MM517: Measure and Integration Theory

Study Board of Science

Teaching language: Danish or English depending on the teacher, but English if international students are enrolled
EKA: N300031102
Assessment: Second examiner: None
Grading: Pass/Fail
Offered in: Odense
Offered in: Spring
Level: Bachelor

STADS ID (UVA): N300031101
ECTS value: 5

Date of Approval: 01-11-2022


Duration: 1 semester

Version: Archive

Comment

The course is taught jointly with: MM543 Measure and Integration and Banach Spaces (1st half) a.nd MM548: Measure and Integration and Banach spaces (7.5 ECTS)

Entry requirements

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

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:
  • apply the thinking and terminology from the subject's basic disciplines.
  • analyze and evaluate the theoretical and practical problems for the application of a suitable mathematical model.
Give knowledge and understanding of: 
  • basic knowledge generation, theory and methods in mathematics. 
  • 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

Content

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

See itslearning for syllabus lists and additional literature references.

Examination regulations

Exam element a)

Timing

Spring

Tests

Mandatory assignments

EKA

N300031102

Assessment

Second examiner: None

Grading

Pass/Fail

Identification

Full name and SDU username

Language

Normally, the same as teaching language

Examination aids

To be announced during the course

ECTS value

5

Indicative number of lessons

42 hours per semester

Teaching Method

At the faculty of science, teaching is organized after the three-phase model ie. intro, training and study phase. These teaching activities are reflected in an estimated allocation of the workload of an average student as follows:
  • Intro phase (lectures) - 28 hours
  • Training phase: 14 hours
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.

Educational activities:
  • Reading of suggested literature
  • Preparation of exercises in study groups

Teacher responsible

Name E-mail Department
Wojciech Szymanski szymanski@imada.sdu.dk Analyse

Timetable

Administrative Unit

Institut for Matematik og Datalogi (matematik)

Team at Educational Law & Registration

NAT

Offered in

Odense

Recommended course of study

Profile Education Semester Offer period

Transition rules

Transitional arrangements describe how a course replaces another course when changes are made to the course of study. 
If a transitional arrangement has been made for a course, it will be stated in the list. 
See transitional arrangements for all courses at the Faculty of Science.