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.

None

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.