Units
Discrete Mathematics
Unit code: MAB461
Contact hours: 4 per week
Credit points: 12
Information about fees and unit costs
Discrete mathematics is playing an ever increasingly important role in society. We live in an electronic age where information security is of paramount importance, and it is discrete mathematics in the main that provides this security. In addition, many real world systems are discrete in nature and therefore lend themselves to a discrete analysis. These methods are therefore vital to the professional mathematician and useful to those with an interest in mathematics. This second level unit will provide you with an introduction to discrete and combinatorial mathematics, and give you a mathematical perspective that is different from the traditional coverage in other mathematics units. It will also provide you with valuable methods to apply in other areas of science and computer science.
Availability
| Semester | Available |
|---|---|
| 2013 Semester 2 | Yes |
Sample subject outline - Semester 2 2013
Note: Subject outlines often change before the semester begins. Below is a sample outline.
Rationale
Discrete mathematics deals with discrete rather than continuous mathematical structures. Since computers store and process data discretely, the increasing use of computers for information and communications technologies means discrete mathematics has widespread practical application in areas such as computer science, cryptography, information theory, programming, software development, game theory and decision making. Discrete mathematical concepts can be applied to represent systems and solve problems in these and many other areas in business and industry. These methods are therefore vital to the professional mathematician and computer scientist, and useful to informed citizens of a technological society, as well as those with an interest in mathematics.
Aims
This second level unit will provide you with an introduction to discrete mathematics, including concepts related to logic, proofs, set theory, counting and number theory. This practical and contemporary branch of mathematics has a different perspective than many of the more traditional mathematics units. The discrete structures and methods presented apply directly to many real-life situations. In addition to the mathematical content, important skills and strategies for problem solving and reasoning that you are exposed to in this unit can be applied in other areas of science and computer science.
Objectives
On completion of this unit you should be able to:
1. Explain the basic concepts and applications of abstract algebra and logic, counting, set theory and number theory.
2. Use mathematical procedures and methods of proof, and recognise the circumstances in which these procedures and proofs apply.
3. Draw on a range of knowledge and thinking skills to solve discrete mathematics problems.
4. Communicate problems and solutions in writing, using expressions appropriate to the context of the problem.
Content
This unit introduces fundamental concepts in discrete mathematics related to topics selected from the following list:
Approaches to Teaching and Learning
You are responsible for your academic progression in this unit. Unit staff provide a learning environment designed to maximise your learning experience. In order to realise your full potential, it is strongly recommended that you actively participate in all of the learning activities offered in this unit.
The content of the unit is delivered through weekly lectures and tutorial sessions, and through the QUT Blackboard site. During the weekly sessions material on various discrete mathematic topics will be presented. The material presented will be context based utilising a wide variety of examples from different areas of application. The emphasis will be on learning through experience, learning as individuals, written communication, and developing skills and attitudes to promote life-long learning. Questions related to the presented material will be provided; answering these questions will direct your focus and aid your preparation for unit assessment tasks. Your participation in the learning activities provides opportunities for you to self assess, and to obtain feedback from unit staff and your peers.
The unit coordinator wil use email and the unit's QUT Blackboard site to make announcements and to post various types of information throughout the semester. It is your responsibility to access your email account and the unit's QUT Blackboard site regularly. You should also familiarise yourself with Science and Engineering Faculty and University student rules, policies and procedures.
You must be able to manage your time and prioritise activities in order to complete the required unit activities. It is your responsibility to ensure that your work is completed in a timely manner. Independent work is required to complete your assessment tasks. Although you may discuss some of the tasks with others, the work you submit for assessment must be your own individual effort.
Assessment
This unit's major aim is to introduce you to a variety of useful discrete mathematical structures and the associated methods and techniques for dealing with these structures. The most appropriate form of assessment is individual written tasks, including exams. The exam component is split into progressive (Quiz) and final sections, to allow us to provide you with early feedback on your progress while also assessing the full range of skills you should develop through the semester. The problem solving task provides an opportunity for you to practise your problem-solving skills on a wider range of problems, without the time pressures or reduced access to resources that apply to examinations.Your scripts for the problem solving tasks will be returned to you after marking, so you can obtain feedback on your performance and identify your areas of strength and weakness. You will also be given the opportunity to review your marked progressive exam paper, for the same purpose. Solutions to the progressive exam and model answers for the problem solving task will also be available.
Assessment name:
Quiz/Test
Description:
This progressive assessment will consist of a 1-hour examination and will be administered in week 7. It will cover the content from weeks 1 to 6.
Relates to objectives:
All
Weight:
20%
Internal or external:
Internal
Group or individual:
Individual
Due date:
Week 7
Assessment name:
Problem Solving Task
Description:
This task will require you to solve various mathematical problems assigned weekly, using the techniques presented in classes. Submission of your written solutions to these problems will be required at several time points during the semester.
Relates to objectives:
All
Weight:
40%
Internal or external:
Internal
Group or individual:
Individual
Due date:
Throughout Semester
Assessment name:
Examination (Theory)
Description:
The final examination will be based on unit material drawn from the full semester, and will allow you to demonstrate the knowledge and skills you have acquired in discrete mathematics, including relevant problem-solving skills
Relates to objectives:
All
Weight:
40%
Internal or external:
Internal
Group or individual:
Individual
Due date:
End of Semester
Academic Honesty
QUT is committed to maintaining high academic standards to protect the value of its qualifications. To assist you in assuring the academic integrity of your assessment you are encouraged to make use of the support materials and services available to help you consider and check your assessment items. Important information about the university's approach to academic integrity of assessment is on your unit Blackboard site.
A breach of academic integrity is regarded as Student Misconduct and can lead to the imposition of penalties.
Resource materials
Texts:
There are no set texts for this unit.
Note: The lecture material will be made available on the unit QUT Blackboard website.
References:
1. Grimaldi RP (1999) Discrete and Combinatorial Mathematics, An Applied Introduction, 4th edition, Addison-Wesley
2. Rosen KH (2000) Elementary Number Theory - and its applications, 4th edition, Addison Wesley Longman
3. Anton H, Kolman B, Averbach B & Deulinger CG (1988) Applied Finite Mathematics, 4th edition, Harcourt Brace Janovich
4. Durbin JR (2000) Modern Algebra - an Introduction, 4th edition, Wiley
Risk assessment statement
There are no out of the ordinary risks associated with this unit. Emergency exits, evacuation procedures and assembly areas will be described in the first few lectures. More information can be found on the university's Health and Safety web site 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: 15-May-2012
