# MTH9040 - Introduction to mathematical structures

## 6 points, SCA Band 2, 0.125 EFTSL

#### Offered

Gippsland Second semester 2007 (Off-campus)

#### 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 categorizing examples using some of the recognized 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, modeling 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%; 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.

#### Off Campus Attendance Requirements

Three weekend residential schools of 4 hours each

#### Prerequisites

MTH9020