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Dansk English

MM549: Topology and Complex Analysis (10 ECTS)

STADS: 13017401

Level
Bachelor course

Teaching period
The course is offered in the spring semester.

Teacher responsible
Email: qin@imada.sdu.dk

Timetable
Group Type Day Time Classroom Weeks Comment
Common I Monday 12-14 U155 6-12,15-18,20
Common I Monday 12-14 U8 19
Common I Tuesday 10-12 U155 6,8,10,14,19
Common I Tuesday 10-12 U151 21
Common I Wednesday 10-12 U155 7,18,20-21
Common I Wednesday 12-14 U20 9
Common I Wednesday 10-12 U17 11
Common I Wednesday 10-12 U23 12
Common I Wednesday 10-12 U56 14
Common I Wednesday 10-12 U31 15
Common I Wednesday 10-12 U20 16-17
H1 TE Tuesday 08-10 U151 12
H1 TE Tuesday 10-12 U155 15-17,20
H1 TE Tuesday 12-14 U151 21
H1 TE Wednesday 10-12 U155 8,19
H1 TE Wednesday 10-12 U20 9
H1 TE Wednesday 10-12 U31 10
H1 TE Friday 08-10 U155 7-12,14-16,18-21
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Comment:
Ubegrænset deltagerantal

Prerequisites:
None

Academic preconditions:
Students taking the course are expected to:
  • Know the content of the course Mathematical analysis in MM533


Course introduction
The first purpose of the course is to develop further the concepts, which are introduced in Mathematical and Numerical Analysis, in more advanced settings. The second objective of the course is to give the students a fundamental knowledge of the theory of analytic functions, which will enable them to use this important theory in other areas of Mathematics and Applied Mathematics.

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.

In relation to the competence profile of the degree it is the explicit focus of the course to:

  • 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
The learning objective of the course is that the student demonstrates the ability to:
  • give an oral presentation of the statement and proofs related to any subject on a previously given list of topics within the course's syllabus
  • formulate the oral or written presentation in a mathematically correct way
Subject overview
The following main topics are contained in the course:
  • 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
    Meddeles ved kursets start


Website
This course uses e-learn (blackboard).

Prerequisites for participating in the exam
None

Assessment and marking:
  1. Obligatory assignments, during the course. Pass7fail, internal evaluation by teacher. (0 ECTS).
  2. Written exam. Danish 7-mark scale, external marking.  (10 ECTS). (13017402).
A closer description of the exam rules will be posted under 'Course Information' on Blackboard.
 

 


Expected working hours
The teaching method is based on three phase model.
Intro phase: 56 hours
Skills training phase: 44 hours, hereof:
 - Tutorials: 44 hours

Educational activities

Educational form
Lectures will introduce general concepts and theory and exercise sessions will be devoted to learn material in depth. Interactive teaching will be used and, if possible, smart boards.
Studying the course material and preparing the weekly exercises, individually or through group work.

Language
This course is taught in Danish or English, depending on the lecturer. However, if international students participate, the teaching language will always be English.

Course enrollment
See deadline of enrolment.

Tuition fees for single courses
See fees for single courses.