Discrete Structures

This subject is not offered in 2013.

120 hours

One first year mathematics subject (12.5 points)

OR

Admission to the Master of Engineering (Software)

None

None

Students cannot enrol in and gain credit for this subject and:

433-255 Logic and Computation

For the purposes of considering request for Reasonable Adjustments under the Disability Standards for Education (Cwth 2005), and Student Support and Engagement Policy, academic requirements for this subject are articulated in the Subject Overview, Learning Outcomes, Assessment and Generic Skills sections of this entry.

It is University policy to take all reasonable steps to minimise the impact of disability upon academic study, and reasonable adjustments will be made to enhance a student's participation in the University's programs. Students who feel their disability may impact on meeting the requirements of this subject are encouraged to discuss this matter with a Faculty Student Adviser and Student Equity and Disability Support: http://services.unimelb.edu.au/disability

Formal logic and discrete mathematics provide the theoretical foundations for computer science. This subject is an introduction to the science of computing. It provides a grounding in the theories of logic, sets, relations, functions, automata and formal languages, providing concepts that underpin virtually all the practical tools contributed by the discipline, for automated storage, retrieval, manipulation and communication of data.

• Use propositional and predicate logic as reasoning tools.

• Explain basic principles of mechanised reasoning, including resolution proof.

• Reason about properties of mathematical objects such as functions and relations.

• Apply discrete mathematical techniques to problems in computer science.

• Design and reason about simple finite-state automata.

Design and reason about regular expressions and context-free grammars.

• An individual 800-word homework set due around Week 6 (12%) (addressing ILOs 1 and 2)

• A 45-minute mid-semester written test around Week 7 (12%) (addressing ILOs 1, 2 and 3)

• An individual 800-word homework set due around Week 11 (12%) addressing ILOs 3, 4, 5, and 6)

• A 2-hour end-of-semester written examination (64%) (addressing all ILOs)

To pass the subject, students must obtain at least:50% overall 32/64 in the written examination

Doets, K. and van Eijck, J. 2004 The Haskell Road to Logic, Maths and Programming. King's College Publ.

Sipser, M. 2006 Introduction to the Theory of Computation. Thomson Course Technology, second edition

This subject potentially can be taken as a breadth subject component for the following courses:

• Bachelor of Arts
• Bachelor of Commerce
• Bachelor of Environments
• Bachelor of Music

You should visit learn more about breadth subjects and read the breadth requirements for your degree, and should discuss your choice with your student adviser, before deciding on your subjects.

On successful completion of this subject students should have:

• Analytical skills.

• Reasoning and problem-solving skills.

• Ability to communicate with precision, rigour and efficacy.

• Ability to apply knowledge of science and engineering fundamentals.

• Capacity for creativity and innovation.

• Ability to undertake problem identification, formulation and solution.

Students taking this subject will be expected to regularly access an internet-enabled computer.

This subject is available for science credit to students enrolled in the BSc (both pre-2008 and new degrees), BASc or a combined BSc course.