Kursens beskrivning

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: 24.02.2022 - 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.

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:

  Substitutes for Courses

Prerequisites

• valid for whole curriculum period:

  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.

Beskrivning