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Dansk English

MM549: Topology and Complex Analysis (10 ECTS)

STADS: 13014901

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 U146 19-21
Common I Tuesday 10-12 U142 16
Common I Tuesday 10-12 U154 18
Common I Wednesday 10-12 U31 6
Common I Wednesday 10-12 U50A 7-8
Common I Wednesday 10-12 U155 9-11
Common I Wednesday 10-12 U146 12,16,18,20-21
Common I Wednesday 10-12 U156 13
Common I Wednesday 10-12 U142 17,19
Common I Friday 12-14 U56 6
Common I Friday 12-14 U153 7
Common I Friday 12-14 U145 8,10
Common I Friday 12-14 U146 9,11,13,16
Common I Friday 12-14 U142 12
H1 TE Monday 12-14 U146 7-14,17
H1 TE Monday 12-14 U154 18
H1 TE Tuesday 14-16 U155 18,21
H1 TE Tuesday 14-16 U146 19
H1 TE Thursday 08-10 U69A 7,9
H1 TE Thursday 08-10 U24 8
H1 TE Thursday 08-10 U155 13
H1 TE Thursday 08-10 U146 14,16
H1 TE Friday 12-14 U146 17,20-21
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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
  • answer supplementary questions from the teacher and the censor on definitions and results from the course syllabus
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. Mandatory assignments. Evaluated by Danish 7-mark scale, internal censorship. 5 ECTS
  2. Oral examination. Evaluated by Danish 7-mark scale, external censorship. 5 ECTS
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.