course-details-portlet

TMA4225

Foundations of Analysis

Choose study year
Credits 7.5
Level Second degree level
Course start Autumn 2025
Duration 1 semester
Language of instruction English
Location Trondheim
Examination arrangement School exam

About

About the course

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.

Further on evaluation

The retake exam may be given as an oral examination. The retake exam is in August.

Students are free to choose Norwegian or English for written assessments.

Course materials

Will be announced at the start of the course.

Credit reductions

Course code Reduction From
SIF5052 7.5 sp
This course has academic overlap with the course in the table above. If you take overlapping courses, you will receive a credit reduction in the course where you have the lowest grade. If the grades are the same, the reduction will be applied to the course completed most recently.

Subject areas

  • Mathematics
  • Technological subjects

Contact information

Course coordinator

Department with academic responsibility

Department of Mathematical Sciences