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University of South Australia

Optimisation

Area/catalogue: MATH 3009
Course ID: 013173

School: School of Mathematics and Statistics

Campus/course component(s):
Mawson Lakes: Lecture
Note: These components may or may not be scheduled in every study period. Please refer to the timetable for further details.

Unit value: 4.5

Offered externally: No

Undergraduate elective course: No

Course details


Prerequisite(s): MATH 2014 Linear Programming and Networks.

Linear programming: convex sets, separating-hyperplane theorem, duality, interior-unit methods. Kuhn-Tucker conditions. Constrained optimisation methods. Nonlinear programming algorithms. Case studies.

Text book/s:

Course coordinator/s:


Area/catalogue: MATH 3010
Course ID: 013167

School: School of Mathematics and Statistics

Campus/course component(s):
Mawson Lakes: Lecture
Note: These components may or may not be scheduled in every study period. Please refer to the timetable for further details.

Unit value: 4.5

Offered externally: No

Undergraduate elective course: No

Course details


Prerequisite(s): MATH 2014 Linear Programming and Networks, MATH 3009 Optimisation.

Characteristics of large-scale real-life decision problems. Typical models of industry, trade and finance. The need for optimisation. Basic measure theory (measurable space and measure space, the Lebesgue integral), basic linear algebra (eigenvalues and eigenvectors, singular value decomposition), basic probability theory (random vectors, covariance matrix).Estimation theory (linear and nonlinear estimators) Principal Component Analysis. Theory of optimal data estimation. Error analysis. Modelling: Basics of modelling. Modelling methodology. Model generation and management. Modelling systems.

Text book/s:

Course coordinator/s:


Area/catalogue: MATH 3015
Course ID: 013172

School: School of Mathematics and Statistics

Campus/course component(s):

Unit value: 4.5

Offered externally: No

Undergraduate elective course: No

Course details


Prerequisite(s): MATH 2010 Numerical Methods 1.

Zeros of polynomials and Muller's method. Cubic spline interpolation. Orthogonal polynomials and least squares function approximation. Rational function approximation. Iterative methods of solving linear systems of equations. Solving systems of nonlinear equations by fixed point iteration, Newton's method and Quasi-Newton methods. Ordinary differential equations: stability, stiffness, multistep methods, nonlinear shooting method, fhite differences, Rayleigh-Ritz and weighted residuals. Partial differential equations: elliptic, parabolic, and hyperbolic problems by finite differences. Introduction to multi-dimensional minimisation.

Text book/s:
  • Burden R L, Faires J D 2001, Numerical Analysis, 7th Ed, Prindle, Weber & Schmidt.

Course coordinator/s:

Area/catalogue: MATH 3016
Course ID: 013178

School: School of Mathematics and Statistics

Campus/course component(s):

Unit value: 4.5

Offered externally: No

Undergraduate elective course: No

Course details


Prerequisite(s): Error in course code , MATH 2016 Statistical Modelling.

Estimation and confidence intervals; standard distributions; central limit theorem; sufficiency; efficiency concepts; likelihood estimates and tests; exponential families; the general linear model; generalised linear models and examples; Bayesian statistics.

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Course coordinator/s:


Decision Science



Area/catalogue: MATH 3017
Course ID: 100303

School: School of Mathematics and Statistics

Campus/course component(s):
City West: Lecture - Tutorial
Note: These components may or may not be scheduled in every study period. Please refer to the timetable for further details.

Unit value: 4.5

Offered externally: No

Undergraduate elective course: No

Course details


Prerequisite(s): A basic understanding of elementary probability and matrices

Fundamental concepts of decision analysis, utility, risk analysis, Bayesian statistics, game theory, Markov decision processes and optimisation. The value of sampling information and optimal sample sizes, given sampling costs, and the economics of terminal decision problems.

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Course coordinator/s:


Financial Time Series



Area/catalogue: MATH 3018
Course ID: 100305

School: School of Mathematics and Statistics

Campus/course component(s):
Mawson Lakes: Lecture - Computer Practical
Note: These components may or may not be scheduled in every study period. Please refer to the timetable for further details.

Unit value: 4.5

Offered externally: No

Undergraduate elective course: No

Course details


Prerequisite(s): MATH 2020 Statistical Foundations.

  • The components of a time series model.
  • Additive and multiplicative models.
  • Multiple regression analyses.
  • Spectral decomposition.
  • Box-Jenkins models.
  • Forecasting techniques.
  • Smoothing of time series.
  • GARCH and other volatility models,
  • Stochastic Differential Equations.
Text book/s:
  • Tsay, R.S. 2005, Analysis of Financial Time Series, 2nd Edition, John Wiley & Sons.

Course coordinator/s:

Investment Science



Area/catalogue: MATH 3019
Course ID: 100307

School: School of Mathematics and Statistics

Campus/course component(s):
City West: Lecture - Tutorial
Note: These components may or may not be scheduled in every study period. Please refer to the timetable for further details.

Unit value: 4.5

Offered externally: No

Undergraduate elective course: No

Course details


Prerequisite(s): MATH 1055 Calculus 2, MATH 2014 Linear Programming and Networks.

Deterministic cash flow streams: present and future values, fixed income securities, term structure of interest rate. Single period random cash flows: mean-variance portfolio theory, general principle of pricing. Derivative securities: forward and futures, models of asset dynamics, basic option theory, Black-Scholes equation. General cash flow streams: optimal portfolio growth, general investment evaluation.

Text book/s:
  • Luenberger, David G 1998, Investment Science, Oxford University Press.

Course coordinator/s:

Risk Theory



Area/catalogue: MATH 3020
Course ID: 100310

School: School of Mathematics and Statistics

Campus/course component(s):
City West: Lecture - Tutorial
Note: These components may or may not be scheduled in every study period. Please refer to the timetable for further details.

Unit value: 4.5

Offered externally: No

Undergraduate elective course: No

Course details


Prerequisite(s): MATH 2020 Statistical Foundations.

Moment generating functions; loss distributions (exponential, gamma, Pareto, Weibull, lognormal); parameter estimation and reinsurance; risk theory; ruin theory; Bayesians statistics; decision theory; credibility theory; run-off triangles (methods for projecting claims).

Text book/s:
  • Klugman, S.A, Panjer, H.H. & Willmot, C.E. 2004 or 1998, Loss models: from data to decisions, 2nd or 1st ed., Wiley, New York.

Course coordinator/s:


Categorical Data Analysis



Area/catalogue: MATH 3024
Course ID: 101175

School: School of Mathematics and Statistics

Campus/course component(s):

Unit value: 4.5

Offered externally: No

Undergraduate elective course: No

Course details


Prerequisite(s): MATH 1036 Statistical Methods.

Exponential families; Generalised linear models; Logistics regressions; Log-linear models and contingency table models; Survival analysis; generalised linear mixed models; special topics.

Text book/s:
  • Agresti, A 2002, Categorical Data Analysis, Wiley.

Course coordinator/s:

Differential Equations 2



Area/catalogue: MATH 3025
Course ID: 101191

School: School of Mathematics and Statistics

Campus/course component(s):
Mawson Lakes: Lecture - Tutorial
Note: These components may or may not be scheduled in every study period. Please refer to the timetable for further details.

Unit value: 4.5

Offered externally: No

Undergraduate elective course: Yes

Course details


Prerequisite(s): MATH 2023 Differential Equations 1.

Series solutions of differential equations, Legendre and other orthogonal polynomials, the Method of Frobenius, Bessel Functions, Self adjoint form, Sturm Liouville problems, eigenfunctions expansions, Fourier series, Partial differential equations, Problems from applied physics.

Text book/s:
  • Edwards, CH & Penney, DE 2008, Differential Equations and Boundary Value Problems, Computer and Modelling, 4th edition, Prentice Hall.

Course coordinator/s:

Applied Functional Analysis



Area/catalogue: MATH 3026
Course ID: 101192

School: School of Mathematics and Statistics

Campus/course component(s):
Mawson Lakes: Lecture - Tutorial
Note: These components may or may not be scheduled in every study period. Please refer to the timetable for further details.

Unit value: 4.5

Offered externally: No

Undergraduate elective course: No

Course details


Prerequisite(s): MATH 2025 Real and Complex Analysis.

Classical Abstract spaces in Modern Functional Analysis:

  • Topological spaces (convergence, continuity, weak topology, and compactness results) ,
  • Metric spaces (Complete metric spaces, Baire Category Theorem, Arzela-Ascoli Theorem, Holder-Minkowski's Inequalities),
  • Normed Vector spaces,
  • Space of Lebesgue Measurable Functions,
  • Hilbert spaces

Fundamental Theorems of Analysis:

  • Hahn-Banach Theorem,
  • Uniform Boundedness Theorem,
  • The Open Mapping Theorem.

Dual Spaces:

  • Weak and Weak* topology
  • Riesz's Representation Theorem,
  • Closed Graph Theorem,
  • Adjoint Operators in Hilbert spaces,
  • Lp spaces.

Differential Calculus in Normed Vector Spaces:

  • Differentiability of functionals (Gateaux and Frechet differentiability)
  • Minimization of Differentiable functionals (optimality conditions for constrained optimization)
  • Gateaux differentiable convex functionals
  • Lower Semicontinuous Functionals and Convexity.
Text book/s:
  • Kurdila, AJ & Zabarankin, M 2005, Convex Funtional Ananlysis, Bikauser.

Course coordinator/s:

Multivariate Statistical Analysis



Area/catalogue: MATH 3030
Course ID: 101736

School: School of Mathematics and Statistics

Campus/course component(s):
City West: Lecture - Tutorial
Note: These components may or may not be scheduled in every study period. Please refer to the timetable for further details.

Unit value: 4.5

Offered externally: No

Undergraduate elective course: No

Course details


Prerequisite(s): MATH 1056 Linear Algebra, MATH 1036 Statistical Methods.

The linear model; the multivariate normal distribution; convariance matrices; Hotelling's T-squared; principal components; Flury test, discriminant analysis; factor analysis.

Text book/s:

Course coordinator/s:


Stochastic Models and Their Application



Area/catalogue: MATH 4006
Course ID: 007389

School: School of Mathematics and Statistics

Campus/course component(s):

Unit value: 4.5

Offered externally: No

Undergraduate elective course: No

Course details


Prerequisite(s): 06418 Quantitative Methods for Business.

Simulation, renewal processes, queuing and Markov decision processes, selected applications of these models and techniques in a wide range of fields such as: scheduling, inventory control, manufacturing process control and water resource management etc.

Modelling techniques and algorithms, mathematical programming (linear, integer, quadratic, general nonlinear, dynamic and goal). Applications in business, management and economics.

Text book/s:

Course coordinator/s:

To be advised


Methods and Applications of Optimal Control



Area/catalogue: MATH 4008
Course ID: 007888

School: School of Mathematics and Statistics

Campus/course component(s):

Unit value: 4.5

Offered externally: No

Undergraduate elective course: No

Course details


Hilbert spaces. The Projection theorem. The singular value decomposition of a compact linear operator. Banach spaces. The Hahn-Banach theorem. Convex cones. Alternative theorems. Lagrange multipliers. The Kuhn-Tucker equations. The Pontryagin principle. Application of the above methods to current research problems.

Text book/s:

Course coordinator/s:

To be advised


Markov Decision Processes and Applications



Area/catalogue: MATH 4009
Course ID: 007893

School: School of Mathematics and Statistics

Campus/course component(s):

Unit value: 4.5

Offered externally: No

Undergraduate elective course: No

Course details


Prerequisite(s): Third year undergraduate mathematics

Markov decision processes are dynamic, stochastic, systems controlled by decision-makers' that have been extensively studied since the 1950s by mathematicians, operations researchers and engineers. The program contains a rigorous presentation of the basic theory and algorithms of MDPs as well as an outline of the many possible applications of these models.

Text book/s:

Course coordinator/s:

To be advised


Optimal and Suboptimal Solutions in Linear and Nonlinear Programming



Area/catalogue: MATH 4010
Course ID: 007894

School: School of Mathematics and Statistics

Campus/course component(s):

Unit value: 4.5

Offered externally: No

Undergraduate elective course: No

Course details


Prerequisite(s): Third year undergraduate mathematics

Existence of a solution; necessary and sufficient conditions of optimality in mathematical programming problems. Regular and singular perturbations of the reduced structure. Nonuniqueness of the reduced solution. Aggregation and decomposition procedures.

Text book/s:

Course coordinator/s:

To be advised


Personnel Scheduling



Area/catalogue: MATH 4013
Course ID: 007890

School: School of Mathematics and Statistics

Campus/course component(s):

Unit value: 4.5

Offered externally: No

Undergraduate elective course: No

Course details


Survey of personnel scheduling environments and requirements. Some early personnel scheduling modules. Analysis of tasks involved in the scheduling process. Temporal personnel requirements, minimum workforce requirements, rest period identification, rest period sequencing, shift assignment. Cyclic personnel scheduling. Crew scheduling models.

Text book/s:

Course coordinator/s:

To be advised


Updated on Oct 15, 2010 by Scott Spence (Version 8)