MM862: Selected topics in numerical anlysis II

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

• understand advanced principles of numerical thinking
• understand and work with numerical analysis in a broad range of applications
• compare and contrast the methods introduced in the course
• transfer the learning content to new problems
  
• 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 thorough understanding on the interplay between theoretical development, feasibility and computational efficiency

• 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
• adapt and transfer known concepts to new, related application scenarios
• to formulate the problems (including proofs) in a correct and formal mathematical language
• to analyze, apply and modify the introduced techniques

• Matrix analysis and matrix decompositions
• Iterative solutions of eigenvalue problems
• Design and analysis of computer experiments
• Model reduction
• Matrix manifolds and applications such as interpolation and optimization
• Matrix completion

(The precise selection complements or expands on the course "MM566").

• Intro phase: 28 hoursS
• kills training phase: 14 hours, hereof tutorials: 14 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.