge (applies in this implementation): Aleksis Koski
Contact information for the course (applies in this implementation):
CEFR level (valid for whole curriculum period):
Language of instruction and studies (applies in this implementation):
Teaching language: English. Languages of study attainment: English
CONTENT, ASSESSMENT AND WORKLOAD
Content
valid for whole curriculum period:
Topological spaces
Continuity and convergence
Product topology
Compactness and Connectedness
Separation and countability axioms
Urysohn's lemma and metrization theorem
Topological vector spaces
Assessment Methods and Criteria
valid for whole curriculum period:
Teaching methods: contact sessions, exercises, video material, and exam.
Assessment methods: homework exercises and final exam.
Workload
valid for whole curriculum period:
contact hours 36h (no compulsory attendance)
self-study ca 100h
DETAILS
Substitutes for Courses
valid for whole curriculum period:
Prerequisites
valid for whole curriculum period:
FURTHER INFORMATION
Further Information
valid for whole curriculum period:
Teaching language : English
Teaching Periods: 2024-2025 Spring IV / 2025-2026 Spring IV