This page contains information on the subjects offered by the nGAME partner Universities via the Access Grid in semester 2, 2008. For a timetable of all courses available via the Access Grid click here For information on all the subjects offered via the Access Grid, including those from Universities outside this project, click here Offered by the University of Sydney
MATH3966 Modules & Group Representations (Advanced)
Description: This unit deals first with generalized linear algebra, in which the field of scalars is replaced by an integral domain. In particular we investigate the structure of modules, which are the analogues of vector spaces in this setting, and which are of fundamental importance in modern pure mathematics. Applications of the theory include the solution over the integers of simultaneous equations with integer coefficients and analysis of the structure of finite abelian groups. In the second half of this unit we focus on linear representations of groups. A group occurs naturally in many contexts as a symmetry group of a set or space. Representation theory provides techniques for analysing these symmetries. The component will deals with the decomposition of representation into simple constituents, the remarkable theory of characters, and orthogonality relations which these characters satisfy.
Pre-requistes: 12 credit point of intermediate maths. MATH3962 Rings, Fields and Galois Theory (Advanced)(assumed knowledge)
Prohibitions: MATH3907, MATH390
Description: This unit of study investigates the modern mathematical theory that was originally developed for the purpose of studying polynomial equations. The philosophy is that it should be possible to factorize any polynomial into a product of linear factors by working over a "large enough" field (such as the field of all complex numbers). Viewed like this, the problem of solving polynomial equations leads naturally to the problem of understanding extensions of fields. This in turn leads into the area of mathematics known as Galois theory. The basic theoretical tool needed for this program is the concept of a ring, which generalizes the concept of a field. The course begins with examples of rings, and associated concepts such as subrings, ring homomorphisms, ideals and quotient rings. These tools are then applied to study quotient rings of polynomial rings. The final part of the course deals with the basics of Galois theory, which gives a way of understanding field extensions.
Lecturer/coordinator: Andrew Henderson. Email - A.Henderson@maths.usyd.edu.au Timetable: Monday 10am-11am
Offered by the University of South Australia
MATH1005 Advanced Optimization (offered as part Honours Mathematical Studies 2)
Description: Overview of subject content: We study
optimization problems and methods in finite dimensional spaces. The
course consists of two parts: (I) Theory and (II) Methods.
Pre-requisites: Available to honours students only.
Lecturer/coordinator: Regina S. Burachik. Email - regina.burachik@unisa.edu.au\ Tuesdays 9-11 am Enroll here MATH 1004 Regular and singular perturbations of optimization problems Description: We will be first studying perturbations theory for problems of mathematical programming and then extend some of the results to problems of optimal control. The main attention will be paid to so called singularly perturbed problems, in which the dependence of the optimal value on the perturbation parameter is not continuous. Various applications of theoretical developments will be discussed - Detailed syllabus: - Regular and singular perturbations in linear programming problems - Regular and singular perturbations in nonlinear programming problems - Occupational measures formulations of optimal control problems and their equivalence to infinite dimensional linear programming (IDLP) problems. Regularly and singularly perturbed IDLP problems. - Numerical analysis of IDLP problems and construction of near optimal feedback controls in the corresponding optimal control problems Basic knowledge of Linear Algebra, Calculus and Linear programming is required. Assessment (i) Exam/assignment/class work breakdown Exam 50% Project 50% Class work N/A (ii) Project due date: Week 11 Compiled by Geoff Prince 13 December 2006 (iii) Approximate exam date 20/11/2008 Required student resources - Text/printed notes N/A - Software (local access) ILOG CPLEX or other LP solver Lecturer/Co-ordinator: Vlad. Gaitsgory. Phone: 8 302 3427 Email: v.gaitsgory@unisa.edu.au Timetable: Wednesdays 9-11am (SA time) Offered by the University of Wollongong
STAT904 Statistical Consulting Description: Project management; Client liaison; Problem identification; Consulting ethics and principles; Sources of data; Choosing design and analysis procedures; Common problems in statistical consulting; Setting sample size - power calculations; Consulting case studies; Report writing. A student who successfully completes this subject should be able to: (i) conduct efficiently a consulting session with a client; (ii) find information on statistical methodology using the resources of the Library and the World Wide Web ; (iii) explain the important principles behind designing and conducting an experiment or sample survey; (iv) determine appropriate statistical procedures to use on a wide variety of data sets; (v) apply and interpret procedures from a statistical package Lecturer/coordinator: Professor David Steel. Email - dsteel@uow.edu.au Timetable: Tuesdays 11.30-1.30 starting 22 July MATH942 Financial Mathematics Description: The aim of the course is to give a practical understanding of the modelling, mathematical and numerical issues involved in building and implementing a mathematical model of a financial derivative. Abstract probabilistic analysis is not an aim of the course and there will be no theorems. The course will focus mainly on the partial differential equation formulation of the underlying problems. The interpretation of results in terms of risk-neutral processes and the connection with Monte Carlo will be achieved using the Kolmogorov - Syllabus, preferably week by week
Basic calculus and statistics (important results are the chain rule, Taylor series in one and two variables, normal distributions, properties of sums of random variables); Partial differential equations and the heat/diffusion equation in particular; Experience programming in a procedural language such as C, Pascal, (visual) Basic or Fortran. All numerical work will be demonstrated in Matlab, although student work will be accepted in most common languages (including R, S+ and Python) -- the criteria here is that the lecturer is able to understand and run it.
Timetable: Thurs 3:30 from 24 July. Lecturer: Jeff Dewynne. Email: dewynne@uow.edu.au Offered by Macquarie University STAT821 Multivariate Analysis Description: Introduces methodologies and techniques for the exploration and analysis of multivariate data. Topics include graphical displays, discriminant analysis, principle Week/Topic
probability distributions,regression, inference,hypothesis testing Assessment Required student resources Lecturer/Coordinator: Dr Jun Ma. Phone: (+61-2) 9850-8548. Email: jma@efs.mq.edu.au
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