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 economics and the physical, environmental and life sciences will be used as a vehicle throughout. Topics to be covered include: combinatorics and counting, induction and recurrence relations, graph theory and networks, matrix arithmetic and Markov chains, logic and finite set theory.

Learning Outcomes

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

On satisfying the requirements of this course, students will have the knowledge and skills to:

1. Recall, invent or interpret examples of motivation for mathematical constructs introduced in the course and used in discrete mathematics as models of processes in the world
2. Be sufficiently familiar with terminology from discrete mathematics used in the course as to be able to interpret, use and attempt to answer questions involving these words
3. Translate representations of mathematical information between the different formats presented in the course
4. Competently perform mathematical calculations in discrete mathematics using methods presented in the course
5. To an extent determined by each student's needs, interests and input, develop maturity of mathematical reasoning as well as general academic skills such as information literacy, tenacity, communication and collaboration. (This learning outcome may not necessarily be achieved by all students who pass the course, but all students will have the opportunity to develop these attributes by participating in course activities such as lectures, tutorials, consultation, assessment and use of the course website.)

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:

• One A4 sheet (both sides) of notes, hand-written by the student and in original form (not printed or photographed).
• A simple (non-programmable) scientific calculator.
• 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.

Worked Examples: For each of the twelve course topics A1 - D3, sets of practice questions will be made available on the course website. Worked solutions to these questions will be provided in time to help with the writing up of solutions to corresponding assignment questions.

Recommended Resources

Optional Text: Susanna Epp: Discrete Mathematics with Applications; 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 a number of 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.
• Homework 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: Students will be given an opportunity to view their exam scripts in a workshop following the exam, to view official solutions, and to ask the demonstrator about any grading issues.

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). The feedback given in these surveys is anonymous and provides the Colleges, University Education Committee and Academic Board with opportunities to recognise excellent teaching, and opportunities for improvement. The Surveys and Evaluation website provides more information on student surveys at ANU and reports on the feedback provided on ANU courses.

Other Information

We know that some of you are able to be on campus, while others are unable to be on campus. It is intended that all lectures will be delivered in-person on-campus for those who can attend on-campus events. Lectures are recorded and the recordings are made available via Wattle shortly after the lecture. Workshops are offered in-person and online workshop via zoom. You should sign up for whichever option suits your situation.

The course convener is available Monday, Wednesday, Thursday up to half an hour immediately after each lecture, at the lecture theatre venue, or by appointment. Also available at various times, including by appointment, in HN 1.56 and via zoom (the latter is intended for those students who cannot attend activities on campus).

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, or 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 Seq Def 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

Workshop registration via Wattle, starting in Week 0.

Assessment Summary

Assessment task	Value	Due Date	Return of assessment	Learning Outcomes
Weekly Written Assignments (Ten)	10 %	*	*	1,2,3,4,5
Participation in Workshops (Ten)	10 %	*	*	1,2,3,4,5
Mid-Semester Examination	20 %	29/03/2021	23/04/2021	1,2,3,4,5
Final Examination	60 %	03/06/2021	01/07/2021	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 Misconduct Rule before the commencement of their course. Other key policies and guidelines include:

• Student Assessment (Coursework) Policy and Procedure
• Special Assessment Consideration Policy and General Information
• Student Surveys and Evaluations
• Deferred Examinations
• Student Complaint Resolution Policy and Procedure

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 ANU Online website Students may choose not to submit assessment items through Turnitin. In this instance you will be required to submit, alongside the assessment item itself, hard copies of all references included in the assessment item.

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

Although there are no participation requirements (hurdles) for this course please note that:

Workshop Participation contributes 10% to your final grade. Details of how this is assessed are given in the details of this assessment item stated earlier in this document.

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.

Attendance has the advantage that the lecturer will be available for up to half an hour after each lecture to answer questions.

Examination(s)

A mid-semester and a final examination will be scheduled by the central ANU Examinations Office.

Students should consult the course wattle site and the ANU final examination timetable to confirm the date, time and venue of the exam.

Assessment Task 1

Weekly Written Assignments (Ten)

Starting in week 3, you will have weekly assignments to complete. Each assignment has questions relating to current Workshop material. Answer types range over requiring examples (LO1), selecting correct terminology (LO2), interpreting and creating diagrams and expressions (LO3), calculating various values and expressions from given data (LO4), correcting or completing simple proofs (LO5) and, occasionally, creating justifications or proofs of statements (LO5).

Assignments will be made available on the course website (Wattle) at 8 pm on the evening of your Workshop day for the relevant material (if your workshop is on Monday, for example, your assignment will become available at 8 pm on Monday). The assignment will be due exactly six days after it becomes available. The completed assignment must be scanned and uploaded to Wattle before the deadline stated on the assignment (exactly six days after it is made available). Late assignments will not be accepted. Your Workshop demonstrator will grade your assignment and you will normally be able to view your grade and possible brief comments online within a week of the submission deadline.

There are 10 assignments due over the semester. All ten assignments count towards your final course grade. It is intended that the marked assignments will be returned within 1 week of submission.

Assessment Task 2

Participation in Workshops (Ten)

You are strongly encouraged to attend the weekly workshops, starting in week 3. You can select from available workshop times when the workshop registration link opens on Wattle. There are online-only zoom workshops and on-campus face-to-face workshops.

A worksheet will be made available on Wattle for each workshop. You will be expected to complete some pre-workshop work and bring it with you to the workshop. In the workshop you will be encouraged to work collaboratively on the worksheet questions, asking for help from the demonstrator as needed. You may also ask the demonstrator about any of the answers to the preparation questions that you did not understand. You may also be asked to present solutions to the class. The aim here is to give you an opportunity to practice and improve your skill in verbal communication of mathematics, and to give the demonstrator an opportunity to correct any misconceptions that you or other class members may have about the underlying theory.

At each workshop, a participation score of up to 1 point will be recorded. You may earn half a point for bringing along substantial attempts at the pre-workshop tasks, and half a point for participating throughout the workshop with energy and enthusiasm. At the end of the semester, your scores will be combined to compute the workshop participation contribution to your final grade. To allow for occasional absences, your workshop participation contribution to your final grade will be calculated from your best eight (out of ten) workshop marks.

Please note that this grading scheme makes no mention of "correct solutions"; rather, it is your energy and commitment to making the most of the learning opportunities that are rewarded. Workshops are formative tasks, meaning we expect that the workshops help you master the material.

Assessment Task 3

Mid-Semester Examination

90 mins + reading time. Covers sections A1,A2,A3,B1,B2 of the course. A sample, plus solutions, will be available on Wattle.

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 will be weighted at 80% instead of 60%.

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 returned electronically within two weeks of taking the exam.

Assessment Task 4

Final Examination

180 mins + reading time. Covers the entire course, but with an emphasis on material not tested in the mid-semester exam. A sample, 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. Please check the ANU final Examination Timetable http://www.anu.edu.au/students/program-administration/assessments-exams/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 our culture as a community of scholars. At its heart, academic integrity is about behaving ethically. This means that all members of the community commit to honest and responsible scholarly practice and to upholding these values with respect and fairness. The Australian National University commits to embedding the values of academic integrity in our teaching and learning. We ensure that all members of our community understand how to engage in academic work in ways that are consistent with, and actively support academic integrity. The ANU expects staff and students to uphold high standards of academic integrity and act ethically and honestly, to ensure the quality and value of the qualification that you will graduate with. The University has policies and procedures in place to promote academic integrity and manage academic misconduct. Visit the following Academic honesty & plagiarism website for more information about academic integrity and what the ANU considers academic misconduct. The ANU offers a number of services to assist students with their assignments, examinations, and other learning activities. The Academic Skills and Learning Centre offers a number of workshops and seminars that you may find useful for your studies.

Online Submission

From Week 3 on, an assignment will be released each week through Wattle at 6pm on the day of your workshop. You should download and print a copy. Your solutions are to be hand-written in the spaces provided in the document. The completed document must then be scanned and saved as a pdf file, and the file uploaded via the same Wattle link that provided the original document. The assignment document will state the deadline for submission, normally allowing for six full days working time. 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 MATH1005.

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 MATH1005.

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 generally be awarded a mark of zero. However, especially for a first 'offence' when the submission is no more than 24 hours late , the marker (generally your workshop demonstrator), at his or her discretion, may simply apply a penalty of 5% of the possible marks. Unless an extension has been granted, Wattle will not allow submissions more than 24 hour late.

Referencing Requirements

Accepted academic practice for referencing sources that you use in presentations can be found via the links on the Wattle site, under the file named “ANU and College Policies, Program Information, Student Support Services and Assessment”. Alternatively, you can seek help through the Students Learning Development website.

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 The Course Convener may grant extensions 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 Diversity 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