MS-C1541 - Metric Spaces, Lecture, 10.1.2022-24.2.2022

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Please note! Course description is confirmed for two academic years, 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.

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: 10.01.2022 - 24.02.2022

Teacher in charge (valid for whole curriculum period):

Teacher in charge (applies in this implementation): Kalle Kytölä

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, exam.

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
Prerequisites

FURTHER INFORMATION

Further Information

  • valid for whole curriculum period:

    Teaching Period:

    2020-2021 Spring III

    2021-2022 Spring III

    Course Homepage: https://mycourses.aalto.fi/course/search.php?search=MS-C1541

    Registration for Courses: In the academic year 2021-2022, registration for courses will take place on Sisu (sisu.aalto.fi) instead of WebOodi.

Rules of Conduct - Students´ Rights and Responsibilities (in force from 1 August 2020)

Aalto University Code of Academic Integrity and Handling Violations Thereof