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. The key words are measure theory including sigma-algebras, measurable spaces, measurable functions, outer measures, construction of the Lebesgue measure. The course also covers the classical convergence theorems, functions of bounded variation, and the fundamental theorem of integral calculus.

Learning outcome

The aim of the course is to develop the students' understanding of the main concepts of real analysis, and enable them to make use of the basic theorems of measure and integration theory.

Learning methods and activities

Lectures, exercises and midterm exam.
The final grade in the course is based on portfolio assessment. The portfolio comprises a written final examination (80%) and on midterm exam(s) (20%). The midterm(s) only count(s) positively. The results for the constituent parts are given as percentage points, while the grade for the whole portfolio (course grade) is given as a letter grade. The lectures will be given in English if they are attended by students from the Master's Programme in Mathematics for International students. 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.

Course materials

Will be announced at the start of the course.

Credit reductions