course-details-portlet

TMA4225 - Foundations of Analysis

About

Examination arrangement

Examination arrangement: Written examination
Grade: Letters

Evaluation Weighting Duration Grade deviation Examination aids
Skriftlig 100/100 4 timer

Course content

The modern concept of integral was introduced on April 29, 1901, in a short article by Henri Lebesgue. That article opened a new chapter of analysis. The flaws of the Riemann Integral will be pointed out, and the Lebesgue integral will be introduced to remedy the situation. Key concepts include measure theory including sigma-algebras, measurable spaces, measurable functions, outer measures, construction of the Lebesgue measure, and product measures. The course also covers the classical convergence theorems, Fubini's theorem, functions of bounded variation, and the fundamental theorem of integral calculus.

Learning outcome

1. Knowledge. The student masters basic concepts from measure theory, including sets of measure zero, measurable functions, the Lebesgue integral and Lebesgue spaces. The student has an overview of the central results of the theory of Lebesgue integration, including convergence theorems and Fubini's theorem. Moreover, the student is familiar with applications of measure theory to probability theory.

2. Skills. The student is able to perform operations using the Lebesgue integral and Lebesgue spaces. Moreover, the student is able to apply integration theory in one or several variables to formulate and solve problems in mathematics and technology, including problems involving discontinuous data.

Learning methods and activities

Lectures and exercises. The lectures will be given in English if the course is attended by students who don't master a Scandinavian language. If the course is taught in English, the exam will be given only in English. Students are free to choose Norwegian or English for written assessments. A makeup exam may be given as an oral examination.

Course materials

Will be announced at the start of the course.

Credit reductions

Course code Reduction From To
SIF5052 7.5
More on the course
Facts

Version: 1
Credits:  7.5 SP
Study level: Second degree level

Coursework

Term no.: 1
Teaching semester:  AUTUMN 2016

Language of instruction: English, Norwegian

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Subject area(s)
  • Mathematics
  • Technological subjects
Contact information
Course coordinator:

Department with academic responsibility
Department of Mathematical Sciences

Examination

Examination arrangement: Written examination

Term Status code Evaluation Weighting Examination aids Date Time Examination system Room *
Autumn ORD Skriftlig 100/100 2016-12-02 09:00
Room Building Number of candidates

Examination arrangement: Oral examination

Term Status code Evaluation Weighting Examination aids Date Time Examination system Room *
Summer KONT Oral examination 100/100 2017-08-07
Room Building Number of candidates
  • * The location (room) for a written examination is published 3 days before examination date. If more than one room is listed, you will find your room at Studentweb.
Examination

For more information regarding registration for examination and examination procedures, see "Innsida - Exams"

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