Syllabus - Master's Programme in Engineering Mathematics

Outcomes

The Master’s Programme in Engineering Mathematics will satisfy the growing need of mathematically educated personnel within industry, society and various areas of technology. The Master’s Programme in Engineering Mathematics aims to give the students a good basis for work in a wide variety of companies and other private and state-owned organisations that conduct activities and the development of technology in which increased knowledge of mathematical methods and mathematical modelling is in great demand, for example in information technology, the internet and computer technology, economics and finance, medicine and biotechnology, energy and the environment.

Knowledge and Understanding

On completion of the degree programme the student shall be able to:

• demonstrate comprehensive knowledge and understanding of fundamental mathematical models, concepts and principles and how they are applied in problem-solving, as well as being able to explain suppositions and limitations with these models, concepts and methods,
• demonstrate comprehensive knowledge and understanding of how mathematical theories, concepts and methods can be applied to form optimal algorithms and solutions in technology,
• demonstrate basic knowledge of important programming languages for technology and mathematical software.

Aptitudes and Accomplishments

Aptitudes and Accomplishments
On completion of the degree programme the student shall be able to:

• give technology problems expressed in non-mathematical language a mathematical formulation and use this for problem-solving,
• make mathematical models of technology problems and apply mathematical expertise in non- mathematical contexts,
• use calculation programmes as aids for advanced mathematical processes and for information retrieval and also have a basic knowledge of programming languages and software of importance to technology,
• formulate complex problems which require optimisation and decision-making and interpret the solutions in the problem’s original context,
• give clear and correct, with regard to both language and content, customised oral and written presentations in English,
• communicate effectively in accordance with the accepted academic norms of the programme’s fields of study, and write both detailed and well-structured reports with advanced content, and also
• demonstrate initiative and personal responsibility in his/her future professional life.

Ability to Evaluate and Assess

On completion of the degree programme the student shall be able to:

• evaluate his/her own strengths and weaknesses, and with conviction question opinions,
• develop and apply, with personal confidence, his/her own conclusions and assessments and make use of feedback, and also
• assess complex situations in business and industrial activities and take into account scientific, social and ethical aspects.

Language of instruction

The language of instruction is English, which includes all teaching, examination and literature, etc.

Contents

The Master’s Programme in Engineering Mathematics is a two-year natural science/technology programme in Mathematics/Applied Mathematics, with engineers and other students educated in technology as important target groups. It deepens the student’s knowledge of mathematics and its technical applications. The programme consists of a compulsory component of 82.5 HE credits in Mathematics/Applied Mathematics. Included in this is a degree project. The remaining 37.5 credits may be chosen freely within Mathematics/Applied Mathematics. Within the programme further optional courses in Mathematics/Applied Mathematics, Computer Science and Energy Engineering are offered.

The compulsory courses account for the mathematical core of the programme. The concluding compulsory course consists of either a degree project comprising 30 credits in Mathematics with applications (for a 120-credit Master’s degree) or a degree project comprising 15 credits in Mathematics with applications (for a 60-credit Master’s degree). The focus of the programme is placed on real problems in working life, and the literature has been chosen to support this specialisation.

Tuition on the programme consists of lectures, problem-solving lessons and seminars. During the lectures the teacher gives a short introduction to the following part of the course. During the problem-solving lessons the students, under the guidance of the teacher, solve suitable problems. During these lessons small groups of students can also present their solutions. The seminars are prepared by the students in groups, choosing a relevant topic, and in their group writing a report on the topic and presenting this at the seminar. The student is expected to reserve untimetabled time for group assignments and individual study.

The courses are examined both by written or oral final examinations and continually during the course by for example seminar reports, assignments for presentation and written tests of knowledge. Four different examination methods are applied: portfolio examination, seminar examination, and also a written and oral examination. To attain a Pass grade on the portfolio examination the student submits to the teacher the answers to the set assignments for presentation. To attain a Pass grade on the seminar assignment the student shall write a report and present this orally at the seminar. Written tests of knowledge may occur during the course.

The programme consists of courses divided according to year of study as indicated below.

Year 1                                                  
Mathematics/Applied Mathematics:    
Applied Mathematics, 7.5 credits           
Applied Matrix Analysis, 7.5 credits
Mathematics of Internet, 7.5 credits
Wavelets, 7.5 credits
 
Elective 30 credits:                                                                        
Mathematics/Applied Mathematics:                                   
Graph Theory, Networks and Applications, 7.5 credits
Stochastic Processes, 7.5 credits                                                                          
Abstract Algebra, 7.5 credits
Biomathematics and Bioinformatics, 7.5 credits
Discrete Mathematics, 7.5 credits
Time Series Analysis, 7.5 credits                                               
Project in Mathematics, 7.5 credits
Degree Project in Mathematics, (60-credit Master’s), 15 credits
 
Optional:
Mathematics/Applied Mathematics:
Discrete Mathematics, 7.5 credits
Probability, 7.5 credits
Numerical Methods with MATLAB, 7.5 credits
Operations Research, 7.5 credits
Differential Equations and Transform Methods, 7.5 credits
Methods of Statistical Inference, 7.5 credits
 
Computer Science:
Programming, 7.5 credits
Learning Systems, 7.5 credits
Computer Graphics, 7.5 credits
 
Energy Engineering:
Introduction to Sustainable Energy Systems, 7.5 credits
Process Modelling, 7.5 credits
Process Optimisation, 7.5 credits

Year 2
Mathematics/Applied Mathematics:
Applied Algebraic Structures, 7.5 credits
Quantum Computing and Information, 7.5 credits
Project in Mathematics II, 7.5 credits
Degree Project in Mathematics, 30 credits

Elective 7.5 credits:                                                                       
Mathematics/Applied Mathematics:
Optimisation, 7.5 credits
Complex Analysis, 7.5 credits                

Optional:
Mathematics/Applied Mathematics:
Foundations of Real Analysis, 7.5 credits
Simulation, 7.5 credits
Differential Equations in Finance, 7.5 credits

Computer Science:
Formal Languages, Automata and Theory of Computation, 7.5 credits

Choices within the program

As a student you are guaranteed a place in the above courses, compulsory as well as elective, of 30 credits in full-time studies or the equivalent in part-time studies. During both years of study, further courses in Mathematics/Applied Mathematics and Engineering can be included in the programme; see the heading Optional above. The choice of courses presupposes that the student is eligible for the desired course.

The choice of courses can affect the possibilities of fulfilling the degree requirements. Depending on the number of applicants for the individual elective courses, as in the above, some courses may be cancelled

University degree

The degree programme is so designed that the studies will lead towards fulfilment of the requirements for the following degree(s):

• Master of Science (60 credits) in Mathematics/Applied Mathematics
• Master of Science (120 credits) in Mathematics/Applied Mathematics 

If the programme contains elective or optional components, or if a student chooses not to complete a certain course, the choices made can affect the possibility of fulfilling the degree requirements. For more information about degrees and degree requirements, consult the local degree regulations which are published on the University website.