Syllabus

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: 08.01.2024 - 22.02.2024

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 and course exam OR exam only

Workload

• valid for whole curriculum period:

  24+12 (4+2).

DETAILS

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 Language : English

  Teaching Period : 2022-2023 Spring III
  2023-2024 Spring III

  Enrollment :

  Registration ftakes place in Sisu (sisu.aalto.fi).

Description