Graphs and Groups
Course content
This course covers a number of fundamental topics concerning groups of graph automorphisms, with an emphasis on group-theoretic notions and results.
Topics include:
1. Fundamentals of graph theory and of group theory
2. Graph automorphisms, transitive graphs
3. Group actions on graphs
4. Cayley graphs, Schreier graphs
5. Fundamental group of a graph, coverings
6. Free group: definition, elementary properties
7. Subgroups of free groups
8. Hanna Neumann conjecture
MSc Programme in Mathematics
MSc Programme in Mathematics with a minor subject
After completing the course, the student will have:
Knowledge about the subjects mentioned in the
description of the content.
Skills to solve problems concerning the
material covered.
The following Competences:
- Have a good understanding of the fundamental concepts and results presented in lectures, including a thorough understanding of various proofs.
- Establish connections between various concepts and results, and use the results discussed in lecture for various applications.
- Be in control of the material discussed in the lectures to the extent of being able to solve problems concerning the material covered.
- Be prepared to work with abstract concepts (from Graph Theory and Group Theory).
- Handle complex problems concerning topics within the areas of Graph Theory and Group Theory.
5 hours of lectures and 4 hours of exercises per week for 7 weeks
Basic group theory and linear algebra, as covered by the courses
LinAlg and Alg1 or equivalent.
Academic qualifications equivalent to a BSc degree is
recommended.
- ECTS
- 7,5 ECTS
- Type of assessment
-
Continuous assessment
- Type of assessment details
- Two written homework assignments and a final 3 hours in-class written exam. Each of the two written homework assignments counts 25% towards the final grade; the students will be given 5 days to work on each. The final 3 hours in-class written exam counts 50% towards the final grade, and it takes place in week 9.
- Aid
- Only certain aids allowed
All aids allowed for the two written homework assignments. The final 3 hours in-class written exam is without aids.
- Marking scale
- 7-point grading scale
- Censorship form
- No external censorship
One internal examiner
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
- 130
- Theory exercises
- 28
- Exam
- 13
- English
- 206
Kursusinformation
- Language
- English
- Course number
- NMAK23004U
- ECTS
- 7,5 ECTS
- Programme level
- Full Degree Master
- Duration
-
1 block
- Placement
- Block 4
- Schedulegroup
-
B
- Capacity
- no limit.
The number of seats may be reduced in the late registration period. - Studyboard
- Study Board of Mathematics and Computer Science
Contracting department
- Department of Mathematical Sciences
Contracting faculty
- Faculty of Science
Course Coordinator
- Damian Longin Osajda (2-6772437064776b316e7831676e)
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Courseinformation of students