Real Analysis

Teaching semester

Autumn

Objectives and Content

The course includes axioms of real number systems, uniform convergence of sequences and series of functions, equicontinuity, compact and complete metric spaces, the inverse function theorem, the Stone-Weierstrass theorem and contraction maps.

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.

Required Previous Knowledge

None

Recommended Previous Knowledge

MAT112 Calculus II

Credit Reduction due to Course Overlap

M221: 10 ECTS

Access to the Course

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.

Compulsory Assignments and Attendance

Excercises

Forms of Assessment

Oral exam

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.