| | Course OutlinesCourse Outlines
On your application form you will be asked to select two full courses and a back-up choice.
| Course: |
Advanced Data Analysis |
| Lecturer: |
Prof Matt Wand |
| Duration: |
4 Weeks |
| Hours: |
28 hours |
| Content: |
This course covers advanced data analysis via contemporary
statistical models and software. Models include generalised linear
models, linear mixed models and generalised additive models. The R and
BUGS computing environments will be used for analysis of a wide array
of data sets. Principles and theory of the underlying methodology will
be covered. |
| Course: |
Groups of Lie Type and their geometries |
| Lecturer: |
Dr James Parkinson |
| Duration: |
4 Weeks |
| Hours: |
28 hours |
| Content: |
This course is an introduction to the theory of groups of Lie type
via the combinatorial/geometric language of buildings. The importance
of these groups is underscored by the classification theorem for finite
simple groups (the atomic building blocks of finite groups) which tells
us that "almost all" finite simple groups are groups of Lie type. The
prerequisites for the course will be kept to a minimum, although some
familiarity with basic linear algebra and group theory will be assumed
(the lecture notes will include review so these topics). In the course
we will focus on concrete examples, and by the end the student should
have a working knowledge of Coxeter groups, spherical buildings, affine
buildings, Chevalley groups, loop groups, and groups with BN-pairs. |
| Course: |
Linear Analysis |
| Lecturer: |
Assoc Prof David Pask |
| Duration: |
4 Weeks |
| Hours: |
28 hours |
| Content: |
This course will be an introduction to the study of operators on a
Hilbert space. We will begin by looking at the basic properties of
Hilbert spaces underpinned by key examples. The inner product on a
Hilbert space may be used to define a norm on the underlying vector
space, and so a Hilbert space is an example of a normed linear space.
Normed linear spaces carry a metric which allows us to define the
notion of continuity for maps between them. We shall show that linear
maps between normed linear spaces are not only continuous but are also
bounded, and form an operator algebra. The extra geometric flavour of
the norm on a Hilbert space allows us to discuss the concept of
orthogonality and its consequences, which culminates in the definition
of the adjoint of a linear operator. The course will consider various
areas of application as the general theory is developed. |
| Course: |
Mathematics for Nanotechnology |
| Lecturers: |
Prof Jim Hill, Dr Barry Cox and Dr Natalie Thamwatanna |
| Duration: |
4 Weeks |
| Hours: |
28 hours |
| Content: |
This course gives an introduction to applied mathematical modelling
in nanotechnology, and in particular the use of elementary geometrical
and mechanical principles. Students are introduced to the basic
physical ideas, such as atoms and bonds forming molecular structures.
The course follows the style of the formal applied mathematics
approach, but very little prior mathematical or physical knowledge is
required, other than a knowledge of basic geometry and mechanics
(Pythagoras' theorem and Newton's second law) and also some knowledge
of special functions. A number of surface integrals lead to some
standard special functions such as hypergeometric functions, elliptical
integrals and Appell hypergeometric functions, which all may be
evaluated using MAPLE. The course includes the geometry of carbon
nanotubes and fullerenes, and the analysis of the mechanics of various
nano-oscillators involving carbon nanotubes and fullerenes. |
| Course: |
Measure Theory and Integration |
| Lecturer: |
Prof Iain Raeburn |
| Duration: |
4 Weeks |
| Hours: |
28 hours |
| Content: |
The main point of the course is to provide an orthodox treatment of
the Lebesgue integral, and to illustrate the power and usefulness of
the integral with applications to theory of the Fourier transform. The
course will cover measures (especially Lebesgue measure on the line),
the construction of the integral, the convergence theorems, the Lp-spaces
and Fubini's theorem. The applications to the Fourier transform will be
aimed at a rigorous discussion of the Fourier inversion theorem for
functions on the line. |
| Course: |
Industrial Maths |
| Lecturer: |
Dr Glenn Fulford |
| Duration: |
2 Weeks |
| Hours: |
14 hours |
| Content: |
This half-course will be a problem-based introduction to the
mathematics needed to solve problems arising in industry and can be
followed by a half-course incorporating the Mathematics in Industry
Study Group (MISG) meeting which will take place 27-30 January.
Problems posed at previous MISG meetings will be used to motivate the
mathematics. The mathematics will then be developed and then used to
solve the problems. |
| Course: |
Mathematics in Industry Study Group (MISG) |
| Lecturer: |
Prof Tim Marchant and Assoc Prof Jacqui Ramagge |
| Duration: |
2 Weeks |
| Hours: |
14 hours |
| Content: |
This half-course is designed to take advantage of the MISG meeting
which will be held in Wollongong 27-30 January 2009. Students will be
expected to join one of the teams working on a problem supplied by
industry to the MISG. Students will continue working on the projects
for the week 2-6 February and assessment will be based on a report
detailing the project, the mathematics used to tackle it and progress
made in its solution during the two weeks of the course. Students will
also be asked to give a presentation in the week of 2-6 Feb. For more
information go to the MISG web site. |
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