• Offered by Mathematical Sciences Institute
• ANU College ANU Joint Colleges of Science
• Course subject Mathematics
• Areas of interest Computer Science, Mathematics, Advanced Computing, Algorithms and Data, Computer Engineering
• Course convener
• Mode of delivery In Person
• Co-taught Course
• Offered in First Semester 2025
Second Semester 2025
• STEM Course
Discrete Mathematical Models (MATH6005)

Introduction to discrete mathematics and its use in mathematical modelling. Emphasis will be placed on developing facility, technique and use in applications. Modelling of processes and phenomena which occur in the physical, environmental and life sciences, especially computer science, will be used as a vehicle throughout. Topics to be covered include: logic and set theory, combinatorics and counting, induction and recurrence relations, graph theory and networks, matrix arithmetic and Markov chains.

This course is co-taught with undergraduate students but assessed separately.

## Learning Outcomes

Upon successful completion, students will have the knowledge and skills to:

1. Recall, invent or interpret examples of motivation for mathematical constructs used in discrete mathematics as models of processes in the world.
2. Recognise, define, explain and use terminology and notation from discrete mathematics.
3. Identify the logical structure of a statement, and then identify the logical structure of an argument that may be used to prove or disprove the statement.
4. Competently perform mathematical calculations in discrete mathematics using methods presented in the course.
5. Write simple proofs/construct explicit counterexamples for statements relating to discrete mathematics topics covered in the course.
6. Use their deep knowledge and understanding of the material presented in the course to formulate responses to complex concrete and abstract problems.
7. Communicate their understanding and skills in discrete mathematics with colleagues and non-experts and apply their knowledge in an occupational situation.

## Indicative Assessment

1. Workshop quizzes (8) [LO 1,2,3]
2. Graduate assignments (four) (16) [LO 1,2,3,4,5,6,7]
3. Mid-Semester Examination (26) [LO 1,2,3,4,5,6,7]
4. Final Examination Regardless of performance on other assessment items, a minimum scaled score of 40% on the final exam is required to pass the course. (This is known as a 'course hurdle'.) (50) [LO 1,2,3,4,5,6,7]

The ANU uses Turnitin to enhance student citation and referencing techniques, and to assess assignment submissions as a component of the University's approach to managing Academic Integrity. While the use of Turnitin is not mandatory, the ANU highly recommends Turnitin is used by both teaching staff and students. For additional information regarding Turnitin please visit the ANU Online website.

The expected workload will consist of approximately 130 hours throughout the semester including:

• Face-to face component which may consist of approximately 33 hours of lecture activities (usually three one-hour lectures each week), and twenty hours of workshop activities (one two-hour workshop per week in ten weeks of the semester).

• Approximately 77 hours of self directed study which will include preparation for lectures and workshops, completion of regular formative assessment items, and study of the course materials.

## Inherent Requirements

There are no course-specific inherent requirements.

## Requisite and Incompatibility

CECS students must be enrolled in a Graduate Diploma of Computing or a Master of Computing to enrol in this course.

## Prescribed Texts

There are no specific reading books required. PDF copies of all lecture slides will be made available on the course website, in addition to the ECHO lecture recordings.

Some students may find it helpful to refer to a text book for an alternative exposition of certain topics and extra practice problems. The following text is recommended for this purpose: Susanna Epp: Discrete Mathematics with Applications; 3rd or 4th or 5th ed. Cengage.

References to this text will be provided for most course topics. The text does not cover every single topic in the course, and covers a number of topics not required for the course, but is nonetheless a good match to course in both level and content.

## Assumed Knowledge

Secondary School Prerequisite: ACT Mathematical Methods or NSW HSC Mathematics Advanced or equivalent.

Students who are concerned about their level of preparation for MATH1005 should contact the MSI first-year coordinator for advice.

## Fees

Tuition fees are for the academic year indicated at the top of the page.

Commonwealth Support (CSP) Students
If you have been offered a Commonwealth supported place, your fees are set by the Australian Government for each course. At ANU 1 EFTSL is 48 units (normally 8 x 6-unit courses). More information about your student contribution amount for each course at Fees

Student Contribution Band:
2
Unit value:
6 units

If you are a domestic graduate coursework student with a Domestic Tuition Fee (DTF) place or international student you will be required to pay course tuition fees (see below). Course tuition fees are indexed annually. Further information for domestic and international students about tuition and other fees can be found at Fees.

Where there is a unit range displayed for this course, not all unit options below may be available.

Units EFTSL
6.00 0.12500
Note: Please note that fee information is for current year only.

## Offerings, Dates and Class Summary Links

ANU utilises MyTimetable to enable students to view the timetable for their enrolled courses, browse, then self-allocate to small teaching activities / tutorials so they can better plan their time. Find out more on the Timetable webpage.

The list of offerings for future years is indicative only.
Class summaries, if available, can be accessed by clicking on the View link for the relevant class number.

### First Semester

Class number Class start date Last day to enrol Census date Class end date Mode Of Delivery Class Summary
2548 17 Feb 2025 24 Feb 2025 31 Mar 2025 23 May 2025 In Person N/A

### Second Semester

Class number Class start date Last day to enrol Census date Class end date Mode Of Delivery Class Summary
8602 21 Jul 2025 28 Jul 2025 31 Aug 2025 24 Oct 2025 In Person N/A