Faculty of Science AMSI Summer School 2013

There will be eight four-week courses offered at the summer school. Click on a course title for a more detailed description.

AustMS SS2013 subject: Modular forms
Wadim Zudilin (University of Newcastle)
The lectures serve as an in introduction to the classical theory of modular forms and their applications. An impact of the theory on Fermat's Last Theorem will be discussed at the end of the course.
Measure theory
Marty Ross
Measure theory is the modern theory of integration, the method of assigning a "size" to subsets of a universal set. It is more general, more powerful and more beautiful (though also more technical) than the classical theory of Riemann integration.
Solitons, instantons, Lax pairs and twistors
Omar Foda (University of Melbourne)
This is a series of introductory lectures on nonlinear partial differential equations that can be solved without approximation, and that play a central role in recent studies of non-perturbative phenomena in string and gauge theories.
Numerical solution of conservation laws and hyperbolic linear systems
Markus Hegland and Stephen Roberts (Australian National University)
This course covers advection equations such as the Euler equations, the shallow water equations and the time-dependent Maxwell equations among others. It includes a hands-on computational lab in addition to a discussion of theoretical topics like convergence (Lax equivalence theorem), characteristics, shocks and rarefaction waves and several numerical schemes like Lax-Wendroff and Crank-Nicholson in addition to Godunov schemes.
Structured Markov models and control theory. A unified approach via linear algebra
Yoni Nazarathy (University of Queensland)
Performance analysis and control of natural and engineered systems evolving over time is a central theme in applied mathematics, operations research and engineering. Many such systems can be modelled as stochastic by means of structured Markov chains, while others are well described by deterministic linear models with feedback control. In both cases the underlying linear algebra is very similar. This course aims to teach the students both types of methodologies, stochastic modelling and control theory via a unified linear algebraic approach.
Complex networks
Stephen Davis (RMIT)
The world around us is brimming with structure that consists of discrete entities and relationship between those entities. These structures can be represented as a set of vertices and a set of links that formally define a graph, and a complex network is nothing more than a very large graph where the links are neither predictable nor completely random. This course will touch on the analysis of real, complex networks that arise in ecology and epidemiology, such as food webs and wildlife contact networks, but will emphasise the mathematical and statistical techniques used to classify and characterise networks.
ANZIAM SS2013 subject: Mathematical epidemiology: stochastic models and their statistical calibration
Joshua Ross (University of Adelaide)
Mathematical models are increasingly used to inform governmental policy-makers on issues that threaten human health or which have an adverse impact on the economy. It is this real-world success combined with the wide variety of interesting mathematical problems which arise that makes mathematical epidemiology, stochastic models and their statistical calibration one of the most exciting topics in applied mathematics.
Methodology and theory for the bootstrap; Introduction to nonparametric regression and functional data
Aurore Delaigle and Peter Hall (University of Melbourne)
The course will begin by discussing the motivation and intuition behind bootstrap methods, and treat a variety of different approaches, including the double bootstrap. In the second part of the course we will introduce techniques for analysing data that are in the form of curves, such as, for example, yearly rainfall or temperature curves, growth curves, etc.
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