PENG9630 Internet Architecture and Measurements Course description

An individual, oral examination. The examination will address both general topics from within the course and the specific project developed by the student.

The oral examination cannot be appealed.

Bachelor's or master's degree in engineering science or related fields.

The student's own project.

Pass or fail.

The course consists of three modules.

In the first module, the course staff and guest lecturers will provide a high-level overview of different parts of the internet's architecture.

The second part is a set of practical exercises that are designed to match the topics discussed in the first module.

The third module will consist of a set of seminars, where students elaborate on different parts of the architecture and how they can be assessed and monitored.

Two examiners. External examiner is used periodically.

A thorough knowledge of advanced calculus, including ordinary and partial differential equations. It is a great advantage if students are familiar with linear algebra and Fourier and Laplace transform theory. In terms of programming, some experience in implementing various numerical methods, including schemes for solving partial differential equations is recommended. Some knowledge of mathematical analysis, modern physics or physiology is recommended, depending on their specialisation.

Introductory module:

• Principles of modelling and derivation of mathematical models
• Analysis of ordinary differential equations (ODEs)
• Linear partial differential equations (PDEs)
• Prominent results from functional analysis and their application to ODEs and PDEs
• Numerical methods for computing of solutions of PDEs

Functional analysis:

• Completeness for normed spaces
• Hilbert spaces, compact and diagonalisable operators
• Theory of topological vector spaces
• Test functions, distributions and the Fourier transform
• Sobolev spaces and fundamental solutions of partial differential equations

Biosystems:

• Mathematical models for biological systems
• Analytical and numerical methods for simulation of system response
• Actuators and sensors for stimulation and measurements of biological systems
• Interaction of biological and measurement system

Modern physics:

• Monte Carlo techniques
• Splines and other expansion techniques
• Applications of expansions in spherical harmonics
• Numerical problems in general relativity and quantum physics
• Manifolds with geometric structures central to physics and engineering.

Within all specializations, the content may be adjusted to accommodate for the research area of each PhD candidate.

All aids are permitted.

Pass or fail.

The presentation will be assessed by the course leader, whereas the tool summary document will be assessed by the course leader together with an additional examiner. External examiner is used periodically.