Mathematics - 2008

Extension Program Mathematics for High Achieving Students

Introduction

This subject is designed for students who enjoy mathematics and are mathematically talented. If you are such a student you may have already been involved in an acceleration or enrichment program during your earlier secondary school program, though this is not necessary. Topics build on those in Specialist Mathematics and thus they provide you with the opportunity to extend your knowledge, as well as to experience and appreciate some of the depth and complex beauty of higher level mathematics.

Career Opportunities

Graduates in Science who have majored in Mathematics and Statistics find employment in areas such as: biology (population modelling); business (quality management and improvement); demography and behavioural science (survey sampling, analysis and prediction of human populations); in finance, commerce and economics (the study and forecasting of production, consumer behaviour and stock prices); engineering (design and testing of structures, flood control and prediction, analysis of computer networks); education (secondary and tertiary teaching); and the medical sciences (epidemiology and analysis of medical research data).

VCE Prerequisites

Completion of Mathematical Methods 3/4 in Year 11 and enrolment in Specialist Mathematics 3/4 in Year 12; or concurrent enrolment in Mathematical Methods 3/4 and Specialist Mathematics 3/4 after completion of Mathematical Methods 1/2 and General Mathematics* (Specialist Mathematics orientation) 1/2.

*Applicants with a B+ average in General Mathematics will be considered. Other prerequisite subjects require A/A+ average.

A B+ average across non prerequisite subjects is required.

Teaching Locations

Extension Program Mathematics is taught at School Centres only. You must list two choices, in order of preference, on your application form. Classes will run at listed locations subject to minimum enrolments.

Contact Hours

• Total class hours per week: 2-3 depending on School Centre
• Total days per week: 1-3 depending on School Centre

In addition there are regular exercises to be completed each week and a number of assignments spread throughout the year.

Credit Arrangements

See Credit Policy for further information.

Subject Description

620-190 Extension Program Mathematics for High Achieving Students (Full year subject)

This subject must be successfully completed in order to obtain the ENTER increment.

This subject develops the concepts of vectors, matrices, sequences, complex numbers and the methods of linear algebra, and extends knowledge of the calculus of functions of one variable to functions of several variables. Students should gain an appreciation of mathematical proof.

Content

• Linear Algebra: Systems of linear equations, row-reduction, matrices and determinants, rank, inverse, solution of linear equations, geometrical interpretation.
• Vectors: vectors in three-dimensional space, cross products, equations of lines and planes, geometrical applications, vector spaces, subspaces, linear independence, bases, dimension, inner products, linear transformations, eigenvalues, eigenvectors.
• Analysis: foundations, methods of proof, proof by induction, convergence of sequences.
• Complex numbers: polar form, de Moivre’s Theorem, complex exponential, complex vector spaces.
• Multivariable calculus: Functions of several variables, level curves, heights; partial derivatives, mixed partial derivatives; total derivative; gradient vector, directional derivatives and applications; chain rule; tangent planes and normal lines, linear approximations; Hessian matrix, maxima and minima of functions of several variables; introduction to double and triple integrals and applications.

Textbooks

H. Anton and C. Rorres, Elementary Linear Algebra, Applications Version, 9 th Edition, Wiley, 2005

Assessment

Up to 50 pages of written assignments (0% or 10%), a 1.5 hour written examination and a 3 hour written examination during the examination period in November (90% or 100%). The relative weighting of the examinations and the assignments will be chosen so as to maximise the final mark.

More Information

Dr Penny Wightwick
Tel: 8344 5212

Department of Mathematics and Statistics
The University of Melbourne VIC 3010

Web: www.ms.unimelb.edu.au