Topology (Top)
Course content
This is a course on topological spaces and continuous maps. Main topics of this course are:
- Topological Spaces
- Subspace, Order, Product, Metric and Quotient Topologies
- Continuous Functions
- Connectedness and Compactness
- Countability and Separation Axioms
Secondary topics are:
- Retractions and fixed points
- Tychonoff Theorem
- Compactifications
- Vistas of algebraic topology
BSc Programme in Mathematics
This course will enable the participants to work with basic topological concepts and methods. At the end of the course, the students are expected to have attained:
Knowledge:
- understand and assimluate the concepts and methods of the main course topics including basic definitions and theorems
- understand secondary topics covered in the specific course
Skills:
- determine properties of a topological space such as Hausdorffness, countability, (path) connectedness, (local) compactness
- construct new spaces as subspaces, quotient spaces and product spaces of known ones
Competences:
- analyze concrete topological spaces using acquired knowledge and skills
- relate the theory of topological spaces and continuous maps to specific settings in past and future math courses
5 hours of lectures and 4 hours of exercises per week for 7 weeks.
Analyse 1 (An1)
- ECTS
- 7,5 ECTS
- Type of assessment
-
Continuous assessment
- Type of assessment details
- Two sets of homework problems and a final 2,5 hour written
in-class test in week 9
of the course. The homework contributes 30% and the final test contributes 70% towards the final grade. - Aid
- Only certain aids allowed (see description below)
Homework assignments: All aids allowed.
For the final written in class test: Handwritten notes and the (printed) lecture notes are allowed. - Marking scale
- 7-point grading scale
- Censorship form
- No external censorship
One internal examiner
- Re-exam
-
Consists of 2 elements:
- A 2,5 hour written in-class
test. Same requirements as for the ordinary exam. Only
certain aids allowed: handwritten notes and the (printed)
lecture notes; no electronic devices. A 15 min oral
examination (without preparation time) of the homework
sets (weighted 30%). Students can choose to keep the - results from their course work in which case they only
participate in the written test, or they can participate in the
15 minutes oral examination, in which case the score from
the oral examination will count as the homework. If
fewer than 10 people are signed up for the re-exam, the 2,5
hour written test will be replaced by a 25 min oral
examination (without preparation). In this case, students
who choose not to keep the results from their homework,
will participate in a 40 minutes oral examination of which 25
minutes substitute for the written test, and 15 minutes are
the examination of the 2 homework sets. The weights are
30% for homework and 70% for the oral exam substituting
the written test.
- A 2,5 hour written in-class
Criteria for exam assessment
The student should convincingly and accurately demonstrate the knowledge, skills and competences described under Intended learning outcome.
Single subject courses (day)
- Category
- Hours
- Lectures
- 35
- Preparation
- 141
- Theory exercises
- 28
- Exam
- 2
- English
- 206
Kursusinformation
- Language
- English
- Course number
- NMAA05010U
- ECTS
- 7,5 ECTS
- Programme level
- Bachelor
- Duration
-
1 block
- Placement
- Block 4
- Schedulegroup
-
B
- Capacity
- No limitation – unless you register in the late-registration period (BSc and MSc) or as a credit or single subject student.
- Studyboard
- Study Board of Mathematics and Computer Science
Contracting department
- Department of Mathematical Sciences
Contracting faculty
- Faculty of Science
Course Coordinator
- Jasmin Matz (4-7165787e447165786c326f7932686f)
Teacher
Jasmin Matz
Er du BA- eller KA-studerende?
Kursusinformation for indskrevne studerende