LEARNING OUTCOMES
After passing the course the student knows
- methods of rigorous reasoning in mathematical analysis
- basic topology of inner product spaces, normed spaces, and metric spaces
- the notions of limit and continuity
- the definitions and fundamental properties of compactness, completeness, and connectedness in metric spaces.
Credits: 5
Schedule: 07.01.2025 - 20.02.2025
Teacher in charge (valid for whole curriculum period):
Teacher in charge (applies in this implementation): Rogovin
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:
real numbers, metric, norm, inner product, open and closed sets, continuous mappings, sequences and limits, compactness, completeness, connectedness.
Assessment Methods and Criteria
valid for whole curriculum period:
lectures, exercises and course exam OR exam only
Workload
valid for whole curriculum period:
24+12 (4+2).
DETAILS
Study Material
valid for whole curriculum period:
W. Rudin: Principles of Mathematical Analysis, 3rd Edition, McGraw-Hill 1976
N.L. Carothers: Real Analysis, Cambridge University Press 2000
J. Väisälä: Topologia I, Limes ry 1999 (in Finnish/Swedish)
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 Period: 2024-2025 Spring III
2025-2026 Spring III