MM517: Measure and Integration Theory (5 ECTS)

STADS: 13014401

Level
Bachelor course

Teaching period
The course is offered in the spring semester.

Teacher responsible

Email: szymanski@imada.sdu.dk

Timetable

Group	Type	Day	Time	Classroom	Weeks
Common	I	Wednesday	12-14	U140	5-9,11
Common	I	Wednesday	08-10	U20	10
Common	I	Friday	08-10	U48A	5-11
H1	TE	Thursday	10-12	U31	6-11
M1	TE	Thursday	10-12	U31	6-11

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Comment:
Ubegrænset deltagerantal. Fælles undervisning med MM543.

Prerequisites:
None

Academic preconditions:
The content of MM533 Mathematical and Numerical Analysis and MM505 Linear algebra or MM538 Algebra and linear algebra is assumed to be known.

Course introduction

The aim of the course is to give a solid presentation of Measure and Integration Theory and thereby give an introduction to modern Functional Analysis. The course will also give the mathematical foundation for modern Probability Theory.

The course builds on the knowledge acquired in the course Mathematical & Numerical Analysis, and gives an academic basis for studying Probability and Functional Analysis, that are part of the degree.

In relation to the competence profile of the degree it is the explicit focus of the course to:

Give the competence to handle complex situations in study
Give skills to:

a) apply the thinking and terminology from the subject's basic disciplines.

b) analyze and evaluate the theoretical and practical problems for the application of a suitable mathematical model.

Give knowledge and understanding of:

a) basic knowledge generation, theory and methods in mathematics.

b) how to conduct analyses using mathematical methods and critically evaluate scientific theories and models.

Expected learning outcome

By the end of the course the student should be able to:

use the basic concepts of the theory, in particular sigma-algebras, measurability and integration
use the methods from the theory to solve concrete problems in Analysis, in particular concerning applications of the convergence theorems for integrals and Fubini's Theorem
give an oral presentation of the statements and proofs related to any subject on a previous given list of topics within the course syllabus
formulate the oral presentation a mathematically correct way

Subject overview
The following main topics are contained in the course: Sigma-algebras and measures, measurable mappings, integration with respect to measures, the Lebesgue measure on the real line and on Rk, product measures, Lp-spaces.

Literature

Meddeles ved kursets start.

Website
This course uses e-learn (blackboard).

Prerequisites for participating in the exam
None

Assessment and marking:

Mandatory assignments. Pass/fail, internal assessment by teacher. (5 ECTS).

Expected working hours
The teaching method is based on three phase model.
Intro phase: 28 hours
Skills training phase: 14 hours, hereof:
- Tutorials: 14 hours

Educational activities

Reading of suggested literature
Preparation of exercises in study groups

Educational form
Teaching is centred on interaction and dialogue. In the intro phase, concepts, theories and models are introduced and put into perspective. In the training phase, students train their skills through exercises and dig deeper into the subject matter. In the study phase, students gain academic, personal and social experiences that consolidate and further develop their scientific proficiency. Focus is on immersion, understanding, and development of collaborative skills.

Language
This course is taught in Danish or English, depending on the lecturer. However, if international students participate, the teaching language will always be English.

Remarks

The course is taught jointly with: MM543 Measure and Integration and Banach Spaces (1st half)

The course cannot be chosen by students who took: MM543 or MM548 Measure and Integration and Banach Spaces

Course enrollment
See deadline of enrolment.

Tuition fees for single courses
See fees for single courses.