Type of course

The subject can be taken as a singular course.

• The PhD course is primarily open to UiT's PhD students (Category 1).

One or more of these categories of course students may also

be admitted:

• Category 2: Participants in the Associate Professor programme that fulfil the educational requirements.
• Category 3: Doctoral students from other universities.
• Category 4: People with a minimum of a master's degree (or equivalent), who have not been admitted to a doctoral programme.

Admission requirements

Course content

The objective of the course is to give a good understanding of some basic concepts in mathematical analysis.

Concepts from real analysis are discussed. Rational and real numbers, countable and uncountable sets are introduced. Also basic topological concepts such as open, closed, bounded and compact sets are introduced. Numerical sequences, series and properties of continuous and differentiable functions are thoroughly discussed. Riemann integral is introduced and its properties are studied. Sequences and series of functions are studied in connection with continuity, integration and differentiation.

Objectives of the course

Knowledge:
After passing the course, the student is expected to be able to

• Account for the main concepts of real analysis.
• Understand and use the basic principles in mathematical analysis on a relatively high level in the forefront of knowledge in the field.

Skills:
After passing the course, the student is expected to be able to

• Solve relatively advanced problems connected to mathematical analysis of high international standard.

Habits of mind:
After passing the course, the student is expected to be able to

• Formulate and solve complicated problems devoted to Mathematical Analysis in a way that enables communication of research on high level in the field.

Language of instruction and examination

Teaching methods

Assessment

Written exam: Passed/Not passed.

A re-sit exam will be arranged for this course

Recommended reading/syllabus