Please note! Course description is confirmed for two academic years, which means that in general, e.g. Learning outcomes, assessment methods and key content stays unchanged. However, via course syllabus, it is possible to specify or change the course execution in each realization of the course, such as how the contact sessions are organized, assessment methods weighted or materials used.

LEARNING OUTCOMES

After this course you will know how to apply real analysis methods in research.

 

Credits: 5

Schedule: 28.02.2022 - 08.04.2022

Teacher in charge (valid for whole curriculum period):

Teacher in charge (applies in this implementation): Juha Kinnunen

Contact information for the course (applies in this implementation):

CEFR level (valid for whole curriculum period):

Language of instruction and studies (applies in this implementation):

Teaching language: English. Languages of study attainment: English

CONTENT, ASSESSMENT AND WORKLOAD

Content
  • valid for whole curriculum period:

    Lebesgue spaces (Hölder's and Minkowski's inequalities, Riesz-Fischer theorem, dual spaces and weak convergence), Hardy-Littlewood maximal function (Vitali covering theorem, Marcinkiewicz interpolation theorem, maximal function theorem, Lebesgue's differentiation theorem), convolution approximations, differentiation of Radon measures (Besicovitch covering theorem, Lebesgue points), Radon-Nikodym theorem, Riesz representation theorem, weak convergence and compactness for Radon measures, Sobolev spaces (Poincare and Sobolev inequalities).

     

Assessment Methods and Criteria
  • valid for whole curriculum period:

    Teaching methods: lectures and tutorials

    Assessment methods: homework assignments and attendance (100%)

     

Workload
  • valid for whole curriculum period:

    Contact hours 36 h

    Self-study ca 100h

     

DETAILS

Substitutes for Courses
Prerequisites

FURTHER INFORMATION

Further Information
  • valid for whole curriculum period:

    Teaching Language : English

    Teaching Period : 2022-2023 No teaching
    2023-2024 Spring IV

    Enrollment :

    Registration takes place in Sisu (sisu.aalto.fi).