URL study guide
https://tue.osiris-student.nl/onderwijscatalogus/extern/cursus?cursuscode=2MBA40&collegejaar=2025&taal=enDescription
- Metric spaces and normed vector spaces
- Real numbers, supremum and infimum
- Sequences
- Series, series of positive terms, convergence tests
- Subsequences, lim inf, lim sup
- Point-set topology of metric spaces
- Closed, complete and compact sets in metric spaces
- Limits and continuity of functions between metric spaces
- Limits and continuity of real-valued functions
Objectives
The student is able to apply logic and set theory to problems in basic real analysis and can give simple proofs.The student can reproduce the definitions, propositions, lemmas, theorems and corollaries introduced in the course.
The student can determine the supremum and infimum of an indicated set of real numbers and can prove that the supremum and infimum are equal to the values found.
The student can determine whether a limit of a sequence exists and prove their answer using limit theorems.
The student can determine whether a series converges and prove their answer using tests for convergence and divergence.
The student can construct subsequences with a certain property, can determine the values of the lim inf and the lim sup of a sequence and can use conclusions about these numbers in the solution of other problems.
The student can prove simple statements in point-set topology of metric spaces.
The student can determine the limits of functions, can prove whether a function is continuous in a point, and can apply important theorems such as the intermediate value theorem and extreme value theorem.