Monash University Handbook 2010 Postgraduate - Units

Synopsis

This unit is designed for the retraining of registered secondary school teachers, to equip them for teaching mathematics in the 21st century classroom. It includes learning activities that develop an awareness of the interplay between the various topics, the characteristics and role of mathematical language, the role of investigative, modelling and problem solving approaches to mathematical inquiry in the teaching and learning of mathematics, and consideration of common misconceptions and difficulties experienced by students.

Objectives

This unit consolidates, strengthens and advances mathematics material from VCE, providing a foundation for further mathematics studies at tertiary level. Topics include number systems, functions, coordinate geometry of the plane and 3D space, vectors and matrices from geometric and algebraic viewpoints; calculus: real functions, limits and continuity, differentiation and integration and their applications.

Assessment

Assignments: 30%
On-line activities: 10% (total time input for assignments and online activities: 26 hours or equivalent length 10,000 words)
Three-hour end-of-unit examination: 60%
Students will be required to satisfactorily complete the assignments, and to pass the final examination in order to be awarded a passing grade in the unit.

Chief examiner(s)

Dr John Arkinstall

Contact hours

An average of 12 hours per week of private study and supplemented off campus residential school sessions.

Prerequisites

The unit assumes a mathematics background equivalent to VCE Mathematical Methods units 3 and 4.

Synopsis

Integration techniques, numerical integration, improper integrals; sequences and series, approximation of functions with polynomials and trigonometric functions; ordinary differential equations and modelling, models of population growth, predator-prey systems, oscillations; multivariable functions: partial and directional derivatives, maxima and minima, multiple integrals; linear systems as matrix equations, Gaussian elimination, the structure of vector spaces, eigenvalues and eigenvectors and their application to dynamical systems.

Assessment

Examination (3 hours): 60%
3 Assignments: 30%; Online activities: 10%
Students will be required to pass at least two assignments and the final examination to be awarded a pass grade in the unit.

Chief examiner(s)

Dr Andrew Percy

Prerequisites

MTH9010

Synopsis

Major topics covered include:

1. a range of basic optimization techniques applicable to quantitative decision making, including linear programming,
2. techniques for collecting, exploring, presenting and interpreting data,
3. modelling and calculation of probabilities relating to outcomes of chance experiments and random variables derived from them,
4. techniques for using computer-generated random numbers to simulate observations on random variables and simple probability models, and
5. techniques for making inferences about population parameters from sample data.

Objectives

On completion of unit MTH9030 students will have extended their knowledge of a range of mathematical and statistical techniques, in the process developing skills in investigation, modelling and problem solving in theoretical and real life contexts incorporating uncertainty; they will be able to make effective use of graphics calculators, spreadsheets and statistical software in data analysis, and will have developed skills in communicating the results of mathematical and statistical analyses. They will also have developed an awareness of common misconceptions they and others have with concepts of probability and statistics.

Assessment

Examination (3 hours): 60%
3 Assignments: 30%
On-line activities: 10%
Students will be required to pass at least two assignments and the final examination to be awarded a pass grade in the unit.

Chief examiner(s)

Dr Andrew Percy

Prerequisites

MTH9010

Synopsis

The unit provides a survey of topics fundamental to a deeper understanding of mathematics including logic and methods of proof, number systems, recurrence relations and difference equations, discrete structures (including graph theory), algebraic structures (groups, rings and fields), and a deeper look at the real number system as a complete ordered field. The unit is specifically designed for the retraining of mathematics teachers, and includes the use of mathematics software.

Objectives

On completion of unit MTH9040, students will be able to demonstrate knowledge of some of the approaches to, and processes of, proof in mathematics; skill in categorising examples using some of the recognised mathematical structures such as graphs, groups, rings and fields, and in applying known properties and results for those structures to problems involving these examples; knowledge of the structure and properties of number systems important to elementary mathematics, including the natural numbers, integers (and "clock arithmetics" based on finite subsets), rationals, reals and complex numbers, and in particular the role of ordering and completeness properties in these systems; a perspective on mathematical truth as local to an axiomatic system rather than absolute, and vulnerable. Students will develop skills in investigation, modelling and problem solving in theoretical and real life contexts related to the unit content, and communication of the results of mathematical analyses; communicating effectively mathematics results and ideas; and making effective and critical use of graphics calculators and spreadsheets. Students will also have developed an awareness of how the VCE mathematics topics fit into the body of mathematics knowledge.

Assessment

Examination (3 hours): 60%
4 Assignments: 40%
Students will be required to pass the final examination to be awarded a pass grade in the unit.

Chief examiner(s)

Dr Andrew Percy

Off-campus attendance requirements

Three weekend residential schools of 4 hours each

Prerequisites

MTH9020