MM543: Measure and Integration and Banach spaces
Study Board of Science
Teaching language: Danish or English depending on the teacher, but English if international students are enrolled
EKA: N300037112, N300037102
Assessment: Second examiner: External, Second examiner: None
Grading: 7-point grading scale, Pass/Fail
Offered in: Odense
Offered in: Spring
Level: Bachelor
STADS ID (UVA): N300037101
ECTS value: 10
Date of Approval: 01-11-2022
Duration: 1 semester
Version: Archive
Comment
Entry requirements
The course cannot be chosen by students who took: MM517 Measure and Integration, or MM514 Hilbert and Banach Spaces.
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 og MM568 should be known.
Course introduction
The aim of the course is 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. The course builds on the knowledge acquired in the course Mathematical & Numerical Analysis, and gives an academic basis for studying Probability, that is 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
The learning objective of the course is that the student demonstrates the ability 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
- 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
Content
The following main topics are contained in the course:
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 Radon-Nikodym theorem.
Literature
Examination regulations
Exam element b)
Timing
June
Tests
Oral exam
EKA
N300037112
Assessment
Second examiner: External
Grading
7-point grading scale
Identification
Student Identification Card
Language
Normally, the same as teaching language
Duration
30 minutes
Examination aids
To be announced during the course
ECTS value
5
Exam element a)
Timing
Spring
Tests
Mandatory assignment
EKA
N300037102
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
Teaching Method
At the faculty of science, teaching is organized after the three-phase model ie. intro, training and study phase.
- Intro phase (lectures) - 56 hours
- Training phase: 28 hours
- Study phase: 20 hours
Form of instruction:
- Reading of suggested literature
- Preparation of exercises in study groups
Educational activities: 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.
Teacher responsible
Timetable
Administrative Unit
Team at Educational Law & Registration
Offered in
Recommended course of study
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.