MM549: Topology and Complex Analysis
Internal Course Code
Entry requirements
Academic preconditions
Students taking the course are expected to know the content of the 'Mathematical analysis'-part of the course MM533.
The course builds on the knowledge acquired in the courses Calculus and Mathematical and Numerical Analysis, and gives an academic basis for studying the topics probability theory, measure and integration and Banach spaces and Hilbert- and Banach Spaces, that are part of the degree.
Course introduction
Expected learning outcome
- in a written exam, apply the concepts and ideas, from the course syllabus, in concrete mathematical examples.
- formulate the written presentation in a mathematically correct way and argue for the validity of achieved results in stringent mathematical language.
Content
- Topological spaces, including construction methods and concepts of continuity, compactness and connectedness.
- Complete metric spaces
- Function spaces
- Normal topological spaces.
- Power series
- Analytic functions.
- Cauchy's integral theorem and integral formulas.
- The fundamental theorem of algebra.
- Taylor- and Laurent series of analytic functions.
- Poles and zeroes. The residue theorem and its applications to compute definite integrals.
Literature
Examination regulations
Exam element a)
Timing
Tests
Written exam
EKA
Assessment
Grading
Identification
Language
Duration
Examination aids
All common aids are allowed e.g. books, notes, computer programmes which do not use internet etc.
Physical calculators, the internet, and any form of generative artificial intelligence are not allowed during the exam. However, you may visit the course site in itslearning to open system "DE-Digital Exam". If you wish to use course materials from itslearning, you must download the materials to your computer the day before the exam. During the exam you cannot be sure that all course materials is accessible in itslearning.