Please note! Course description is confirmed for two academic years (1.8.2018-31.7.2020), which means that in general, e.g. Learning outcomes, assessment methods and key content stays unchanged. However, via course syllabus, it is possible to specify or change the course execution in each realization of the course, such as how the contact sessions are organized, assessment methods weighted or materials used.
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.
Schedule: 11.01.2021 - 25.02.2021
Teacher in charge (valid 01.08.2020-31.07.2022): Pekka Alestalo
Teacher in charge (applies in this implementation):
Contact information for the course (applies in this implementation):
CEFR level (applies in this implementation):
Language of instruction and studies (valid 01.08.2020-31.07.2022):
Teaching language: English
Languages of study attainment: English
CONTENT, ASSESSMENT AND WORKLOAD
real numbers, metric, norm, inner product, open and closed sets, continuous mappings, sequences and limits, compactness, completeness, connectedness.
Assessment Methods and Criteria
lectures, exercises, exam.
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
Substitutes the course Mat-1.2990 Foundations of Modern Analysis, and the course MS-C1540 Euclidean spaces.