Course - Foundations of Analysis - TMA4225
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.
Recommended previous knowledge
The course is based on TMA4100/05/15/20 Calculus 1/2/3/4K and TMA4145 Linear Methods. Calculus 4K for students with their background from Mathematical Sciences.
Course materials
Will be announced at the start of the course.
Credit reductions
Course code | Reduction | From | To |
---|---|---|---|
SIF5052 | 7.5 |
Version: 1
Credits:
7.5 SP
Study level: Second degree level
Term no.: 1
Teaching semester: AUTUMN 2016
Language of instruction: English, Norwegian
-
- Mathematics
- Technological subjects
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.
For more information regarding registration for examination and examination procedures, see "Innsida - Exams"