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Dansk English

MM543: Measure and Integration and Banach spaces (10 ECTS)

STADS: 13014701

Level
Bachelor course

Teaching period
The course is offered in the spring semester.

Teacher responsible
Email: dkyed@imada.sdu.dk

Additional teachers
szymanski@imada.sdu.dk
barlak@imada.sdu.dk

Timetable
Group Type Day Time Classroom Weeks Comment
Common I Tuesday 08-10 U140 5-7,9-11,13-14
Common I Tuesday 08-10 U155 15-19,21
Common I Wednesday 08-10 U20 5,19
Common I Thursday 12-14 U20 16
Common I Friday 12-14 U166 6
Common I Friday 12-14 U20 7,9-11,13-15,17-18,21
H1 TE Wednesday 12-14 U14 15
H1 TE Wednesday 14-16 U155 16
H1 TE Wednesday 12-14 U154 19
H1 TE Thursday 10-12 U24 6-7,21
H1 TE Friday 10-12 U14 5,9-11,13-14
H1 TE Friday 08-10 U155 17-18
H2 TE Tuesday 10-12 U157 10
H2 TE Wednesday 14-16 U157 11,18
H2 TE Wednesday 14-16 U142 14
H2 TE Wednesday 14-16 U14 15
H2 TE Wednesday 16-18 U157 16
H2 TE Thursday 14-16 U157 5,7,9,21
H2 TE Thursday 08-10 U145 6
H2 TE Thursday 14-16 U156 13
H2 TE Thursday 12-14 U157 17,19
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Comment:
Ubegrænset deltagerantal. Fælles undervisning med MM514/MM815, MM517 og MM548.

Prerequisites:
None

Academic preconditions:
Material from MM533 Mathematical and Numerical Analysis (or MM535 Topology) together with MM505 Linear Algebra or MM538 Algebra and Linear Algebra or MM540 Mathematical Methods for Economics should be known.

Course introduction
To introduce measure and integration theory as well as modern functional analysis focused on Hilbert and Banach space theory. Moreover, this course lays foundation for further study of probability theory.

Qualifications
At the conclusion of the course the student should be able to:

  • use methods from the theory to solve practical problems, especially related to the integral convergence theorems, Fubini’s theorem, and calculate Fourier series
  • present statements and proofs of items from an a priori given list of topics
  • Answer additional questions from teachers and examiners around the central concepts and results from the above list
Expected learning outcome
At the conclusion of the course the student should be able to:

  • Understand the basic theory in this area, including in particular concepts of sigma-algebra, measurability, integral
  • use methods from the theory to solve problems related to measure and integration and Banach space theory
  • give an oral and written presentation in correct mathematical language
Subject overview
sigma-algebras, measurable maps, measure and integration with respect to measure, the Lebegue measure on the real line and on Rn, product measure, Lp-spaces, Hilbert spaces, Fourier series in Hilbert space, the projection theorem, introductory Banach space theory, the open mapping theorem and the Hahn-Banach extension theorem.

Literature
There isn't any litterature for the course at the moment.

Website
This course uses e-learn (blackboard).

Prerequisites for participating in the exam
None

Assessment and marking:
  1. Mandatory assignment 1. Evaluated on a pass/fail basis by lecturer (2,5 ECTS).
  2. Mandatory assignment 2. Evaluated on a pass/fail basis by lecturer (2,5 ECTS).
  3. Oral exam. Evaluated by external censorship by the Danish 7-mark scale (5 ECTS).
Expected working hours
The teaching method is based on three phase model.
Intro phase: 56 hours
Skills training phase: 28 hours, hereof:
 - Tutorials: 28 hours

Educational activities Study phase: 20 hours

Language
This course is taught in Danish or English, depending on the lecturer.

Course enrollment
See deadline of enrolment.

Tuition fees for single courses
See fees for single courses.