(05)UC/12 MEngSt, PGCertEng (Engineering Mathematics)/1
UNIVERSITY OF CANTERBURY
Te Whare Wānanga o Waitaha
Section A
Proposal Description
Purpose of the proposal
The purposes of this proposal are to add an endorsement in Engineering Mathematics to the Master of
Engineering Studies (MEngSt) and the Postgraduate Certificate in Engineering. (PGCertEng)
Justification
Engineering mathematics is the discipline underpinning all modern engineering practice. The key feature
we propose teaching is the use of advanced mathematics and its consequential technology that can be
used to solve real world engineering and industrial problems. Current undergraduates in engineering at
Canterbury are not exposed to sufficient mathematics in their undergraduate degree to call themselves
experts in mathematical science for their discipline. Furthermore, there is also a base of international
students wishing to proceed into mathematically sophisticated postgraduate degrees in engineering, but
whose background may not be sufficient to ensure success without further mathematics. Finally, there
may be engineering graduates whose professional career requires a higher level of mathematics than
they have learned as undergraduates.
These programmes will provide sufficient teaching and learning in mathematics and advanced
computational techniques to enable graduates to have the knowledge to work in modern advanced
areas of engineering. The programme will enable access to the high performance computer facilities at
the University.
The key principle behind all the taught courses is to provide the fundamental mathematical concepts
which underpin the often seemingly disparate specialisation topics that appear in curricular.
The Department of Mathematics & Statistics has been teaching and examining in the area of
engineering mathematics within the School of Engineering since the school came into existence. The
School has a national and international reputation for its engineering teaching and research. This is in
part built by the curriculum and teaching of the Department. Graduates now hold positions in
government, local government, consultancy firms, universities and research organisations in New
Zealand and overseas.
The proposed courses and the programmes of the MEngSt and the Postgraduate Certificate will create
graduates capable of researching both within UC or importantly outside by providing them with the
skills of utilising and enhancing the use of advanced mathematical sciences. Moreover, this programme
will enable engineering students to tackle engineering Ph.D. programmes requiring a high level of
mathematical ability.
A unique feature of this course within New Zealand is the use of high performance computing (HPC) via
access to the Blue Gene supercomputer enabling students to gain high performance computing skills
along with enhanced mathematical knowledge. Government funding in collaboration with IBM has
enabled BlueFern to provide a dedicated set of hardware that can be used for this programme of study
in HPC. This hardware consists of a 4096 core Blue Gene/L and a power 720 (4 cores, 64 Gb). Few other
academic institutions worldwide provide dedicated hardware of this type to students of this level and it
thus supports the intention of UC and BlueFern to provide international quality training at the leading
edge of HPC.
Furthermore, the proposed programmes complement a suite of qualifications in the area of high
performance computing which will include both Masters and Ph.D.
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The proposal meets the UC Strategic Plan’s strategies of “Challenge, Concentrate, and Connect” by
seeking to develop a qualification of international standing across a variety of disciplines and
communities with input from those communities to prepare students for future careers in NZ and
beyond. It also specifically addresses the intention to increase postgraduate enrolments and
completions. The skills of the graduates will clearly support the generation of new research. This
proposal will build on our recognised success in Engineering Mathematics and HPC.
The College of Engineering Strategic Plan states that it wishes to “Increase conversion of Undergraduate
to Postgraduate”. This proposal is giving effect to the strategic plans of the Department and College.
The College also discussed the need to bring the postgraduate offerings into a similar format to avoid
confusion to both students and staff.
The proposal will not compete with other qualifications at the University of Canterbury. First, there is no
other qualification offering a broad suite of advanced engineering mathematics. Secondly very few
other qualifications offer high performance computing within New Zealand and very few are currently
available worldwide.
Finally, it is anticipated that the programme will generate new research, by becoming a principal avenue
through which interested groups can initiate collaborative ventures with academic staff on engineering
mathematics related issues, both through student thesis research and through longer-term research
programmes. This will help to further develop interdisciplinary research.
Acceptability
This proposal has the support of the PVC and the College Management Team in the College of
Engineering.
The following groups were consulted on the proposal. Centre for Atmospheric Research;
Biomathematics Centre; Waterways Centre; College of Engineering departments.
Goals of the programme
The MEngSt and PG Certificate with endorsement in Engineering Mathematics aims to provide a
fundamental set of skills to those wishing either to enter the research domain or use high-level
mathematics and advaned computational techniques in engineering as a part of their career. For
example, graduates entering into an engineering firm may be asked to do a substantial amount of
computational work with advanced computational software. Students obtaining the proposed
qualifications will be able to quickly understand and utilise powerful algorithms and computing
hardware. This will lead and encourage others within their career environment to exploit the power of
modern engineering mathematics.
The students entering this programme will be required to have achieved high grades in their respective
final year courses that require mathematical skills. The delivery of this programme has a difficult
challenge in bringing students from the mathematical knowledge base currently being required of
BE(Hons) students within the engineering programme up to 600 level. Engineering mathematics is
currently taught to the second or third year depending upon the Department. However the students
taking the more mathematical 400 year topics, from various Departments, are meeting challenging
mathematical ideas and these ideas will be built upon in this programme. Therefore, the prerequisite
required of the students is they must have good passes in topics at 400 level requiring engineering
mathematical skills.
The MEngSt programme consists of five core courses, details of which are outlined below. Any
remaining courses may be selected from the list of 400 or 600 (in Schedule B) level courses offered by
the Engineering programmes.
The Postgraduate Certificate in Engineering (PGCertEng) programme consists of three fundamental
courses, details of which are outlined below. The remaining course may be selected from the list of 400
level courses offered by the Engineering programmes.
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Graduate profile
Master of Engineering Studies (Engineering Mathematics)
Outline
The MEngSt is an advanced programme of engineering education that is aimed at current, or future,
professional engineers and researchers wishing to develop high-level mathematical and computational
skills. It is not research focussed, although students can undertake a small research project.
Learning Outcomes
The graduates from the MEngSt degree will demonstrate the following attributes:
 To appreciate and enjoy the application of mathematical techniques to engineering problems
 Advanced knowledge of the fundamental principles of engineering mathematics and
computation, and application of these principles.
 Breadth of knowledge in engineering mathematics and computation.
 The ability to communicate in a clear and concise manner.
 The ability to undertake independent study.
 The ability to apply their knowledge to new and complex engineering problems.
 Recognition of the importance of lifelong learning.
Particular Attributes Gained in Engineering Mathematics
The aim of the Master of Engineering Studies (Engineering Mathematics),MEngSt (Engineering
Mathematics), is to enable graduates to:
 Understand and explain mathematical concepts as applied to a variety of engineering situations.
 Understand, analyse and make conclusions and recommendations on applications of
mathematical techniques in an engineering discipline.
 Comprehend and interpret complex mathematical software as applied to engineering
applications.
 To understand the concepts and principles involved in computational mathematics and be able
to apply these to HPC.
 The ability to undertake independent study.
 The ability to apply their knowledge to new and complex engineering problems.
 Communicate design solutions to a range of clients.
Outcome statement
Students gaining this degree will have skills useful to the engineering profession, world-wide.
Additionally students will be able to gain employment in a large number of research areas in which
advanced engineering mathematical and computational techniques are used on a daily basis both in
New Zealand and overseas.
Programme overview
Students wishing to take this programme will normally have an engineering degree (at Honours level).
Master of Engineering Studies
A course-based programme aimed at providing an advanced technical foundation and industrial
perspective. The programme will provide the mathematical foundations in engineering incorporating
statistical methods and modern computational practices. This will make it unique in New Zealand.
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The proposed programme will require (for a full time student) one year of course work (120 points). The
course work will require students to enrol in five of the core courses (EMTH 611, 612, 613, 614, 620).
Each of these courses is worth 15 points.
Any remaining courses may be selected from the list of 400 or 600(in Schedule B) level courses offered
by the Engineering programmes.
The total points value of the programme to add to 120 points. Each course is an independent unit in
itself. The programme will usually be completed in a single academic year.
Postgraduate Certificate in Engineering (Engineering Mathematics)
Candidates enrol in three of the above core courses and one (15 point) course at 400 level chosen from
appropriate topics in an engineering discipline.
Proposed teaching/delivery method
All five EMTH courses will be presented by lectures, with tutorials and directed and self-directed
learning.
Assessment procedures
Assessments for all five EMTH courses in the programme will consist of marked assignments and a final
exam in line with the UC Assessment Policy. Assessment in all courses will give substantial weighting to
deep learning - that is, the development of conceptual understanding and skills in applying knowledge
to new situations - while not neglecting to give credit for learning core factual material. The weightings
given to different assessment tasks will be decided by the examiner to best assess students’ capabilities
and performance in the course, and will be related to the amount of work involved in each task and the
relative importance of each learning outcome.
Predicted student numbers/EFTS
It is expected that an average of 10-15 students will enrol on this programme in the first year. It is
expected that a maximum of 20 students is desirable due to computer laboratory and HPC access
constraints.
Resources
Lecture rooms and computer laboratories will be used to support this teaching programme. Many
lecturers in the Department of Mathematics & Statistics are already recognised as international
researchers and teachers in the area. This is verified by peer reviewed journal articles and international
visitors to the Department from engineering and applied mathematics institutes around the world.
A major resource required is access to the HPC Blue Fern Supercomputing Unit. This is currently
available to all enrolled students on any of the three HPC courses and so will be available to all students
enrolled in the proposed qualification. As noted in the justification section above, students enrolled in
these programmes will have dedicated access to the 4096 core Blue Gene/L and the power 720.
Desk space and IT support for postgraduate students enrolling is currently being considered.
The Library has excellent access to a wide range of engineering mathematics serials and monographs, in
print and digital form.
Plans for monitoring programme quality
Programme quality will be monitored by a variety of means:
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 For the first three years, student course evaluations will be undertaken annually, at the
conclusion of each of the core courses. Programme evaluations/interviews will also be
undertaken annually with graduating students.
 After the first three years, course and programme evaluations will be undertaken regularly but
less frequently (initially every second year). Actual outcomes will be checked against target
outcomes for the courses and for the programme, and course content refined and
content/assessment methods modified as required. Particular emphasis will be placed on
ensuring that assessment aligns with learning outcomes, and that these in turn connect with the
graduate profile. Regular external moderation will be also be used to monitor the quality of
taught courses, as well as for the research project dissertation (for which internal examination
will be required).
 Graduates of the first three years will also be contacted two years after graduation (where
possible) for their feedback on how applicable and relevant the teaching programme has been
to their chosen profession, and to seek feedback on how this could be improved if necessary.
New Regulations
Calendar form
UC Calendar 2012 pages 174 and 178
Schedule to the Regulations for the Degree of Master of Engineering Studies (endorsed)
Engineering Mathematics
Courses with a total course weighting of not less than 75 points shall be selected from the core Engineering
Mathematics courses listed in Schedule B of the Master of Engineering regulations.
Engineering Mathematics
EMTH 600 Dynamical Systems
EMTH 601 Continuous Biological Systems
EMTH 602 Fluid Mechanics
EMTH 603 Numerical Solution of Partial Differential Equations
EMTH 604 Unconstrained Optimisation
EMTH 605 Approximation Theory
EMTH 606 Algebraic and Symbolic Computation
EMTH 607 Coding Theory
EMTH 608 Industrial Case Studies
Core courses for the endorsement for PGCertEng and MEngst
EMTH611 Advanced Mathematical Methods
EMTH612 Advanced Computational Techniques
EMTH613 Advanced Statistical Methods
EMTH614 Advanced Differential Equations
EMTH620 High Performance Technical Computing
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Schedule to the Regulations for the Postgraduate Certificate in Engineering (endorsed)
Engineering Mathematics
Courses with a total course weight of not less than 45 points must be selected from the core Engineering
Mathematics course list listed in Schedule B of the ME regulations.
Course Catalogue
EMTH611: Advanced mathematical methods
Advanced linear algebra: decomposition of linear systems, eigen-system methods, conjugate gradients, GMRES.
Advanced calculus: multivariate calculus; linearisation, surface integrals, tensor analysis. Complex variable
methods. Modelling of engineering systems. Asymptotic methods.
EMTH612: Advanced computational techniques
Numerical approximation and cubic splines; numerical solution of non-linear algebraic equations; numerical
optimisation for unconstrained and constrained problems; numerical solution of initial value and boundary value
ordinary differential equation problems and differential algebraic systems; numerical solution of partial differential
equations by finite differences, multigrid, spectral methods and finite element techniques.
EMTH613: Advanced statistical methods
Probability theory and stochastic processes; Monte Carlo methods and simulation; stochastic optimisation;
machine learning; pattern recognition; classification and regression; time series; information engineering.
EMTH614: Advanced differential equations
Solution of odes: Linear problems: Initial value problems, Boundary value problems; Non-linear quantitative
methods, dynamical systems. Solution of pdes: method of characteristics, classification of pde; Fourier series,
Hilbert space, Sturm-Liouville: separation of variables solution of elliptic, parabolic and hyperbolic equations.
Integral transforms and green functions. Variational methods.
EMTH620: High Performance Technical Computing
Features of HPTC: HPTC programming considerations, software technologies, enabling technologies and
algorithms. HPTC Programming, Parallel programming. Applications of HPTC to engineering science: Parallel and
distributed computing in numerical linear algebra, pdes, odes and optimisation. Applications to: nonlinear
dynamical systems, nonlinear fluid mechanics, bio-engineering.
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