Course Title: Mathematics for Cartography

Part A: Course Overview

Course Title: Mathematics for Cartography

Credit Points: 12.00

Course Code




Learning Mode

Teaching Period(s)


City Campus


145H Mathematical & Geospatial Sciences


Sem 1 2006,
Sem 1 2007,
Sem 1 2008,
Sem 1 2009,
Sem 1 2010

Course Coordinator: Yanqun Liu

Course Coordinator Phone: +61 3 99252275

Course Coordinator Email:

Course Coordinator Location: 8.9.26 City Campus

Pre-requisite Courses and Assumed Knowledge and Capabilities

You are expected to have capabilities consistent with the successful completion of any VCE mathematics course at Year 12 level.

Course Description

Mathematics for Cartography provides the mathematics needed for your program of Multimedia Cartography of Geospatial Science, so that you may practice, with understanding, the mathematical techniques required throughout your program and gain experience in applying mathematics in your field. The topics covered in this stream have been developed using the recommendation made by the program team of Multimedia Cartography.

Weekly practice classes aim to develop your capability to solve problems and to apply mathematical ideas and techniques. You generally work collaboratively in these classes, discussing the problems amongst yourselves and with practice class tutors in attendance before submitting your individual solutions. WebLearn tests aim to reinforce and develop your basic algebra skills and help to identify any basic misconceptions you may have about the new material being presented. In order to interest and motivate you, lectures are example-driven and application-based. Student-centred learning features prominently in this course through the use of self-help tutorials.

Objectives/Learning Outcomes/Capability Development

On successful completion of this course you will be able to:
• discuss cyclometric functions in two- and three-dimensions and apply them to spherical earth problems
• use complex numbers to solve quadratic equations
• utilize the algebra of complex numbers in cartographic applications
• determine projections, and areas of regions, using vector algebra methods
• evaluate dot and cross products
• construct the equation of a line in two dimensions
• calculate the distance between points in two and three dimensions
• calculate the angle between lines in two dimensions
• convert between rectangular and polar coordinates in two dimensions
• calculate the sum, transpose and product of matrices
• evaluate the determinant of square matrices
• manipulate matrices using row transformations
• determine solutions of simultaneous equations, using, where appropriate, Cramer’s rule
• find eigenvalues and eigenvectors of a square matrix
• use matrices to carry out linear transformations in two- and three-dimensions
• identify transformations as rotations or reflections
• make effective use of appropriate technology.

As you achieve these outcomes the capabilities that you will learn, develop and exercise are detailed below.

Capability  Level
GC1.1/1.2 Knowledge - 1
GC 2.1/2.2 Technical - 1
GC 3.1/3.2 Critical Analysis & Problem Solving - 1
GC 4.1/4.2 Communication - N/A
GC 5.1/5.2 Personal & Professional Awareness - N/A
GC 6.1/6.2 Independent & Integrated Practice - N/A

On successful completion of the course, you should be able to:

• understand the notions of trigonometric functions;       
• represent points in 2D plane and 3D space by their coordinates;    
• convert between rectangular and polar coordinates in 2D plane;
• calculate distance between points, angles between lines and area of simple geometric figures in 2D plane; 
• calculate the sum, transpose, product of matrices; 
• evaluate determinants of square matrices;
• determine solutions of simultaneous equations;
• find eigenvalues and eigenvectors of a square matrix;
• use matrices to carry out linear transformations in two- and three-dimensions
• determine scalar multiple, sum, dot product, cross product of vectors;
• make effective use of appropriate technology. 

Overview of Learning Activities

You will attend lectures where the underlying theory will be presented. A practice class will reinforce the material covered in lectures and in your own personal study. It will also provide you with an opportunity to practice your problem solving skills, to test your understanding, to exchange ideas with others and to discuss your progress with teaching staff. You are encouraged to work in teams, but are expected to hand in individual solutions.

Overview of Learning Resources

This course is taught through a mixture of classroom instruction, supervised problem-based practice classes, online tests and quizzes.
A number of homework problems will be set. You should aim to do as many of these as you need to obtain proficiency.
On-line self-help will be available to you in the form of topic-specific WebLearn quizzes. The quizzes are designed to provide instant feedback, and can be attempted repeatedly until proficiency is achieved.

This course will be supported online using the Learning Hub of the Distributed Learning System (DLS). The DLS will give access to important announcements, a discussion forum, staff contact details, the teaching schedule, online notes, assessment timelines,  review exercises and past exam papers. The Learning Hub is located at

You are advised to read your student EMS e-mail frequently for important announcements. You should also frequently visit the Learning Hub, as important announcements regarding the course will be made there.

Overview of Assessment

The weekly class exercise (which is completed in the practice class) will be marked and will count towards the final assessment.
The aim of the class exercises is to assist your understanding of the material covered in class and in your personal study, as well as providing two-way feedback. Qualities that will be highly regarded in your class exercise solutions include clear setting out, correct use of mathematical terminology and symbols, and clear explanation of steps to the solution. All working should be shown fully.  At a more advanced level, the class exercises will address your capacity to formulate and solve problems and to think critically and analytically. Although the work submitted at the end of each practice class must be individual (copying is forbidden), you are strongly encouraged to discuss the problems amongst yourselves and to seek help from, and interact with, the practice class tutors.