MM566: Selected topics in numerical anlysis I
The Study Board for Science
Teaching language: English
EKA: N300054102
Assessment: Second examiner: Internal
Grading: 7-point grading scale
Offered in: Odense
Offered in: Spring
Level: Bachelor
STADS ID (UVA): N300054101
ECTS value: 5
Date of Approval: 04-11-2024
Duration: 1 semester
Version: Approved - active
Comment
Entry requirements
Academic preconditions
Students taking the course are expected to:
- Have knowledge of elementary mathematical background as provided by the courses Calculus, Linear Algebra, Mathematical and Numerical Analysis and Ordinary Differential Equations
Basic skills in scientific programming may be helpful but are not mandatory
Course introduction
The aim of the course is to enrich the students' skills and range in numerical analysis and applied mathematics and to show prospects for possible thesis topics.
The student is enabled:
The student is enabled:
- understand advanced principles of numerical thinking
- understand and work with numerical methods in a broad range of applications
- compare and contrast the methods introduced in the course
- to make use of the techniques in practical applications
In relation to the competence profile of the degree it is the explicit focus of the course to:
- Provide the competence to analyze and apply mathematical models
- Provide a basic understanding on the interplay between theoretical development, feasibility and computational efficiency
The course provides the basis for MM862: Selected topics in numerical analysis II.
The course may be used as a basis for BAMM501: Bachelorproject in applied mathematics.
Expected learning outcome
The learning objective of the course is that the student demonstrates the ability to:
- know the definitions of the quantities and terms that were introduced in the lecture.
- relate the main purpose and raison d'être of every section of the whole lecture
- know the key ideas for the derivation of the main theorems and algorithms that are introduced in the lecture
- demonstrates the ability to cover some selected topics in full detail, including proof techniques
- to formulate the problems (including proofs) in a correct and formal mathematical language
Content
The following main topics are contained in the course: Introduction to one or more topics in numerical analysis.
This could, for example, be:
- Matrix analysis and matrix decompositions
- Iterative solutions of linear equation systems
- Iterative solutions of eigenvalue problems
- Design and analysis of computer experiments
- Model reduction
- Matrix manifolds and applications
- Numerical solution of stochastic differential equations, with application to e.g. European options
- Monte Carlo simulation of stochastic differential equations, with focus on variance reduction methods
- Multilevel Monte Carlo simulation of stochastic differential equations
Literature
Examination regulations
Exam element a)
Timing
April
Tests
Oral
EKA
N300054102
Assessment
Second examiner: Internal
Grading
7-point grading scale
Identification
Student Identification Card - Name
Language
Normally, the same as teaching language
Examination aids
To be announced during the course
ECTS value
5
Indicative number of lessons
Teaching Method
At the faculty of science, teaching is organized after the three-phase model ie. intro, training and study phase. The teaching method is based on a three phase model.
- Intro phase: 28 hours
- Skills training phase: 14 hours, hereof tutorials: 14 hours
- Study phase: 70 hours
- Preparation of exam incl. presentation: 13 hours
Total: 125 hours
Activities during the study phase:
- Reading of suggested literature
- Preparation of exercises in study groups
- Contributing to online learning activities related to the course
Teaching is centered on interaction and dialogue. In the intro phase, concepts, theories and models are introduced and put into perspective. In the training phase, students train their skills through exercises and dig deeper into the subject matter. In the study phase, students gain academic, personal and social experiences that consolidate and further develop their scientific proficiency. Focus is on immersion, understanding, and development of collaborative skills.
Teacher responsible
Timetable
Administrative Unit
Team at Registration
Offered in
Recommended course of study
Transition rules
Transitional arrangements describe how a course replaces another course when changes are made to the course of study.
If a transitional arrangement has been made for a course, it will be stated in the list.
See transitional arrangements for all courses at the Faculty of Science.