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Courses
The AMSI Summer School will consist of six full courses. Five of these are single courses that will run for the four weeks of the AMSI Summer School, and one full course consists of two half courses that run for two weeks each.
| Course Name |
Lecturer |
| Full Courses |
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| Advanced Data Analysis |
Prof. Matt Wand |
| Groups of Lie Type and their Geometries |
Dr James Parkinson |
| Linear Analysis |
Assoc Prof David Pask |
| Mathematics for Nanotechnology |
Prof Jim Hill, Dr Barry Cox and Dr Natalie Thamwatanna |
| Measure Theory and Integration |
Prof Iain Raeburn
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| Half Courses |
|
| Industrial Mathematics |
Dr Glenn Fulford |
| Mathematics in Industry Study Group (MISG) |
Prof Tim Marchant and Assoc Prof Jacqui Ramagge |
Course 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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