MM549: Topology and Complex Analysis
Entry requirements
Academic preconditions
Course introduction
- have a fundamental understanding of the theory of topological spaces, complete metric spaces, function spaces, normal topological spaces and its applications.
- have a fundamental understanding of the theory of analytic functions and its applications
- be able to use the calculation of residues to compute important types of integrals
- be able to expand the most important holomorphic functions into power series and expand meromorphic functions into Laurent series
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.
Internet is 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.
ECTS value
Indicative number of lessons
Teaching Method
Teaching activities result in an estimated indicative distribution of the work effort of an average student in the following way:
- Intro phase (lectures) - 56 hours
- Training phase: 36 hours
- Study phase: 20
Lectures will introduce general concepts and theory and exercise sessions will be devoted to learning the material in depth.
Other study activities include studying the course material and preparing the weekly exercises, individually or through group work.