ACIT4330 Mathematical Analysis Course description

The student should have the following outcomes upon completing the course:

Knowledge

Upon successful completion of the course, the student:

• have advanced knowledge of how system administration and operations facilitate organizations
• have advanced knowledge of the terms and terminology used when system administration interfaces with an organization
• have advanced knowledge of processes applied to system administration in order to facilitate requests from other parts of an organization
• have deep knowledge of how an IT infrastructure is organized and what components it traditionally comprises of
• have a good understanding of the support architecture of an IT infrastructure, such as backup, issue tracking and configuration management

Skills

Upon successful completion of the course, the student:

• can analyze an IT infrastructure with regard to its components and their purpose
• can apply feature analysis in order to rank alternative components relative to their purpose
• can organize the flow of tasks in an operations team
• can propose ways to measure the performance of an operations team
• can leverage IaaS (cloud computing and virtual infrastructures) to provide systems, network and storage components to users
• can utilize infrastructure support services in order to leverage system deployment to users

General competence

Upon successful completion of the course, the student should:

• can discuss the role of system administration in an organization and society at large
• can analyze how operations can interface with the rest of an organization in order to improve overall proficiency

A course in analysis at bachelor level is an advantage, preferably with some knowledge of real numbers, cardinality, metric spaces and uniform convergence.

A student who has completed this course should have the following learning outcomes defined in terms of knowledge, skills and general competence:

Knowledge

On successful completion of the course the student:

• knows the relevance of a selection of mathematical models to real-world phenomena
• has a thorough understanding of how mathematical modelling and scientific computing are utilized in various industrialized settings
• has a repertoire of methods to solve and/or analyze ordinary and partial differential equations (ODEs and PDEs)
• knows how to analyze the dynamics of an ODE system
• has a thorough understanding of the definitions of a smooth manifold and the tangent space
• knows the definitions and algebra of tensors and differential forms on a smooth manifold

Skills

On successful completion of this course the student:

• is able to derive mathematical models from facts and first principles for a selection of dynamical systems
• can apply mathematical modelling techniques on scenarios relevant to industry
• can implement mathematical models within the context of applied computer and information technology
• is able to analyse ODE systems and use bifurcation theory to elucidate the qualitative behavior of the systems
• is able to implement and use a selection of numerical methods for solving ODEs and PDEs
• is able to give examples of smooth manifolds and prove their smooth manifold property from the definition
• is able to use the geometric concepts and tools associated with smooth manifolds in the analysis of mathematical problems within mathematics, physics and engineering

General competence

On successful completion of this course the student:

• is aware of the usefulness and limitations of mathematical modelling as well as of pitfalls frequently encountered in modelling and simulation
• is able to discuss properties of a system using the equations of the mathematical model
• can explain and use numerical methods and interpret results of numerical simulations
• is aware of the role of smooth manifolds as one of the most fundamental concepts in mathematics and physics

The course is organized as a series of lectures and seminars where the subject material is presented and discussed. Between these sessions the students should work with problem solving, implementation of numerical methods and model simulations. The last part of the semester, students will work with a compulsory individual project supervised by the course lecturer. The project will involve studies and analyses of a mathematical model and a rather extensive implementation of the numerical solution of the model. This will result in a report that should be 2000 - 4000 words of length plus figures.

• General topology, including locally compact Hausdorff spaces
• Measure theory, including Riesz¿ representation theorem
• Completeness of Lp spaces, product measures, and complex measures with the Radon- Nikodym theorem
• Fourier analysis, including the inversion theorem
• Complex function theory, including the Cauchy- and Liouville theorems, and harmonic functions

Lecturer might exclude or include topics depending on the students attending the course.

The report of the individual project must be approved before examination.

The course is concluded by an individual oral examination. As a part of this examination, the student will provide a brief presentation of her/his project.

The oral exam cannot be appealed.

The student can bring his/her own project report. The student is also allowed to make use of his/her own computer for the presentation.

For the final assessment a grading scale from A to E is used, where A denotes the highest and E the lowest pass grade, and F denotes a fail.

For the final assessment a grading scale from A to E is used, where A denotes the highest and E the lowest pass grade, and F denotes a fail.

Two internal examiners will assess the individual report and the oral presentation. External examiner is used periodically.

• Approaches to scientific computing and implementation of mathematical models
• Principles of modelling and derivation of mathematical models
• Analysis, numerical solution and bifurcations of ODEs
• Numerical methods for computation of solutions of ODEs and PDEs