EPN-V2

ACIT4330 Mathematical Analysis Course description

Course name in Norwegian
Mathematical Analysis
Weight
10.0 ECTS
Year of study
2019/2020
Course history
Curriculum
SPRING 2020
Schedule
Programme description

  • Introduction

    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.

  • Recommended preliminary courses

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

  • Required preliminary courses

    None.

  • Learning outcomes

    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.

  • Content

    • 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.

  • Teaching and learning methods

    Lectures and tutored exercises.

  • Course requirements

    None.

  • Assessment

    Individual oral exam.

    The oral exam cannot be appealed.

  • Permitted exam materials and equipment

    None.

  • Grading scale

    Pass/fail.

  • Examiners

    Two internal examiners. External examiner is used periodically.