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.

Research-Led Teaching

Where appropriate, indication will be given of current research areas related to topics in the course.

Examination Material or equipment

In both the mid-semester exam and the final exam the permitted materials will be:

• A non-annotated translation dictionary (for ESL students).

Required Resources

Course Notes: PDF copies of all lecture slides will be made available on the course website, in addition to the ECHO lecture recordings.

Recommended Resources

Optional Text: Susanna Epp: Discrete Mathematics with Applications; 3rd or 4th or 5th ed. Cengage.

References to this text will be provided for all course topics except the last (Random Walks).

The text does not cover every single subtopic in the course, and does cover some subtopics not required for the course, but is nonetheless a good match to course in both level and content.

Recommended student system requirements 

ANU courses commonly use several online resources and activities including:

• video material, similar to YouTube, for lectures and other instruction
• two-way video conferencing for interactive learning
• email and other messaging tools for communication
• interactive web apps for formative and collaborative activities
• print and photo/scan for handwritten work
• home-based assessment.

To fully participate in ANU learning, students need:

• A computer or laptop. Mobile devices may work well but in some situations, a computer/laptop may be more appropriate.
• Webcam
• Speakers and a microphone (e.g. headset)
• Reliable, stable internet connection. Broadband recommended. If using a mobile network or wi-fi then check performance is adequate.
• Suitable location with minimal interruptions and adequate privacy for classes and assessments.
• Printing, and photo/scanning equipment

For more information please see https://www.anu.edu.au/students/systems/recommended-student-system-requirements

Staff Feedback

Students will be given feedback in the following forms in this course:

• Workshops: Demonstrators will give individual guidance and correction to student work on, and presentation of, worksheet problems.
• Graduate Assignments: Demonstrators will grade, but not correct, assignment work. Brief indications of where and how errors have been made will be provided with each student’s work. Common errors may be briefly discussed with the whole class during workshops. Students will then have an opportunity to ask the demonstrator about other errors.
• Mid-semester exam and final exam: Students will be given an opportunity to view their exam scripts online, to view official solutions and rubrics, and to ask the convener about any grading issues using a grade appeal process.

Student Feedback

ANU is committed to the demonstration of educational excellence and regularly seeks feedback from students. Students are encouraged to offer feedback directly to their Course Convener or through their College and Course representatives (if applicable). Feedback can also be provided to Course Conveners and teachers via the Student Experience of Learning & Teaching (SELT) feedback program. SELT surveys are confidential and also provide the Colleges and ANU Executive with opportunities to recognise excellent teaching, and opportunities for improvement.

Other Information

It is intended that all lectures will be delivered in-person on-campus. Lectures are recorded, and the recordings are made available via Wattle shortly after the lecture. Workshops are offered in-person and online workshops via zoom. The online workshops are intended to serve only those students who are unable to be on campus. You should sign up for an in-person workshop if you possibly can.

Finally, please also note that, as with all courses at ANU, a moderation process takes place after the marks for the various assessment components of the course are aggregated. Moderation is to provide consistency of grade standards across years and courses. It may result in the scaling up or scaling down, of your raw total score.

Class Schedule

Week/Session	Summary of Activities	Assessment
1	A1 Logic: Statements and Predicates. Valid Arguments.	Weekly assignments and workshop work will reinforce the content.
2	A2 Sets: Set Operations and identities. Russell's Paradox.	Weekly assignments and workshop work will reinforce the content.
3	A3 Relations and Functions: Definition & Properties of Relations and Functions.	Weekly assignments and workshop work will reinforce the content.
4	B1 Numbers: N,Z,Q,R. Base n. Computer & Modular Arithmetic.	Weekly assignments and workshop work will reinforce the content.
5	B2 Sequences and Induction: Implicit to Explicit Sequence Definition by Induction. Sorting. B3 Matrices: Matrix & Vector Operations. Linear Functions.	Weekly assignments and workshop work will reinforce the content.
6	C1 Counting: Cardinality. Permutations & Combinations. Stars & Bars. Pigeonhole Principle.	Weekly assignments and workshop work will reinforce the content.
7	C2 Probability: Probability Properties. Distributions. Random Variables.	Weekly assignments and workshop work will reinforce the content.
8	C3 Markov Processes: Markov States &Transition Matrices. Steady State.	Weekly assignments and workshop work will reinforce the content.
9	D1 Graph Theory: Graphs & Digraphs. Degree. Euler & Hamilton Graphs. Trees.	Weekly assignments and workshop work will reinforce the content.
10	D2 Weighted Graphs: Minimum Span. Travelling Sales Person Problem. Shortest Path. Max Flow. Matching.	Weekly assignments and workshop work will reinforce the content.
11	D3 Random Walks: Graph 'Walking'. Webgraphs & PageRank Algorithm.	Weekly assignments and workshop work will reinforce the content.
12	Revision	Weekly assignments and workshop work will reinforce the content.

Tutorial Registration

Students are required to enrol in one of the available weekly workshop groups by following a process that will be detailed on the course Wattle page, starting in Week 0. Remote participation options will be provided for students who require them due to travel restrictions or COVID-safe guidelines. However, not all times will be available for both remote and in-person attendance. Please refer to the course Wattle site for more information.

Assessment Summary

Assessment task	Value	Learning Outcomes
Workshop Quizzes (Best 8 of 10)	8 %	1,2,3
Graduate Assignments (Four)	16 %	1,2,3,4,5,6,7
Mid-Semester Examination	26 %	1,2,3,4,5
Final Examination	50 %	1,2,3,4,5

* If the Due Date and Return of Assessment date are blank, see the Assessment Tab for specific Assessment Task details

Policies

ANU has educational policies, procedures and guidelines , which are designed to ensure that staff and students are aware of the University’s academic standards, and implement them. Students are expected to have read the Academic Integrity Rule before the commencement of their course. Other key policies and guidelines include:

• Academic Integrity Policy and Procedure
• Student Assessment (Coursework) Policy and Procedure
• Special Assessment Consideration Guideline and General Information 
• Student Surveys and Evaluations
• Deferred Examinations
• Student Complaint Resolution Policy and Procedure
• Code of practice for teaching and learning

Assessment Requirements

The ANU is using 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. For additional information regarding Turnitin please visit the Academic Skills website. In rare cases where online submission using Turnitin software is not technically possible; or where not using Turnitin software has been justified by the Course Convener and approved by the Associate Dean (Education) on the basis of the teaching model being employed; students shall submit assessment online via ‘Wattle’ outside of Turnitin, or failing that in hard copy, or through a combination of submission methods as approved by the Associate Dean (Education). The submission method is detailed below.

Moderation of Assessment

Marks that are allocated during Semester are to be considered provisional until formalised by the College examiners meeting at the end of each Semester. If appropriate, some moderation of marks might be applied prior to final results being released.

Participation

In Semester 1 2023, this course is delivered on campus with adjustments for remote participants. Although there are no participation requirements (hurdles) for this course please note that:

You must attend the workshop in which you are enrolled in order to take the workshop quiz, and quiz scores contribute 8% of your final grade.

Assessable material for the course is specified by lecture content (rather than any text). So it is important to keep up regular monitoring of lectures, preferably by attending but otherwise by accessing the lecture recordings and/or PDF notes on Wattle.

Examination(s)

This course includes a mid-semester and a final examination. The details and mode of delivery for exams will be communicated through the course Wattle site and the ANU examination timetable.

 

Please note that, where a date range is used in the Assessment Summary in relation to exams, the due date and return date for mid-semester exams indicate the approximate timeframe in which the exam will be held; the due and return date for end of semester exams indicate the approximate timeframe in which the exam will be held and the date official end of Semester results are released on ISIS. Students should consult the course Wattle site and the ANU final examination timetable to confirm the date, time and mode of the exam.

Assessment Task 1

Workshop Quizzes (Best 8 of 10)

At the start of each workshop, you will complete a very short quiz, primarily on the material from lectures in the week preceding the quiz (the quiz in week x will primarily address material covered in lectures during week x-1). A typical quiz question will ask you to demonstrate your ability to recall or invent examples to illustrate ideas and motivations (LO1), your proficiency with the ideas, vocabulary and notation of the material (LO2), or your ability to recognize the logical structure of an argument or to describe the logical structure of an argument that may be used to prove a given statement (LO3). Given the nature of the problems, no partial credit will be given on quizzes. Your scores on each problem will be used to assign a score out of 1 for each quiz. To allow for occasional absences, the quiz contribution to your final grade will be calculated from your best eight (out of ten) quiz marks.

Assessment Task 2

Graduate Assignments (Four)

You have four assignments throughout the semester, as follows:

Graduate Assignment A: Available from 2 pm on the Friday of Teaching Week 1, due at 2 pm on the Friday of Teaching Week 3.

Graduate Assignment B: Available from 2 pm on the Friday of Teaching Week 4, due at 2 pm on the Friday of Teaching Week 6.

Graduate Assignment C: Available from 2 pm on the Friday of Teaching Week 7, due at 2 pm on the Friday of Teaching Week 9.

Graduate Assignment D: Available from 2 pm on the Friday of Teaching Week 10, due at 2 pm on the Friday of Teaching Week 12.

Each assignment has questions relating to the current lecture and workshop material. Answer types range over requiring examples (LO1), selecting correct terminology (LO2), interpreting and creating diagrams and expressions (LO1, 2, 4), calculating various values and expressions from given data (LO4), identifying the logical structure of a statement, and then identifying the logical structure of an argument that may be used to prove or disprove the statement (LO3), creating justifications or proofs of statements (LO5), formulating responses to complex concrete and abstract problems (LO6), communicating your understanding and skills in discrete mathematics with colleagues and non-experts, and applying your knowledge in an occupational situation (LO7).

Solutions need to be detailed and clearly written with attention to good English and mathematical rigour. The assignment may be hand-written or typeset.

Assignments will be made available via the course website (Wattle), and completed assignments must be scanned and uploaded through the same portal.

Except in very exceptional circumstances, late assignments will not be accepted - see "Assignment Submission" section later in this document. It is intended that you should be able to view your grade and brief comments via Wattle about a week after the submission deadline.

Assessment Task 3

Mid-Semester Examination

120 mins. Covers the material from the first six weeks of lectures. A sample exam, plus solutions, will be available on Wattle.

The mid-semester exam will be held during the ANU mid-semester examination period at a time and date determined by the ANU Examinations Office. Please check the course Wattle site and the ANU Examination Timetable to confirm the date, time and location of the mid-semester exam.

It is intended that results will be released electronically within two weeks of the exam date.

This exam is redeemable via the final exam: if the percentage score on the mid-semester exam is less than the percentage score on the final exam, only the final exam will count and it will be weighted at 76% instead of 50%.

Assessment Task 4

Final Examination

180 mins. Covers the entire course, but with an emphasis on material not tested in the mid-semester exam. A sample exam, plus solutions, will be available on Wattle.

Some scaling of marks on the final exam may occur if the distribution of marks leads to results significantly out of line with previous years.

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'.)

The exam will be held during the ANU mid-semester examination period at a time and date determined by the ANU Examinations Office. Please check the course Wattle site and the ANU Examination Timetable to confirm the date, time and location of the exam.

It is intended that results will be released electronically on the date that first-semester results are published, as specified by the ANU academic calendar.

Academic Integrity

Academic integrity is a core part of the ANU culture as a community of scholars. The University’s students are an integral part of that community. The academic integrity principle commits all students to engage in academic work in ways that are consistent with, and actively support, academic integrity, and to uphold this commitment by behaving honestly, responsibly and ethically, and with respect and fairness, in scholarly practice.

The University expects all staff and students to be familiar with the academic integrity principle, the Academic Integrity Rule 2021, the Policy: Student Academic Integrity and Procedure: Student Academic Integrity, and to uphold high standards of academic integrity to ensure the quality and value of our qualifications.

The Academic Integrity Rule 2021 is a legal document that the University uses to promote academic integrity, and manage breaches of the academic integrity principle. The Policy and Procedure support the Rule by outlining overarching principles, responsibilities and processes. The Academic Integrity Rule 2021 commences on 1 December 2021 and applies to courses commencing on or after that date, as well as to research conduct occurring on or after that date. Prior to this, the Academic Misconduct Rule 2015 applies.

 

The University commits to assisting all students to understand how to engage in academic work in ways that are consistent with, and actively support academic integrity. All coursework students must complete the online Academic Integrity Module (Epigeum), and Higher Degree Research (HDR) students are required to complete research integrity training. The Academic Integrity website provides information about services available to assist students with their assignments, examinations and other learning activities, as well as understanding and upholding academic integrity.

Online Submission

You will be required to agree to a declaration as part of the submission of your assignments, that will record your understanding of ANU academic integrity principles. The assignment document will state the deadline for submission. You should keep a copy of both your completed document and its pdf file. Note that pdf is the only file format permitted for online submission in MATH6005. MATH6005 does not use Turnitin, having been granted an exemption.

Hardcopy Submission

Except under very special course-wide conditions (e.g. major breakdown of the Wattle system) hardcopy submission of assignments will not be permitted in MATH6005.

Late Submission

Except in rare cases, such as documented illness or temporary disability, extensions to assignment deadlines will be not be granted in this course. In particular, extensions will not be granted to cover timing misjudgements. So you need to leave enough time to scan and upload your document, remembering to allow time for possible mishaps in the process.

An assignment not submitted by the due date and time, and without an extension, will be awarded a mark of zero.

Referencing Requirements

The Academic Skills website has information to assist you with your writing and assessments. The website includes information about Academic Integrity including referencing requirements for different disciplines. There is also information on Plagiarism and different ways to use source material.

Returning Assignments

Except in exceptional circumstances, you will be able to view your marked assignment via Wattle within a week of the due date. Exceptions include, but are not restricted to, unexpected unavailability of the marker and disruptions to the timetable resulting from public holidays.

Extensions and Penalties

Extensions and late submission of assessment pieces are covered by the Student Assessment (Coursework) Policy and Procedure. Extensions may be granted for assessment pieces that are not examinations or take-home examinations. If you need an extension, you must request an extension in writing on or before the due date. If you have documented and appropriate medical evidence that demonstrates you were not able to request an extension on or before the due date, you may be able to request it after the due date.

Resubmission of Assignments

Assignments cannot be resubmitted.

Privacy Notice

The ANU has made a number of third party, online, databases available for students to use. Use of each online database is conditional on student end users first agreeing to the database licensor’s terms of service and/or privacy policy. Students should read these carefully. In some cases student end users will be required to register an account with the database licensor and submit personal information, including their: first name; last name; ANU email address; and other information.
In cases where student end users are asked to submit ‘content’ to a database, such as an assignment or short answers, the database licensor may only use the student’s ‘content’ in accordance with the terms of service – including any (copyright) licence the student grants to the database licensor. Any personal information or content a student submits may be stored by the licensor, potentially offshore, and will be used to process the database service in accordance with the licensors terms of service and/or privacy policy.
If any student chooses not to agree to the database licensor’s terms of service or privacy policy, the student will not be able to access and use the database. In these circumstances students should contact their lecturer to enquire about alternative arrangements that are available.

Distribution of grades policy

Academic Quality Assurance Committee monitors the performance of students, including attrition, further study and employment rates and grade distribution, and College reports on quality assurance processes for assessment activities, including alignment with national and international disciplinary and interdisciplinary standards, as well as qualification type learning outcomes.

Since first semester 1994, ANU uses a grading scale for all courses. This grading scale is used by all academic areas of the University.

Support for students

The University offers students support through several different services. You may contact the services listed below directly or seek advice from your Course Convener, Student Administrators, or your College and Course representatives (if applicable).

• ANU Health, safety & wellbeing for medical services, counselling, mental health and spiritual support
• ANU Access and inclusion for students with a disability or ongoing or chronic illness
• ANU Dean of Students for confidential, impartial advice and help to resolve problems between students and the academic or administrative areas of the University
• ANU Academic Skills and Learning Centre supports you make your own decisions about how you learn and manage your workload.
• ANU Counselling Centre promotes, supports and enhances mental health and wellbeing within the University student community.
• ANUSA supports and represents undergraduate and ANU College students
• PARSA supports and represents postgraduate and research students