Please note - Swinburne University of Technology

Advanced forecasting
The Box-Jenkins methodolpgy, differencing of time series,
sample autocorrelation and sample partial autocorrelation
(SAC and SPAC), checking stationarity of time series using
SAC and SPAC, autoregressive models; moving average
models; general ARMA models, autoregressive integrated
moving average models (ARIMA). general ARIMA with
seasonality, use of computer packages such as SASIETS.
Decision analysis
lntroduction to decision problems, deterministic decision
problem vs stochastic single criterion decision tree analysis
and related topics, financial comparisons of projects, multiple
criteria decision methods. Use of computer packages such as
PROPS and EC.
sM526 Applied Statistics 5
TI
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n
10.0 credit points
C_ -+ No. of hours per week: three hours
Y
Assessment: testslexamination and assignments
' A third-year subject of the degree course in mathematics
8 and computer science.
o_
m' Subject description
Q Sampling methods for sample surveys
VI
9. Basic designs for sample surveys: simple random sampling,
stratified sampling and systematic sampling.
;d Estimators for means, totals and proportions; variance
estimation. The design effect; sample size determination;
EPSEM samples. Practical issues and methods: questionnaire
design.
lntroduction to multivariate methods
An informal introduction to sampling from multivariate
populations. The variance-covariance matrix, the multivariate
normal distribution, multi-variate means, Hotelling's T 2
statistic, the multivariate anal~is of variance. Wilk's lambda.
An introduction to principal components analysis, factor
analysis and cluster analysis.
SM581 Discrete Mathematics
10.0 credit points
No. of hours per week: three hours
Prerequisite: SM 180
Assessment: testslexamination and assignments
A third-year subject of the degree courses in mathematics
and computer science and applied and industrial
mathematics.
Subject description
Set theory and relations: review of formal set theory;
operations on sets; ordered sets; Cartesian product.
Relations: binary relations, especially equivalence relations
and partitions; ordering and partial ordering; functions.
Logic: introduction to propositional calculus and to predicate
calculus; traditional and modern symbolic logic.
The nature of formal (pure) mathematics: mathematical
proof and theorems; necessaly and sufficient conditions;
types of proof, including mathematical induction.
Boolean algebra: review of algebraic structures; rules of
Boolean algrebra, with examples; simplification of Boolean
expressions. Boolean functions: truth tables and Karnaugh
maps, normal and minimal forms.
Combinatorial analysis: systematic techniques of listing and
of counting for arrangements, selections, partitions etc. Use
of recurrence relations and series. Applications to selected
problems. Use of generating functions.
Elementary number theory: division in integers; greatest
common divisors; congruence; computer applications.
Selected applications of discrete mathematics (e.g. graph
theory). Selective introduction to other areas of pure
mathematics (e.g. abstract algebra).
Textbooks and References
Albertson. M. and Hutchinson, J. Discrete Mathematics with
Algorithms. New York: Wiley. 1988
Gersting. 1. Mathematical Structures for Computer Science. 2nd ed,
New York: Freeman, 1987
Mathematics Department notes
Skvarcius, R. and Robinson, W. Discrete Mathematics with Computer
Science Applications. Menlo Park, Calif.: BenjaminlCummings. 1986
SM584
Multivariate Statistical Methods
10.0 credit points
No. of hours per week: three hours
Prerequisite: SM484
Assessment: testslexamination and assignments
A third-year subject of the degree courses in mathematics
and computer science and applied and industrial
mathematics.
Subject description
Sampling from multivariate populations, the variancecovariance
matrix, the multivariate normal distribution,
multivariate means, Hotelling's T2 statistic, the multivariate
analysis of variance, Wilk's lambda.
An introduction to principal components analysis and factor
analysis.
Classification methods: cluster analysis, linear discriminant
analysis.
Multidimensional scaling
Computer packages such as Minitab and SA5 may be used.
Textbooks and References
Aldenderfer, M.S. and Blashfield, R.K. Cluster Analysis. Beverley Hills:
Saae. 1984
~ilron, W.R. and Goldstein, M. Multivariate Analysis. New York: Wiley,
1984
Everitt, 6.5. and Dunn, G. Advanced Methods of Data Exploration
and Modelling. London: Heinemann, 1983
Johnson, R.A. and Wichern, D.W. Applied Multivariare Statistical
Analysis. 2nd ed, Englewood Cliffs: Prentice Hall, 1982
Kruskal, J.B. and Wish, M. Multidimensional Scaling. Beverley Hills:
Sage, 1978
SM585 Sample Survey Design
10.0 credit points
No. of hours per week: three hours
Prerequisite: SM484
Assessment: testslexamination and assignments
A third-year subject of the degree courses in mathematics
and computer science and applied and industrial
mathematics.
Subject description
The basic designs for sample surveys: simple random
sampling, stratified sampling, systematic sampling and cluster
sampling.
Estimators for the mean total and proportion for simple
random samplies and stratified samples; variance estimation
for these two sample designs.
The design effect; sample size determination; EPSEM
samples.
Ratio estimation; cluster sampling, multi-stage sampling, PP5
sampling.
Practical issues and methods; questionnaire design; pilot
surveys, mail, interviewer-based and telephone surveys; nonsampling
errors; weighting.