Real Analysis

Language of Instruction

English

Pre-requirements

None

Learning Outcomes

After completed course, the students are expected to be able to

• Describe the basic differences between the rational and the real numbers.
• Understand and perform simple proofs
• Answer question concerning uniform convergence of concrete numerical sequences and series
• Give the definition of concepts related to metric spaces, such as continuity, compactness, completeness and connectedness
• Give the essence of the proof of Stone-Weierstrass' theorem, the contraction theorem as well as the existence of convergent subsequences using equicontinuity.

Contact Information

advice@mi.uib.no

Course offered (semester)

Autumn

Language of Instruction

English

Access to the Course Unit

Students will be able to demonstrate basic knowledge of key topics in classical real analysis. The course provides the basis for further studies within functional analysis, topology and function theory.

Learning Outcomes

After completed course, the students are expected to be able to

• Describe the basic differences between the rational and the real numbers.
• Understand and perform simple proofs
• Answer question concerning uniform convergence of concrete numerical sequences and series
• Give the definition of concepts related to metric spaces, such as continuity, compactness, completeness and connectedness
• Give the essence of the proof of Stone-Weierstrass' theorem, the contraction theorem as well as the existence of convergent subsequences using equicontinuity.

Pre-requirements

None

Recommended previous knowledge

MAT112 Calculus II

Subject Overlap

M211: 9 ECTS

Assessment methods

Oral examination

Grading Scale

The grading scale used is A to F. Grade A is the highest passing grade in the grading scale, grade F is a fail.

Contact Information

advice@mi.uib.no