EPN

ACIT4330 Mathematical Analysis Emneplan

Engelsk emnenavn
Mathematical Analysis
Studieprogram
Master's Programme in Applied Computer and Information Technology
Omfang
10.0 stp.
Studieår
2019/2020
Pensum
VÅR 2020
Timeplan
Programplan
Emnehistorikk

Innledning

The course focuses on a broad and rigorous approach necessary to do reliable research within the area of analysis and offers a deeper theoretical understanding that can supplement and be leveraged alongside the knowledge and skills from the previous two specialization courses.

The course provides a perfect basis for any person who wants to venture into this area. It is also a springboard for functional analysis and operator algebras.

Anbefalte forkunnskaper

A course in analysis at bachelor level is an advantage, preferably with some knowledge of real numbers, cardinality, metric spaces and uniform convergence.

Forkunnskapskrav

None.

Læringsutbytte

A student who has completed this course should have the following learning outcomes defined in terms of knowledge, skills and general competence:

Knowledge

On successful completion of this course the student:

  • has basic knowledge of point set topology
  • has basic knowledge of measure theory
  • has basic knowledge of Fourier analysis
  • has basic knowledge of complex function theory

Skills

On successful completion of this course the student:

  • is able to prove some of the most fundamental results of mathematical analysis
  • is able to apply basic notions and results in proofs and derivations

General competence

On successful completion of this course the student:

  • is able to understand literature within these topics
  • can transfer with trust this understanding to own research.

Innhold

  • General topology, including locally compact Hausdorff spaces
  • Measure theory, including Riesz¿ representation theorem
  • Completeness of Lp spaces, product measures, and complex measures with the Radon- Nikodym theorem
  • Fourier analysis, including the inversion theorem
  • Complex function theory, including the Cauchy- and Liouville theorems, and harmonic functions

Lecturer might exclude or include topics depending on the students attending the course.

Arbeids- og undervisningsformer

Lectures and tutored exercises.

Arbeidskrav og obligatoriske aktiviteter

None.

Vurdering og eksamen

Individual oral exam.

The oral exam cannot be appealed.

Hjelpemidler ved eksamen

None.

Vurderingsuttrykk

Pass/fail.

Sensorordning

Two internal examiners. External examiner is used periodically.