Units

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Sample subject outline - Semester 1 2012

Note: Subject outlines often change before the semester begins. Below is a sample outline.

Rationale

Discrete mathematics is finding increasing numbers of applications in many fields of human endeavour. It is therefore important that professional mathematicians have a sound knowledge in this area both from practical and historical viewpoints. This unit will provide both of these perspectives.

Aims

This unit will provide you with advanced ideas, methodologies, techniques and applications in graph theory and number theory.

Objectives

If you complete this unit successfully you should be able to:

1. Know and understand advanced concepts and methodologies in graph theory and number theory.
2. Apply these concepts to a range of problems and applications
3. Express clearly and precisely mathematical arguments using the theory, symbolism and language developed.
4. Engage analytical thinking skills.

Content

There will be 2 distinct sections to the content. In one section you will learn the mechanics of graph theory and then apply these in some commonly encountered problems such as tree structures and optimizations including shortest path problems.

The other section will cover another six weeks and introduce more advanced concepts and methodologies in number theory such as congruence, multiplicative functions, primitive roots and quadratic residues and applications of these concepts and methodologies.

Approaches to Teaching and Learning

You will be required to attend 2 hours of lectures and a 1 hour tutorial each week. You will be exposed to the theory in lectures, and applications will be demonstrated. The tutorial will provide you with additional problems to test your understanding and enable you to get immediate feedback on your attempts, or help with a problem.

Assessment

The nature of the material presented and the necessity for a thorough understanding of the theory in this unit make the most appropriate form of assessment formal examination.Formative assessment will be provided to you by feedback from your assignments and from solutions to tutorial problems.

Assessment name: Examination (Theory)
Description: Formal 3 hour formal examination.
Relates to objectives: All.
Weight: 60%
Internal or external: Internal
Group or individual: Individual
Due date: Negotiated by Cohort

Assessment name: Problem Solving Task
Description: Problems to help you develop mathematical skills and give you insight into what you might expect to encounter in the final examination.
Relates to objectives: 2, 3 and 4.
Weight: 30%
Internal or external: Internal
Group or individual: Individual
Due date: Throughout Semester

Assessment name: Presentation (Oral or Group)
Description: During weekly lectures and tutorials, students will present a portion of the lecture material and their solutions to exercises; depending on the number of students enrolled in the unit, you can expect to present 1-3 times over the course of the semester.
Relates to objectives: 1, 2, 3 and 4.
Weight: 10%
Internal or external: Internal
Group or individual: Individual
Due date: Between Weeks 2 & 13

Academic Honesty

Academic honesty means that you are expected to exhibit honesty and act responsibly when undertaking assessment. Any action or practice on your part which would defeat the purposes of assessment is regarded as academic dishonesty. The penalties for academic dishonesty are provided in the Student Rules. For more information you should consult the QUT Library resources for avoiding plagiarism.

Resource materials

Reference Texts:

V. Shoup. A Computational Introduction to Number Theory and Algebra, second edition. Cambridge University Press, 2008. Available for free online from the author's website at: http://shoup.net/ntb

J.A. Bondy and U.S.R. Murty. Graph Theory with Applications. North-Holland, 1976. Available for free online from the author's website at: http://people.math.jussieu.fr/~jabondy/books/gtwa/gtwa.html

Risk assessment statement

There are no out of the ordinary risks associated with this unit. Evacuation procedures and assembly areas will be indicated to you in the first few lectures and tutorials. More detail on health and safety can be found at http://www.hrd.qut.edu.au/healthsafety/healthsafe/index.jsp

Disclaimer - Offer of some units is subject to viability, and information in these Unit Outlines is subject to change prior to commencement of semester.

Last modified: 31-Oct-2011