This course will offer an 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 computer science, economics and the physical, environmental and life sciences will be used as a vehicle throughout. 

Learning Outcomes

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

Upon successful completion 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 proficient with terminology from discrete mathematics used in the course and be able to interpret, use and answer questions from other contexts which use this terminology.
3. Translate representations of mathematical information between the different formats presented in the course.
4. Reason mathematically and competently perform mathematical calculations in discrete mathematics using methods presented in the course.
5. Use their deep knowledge and understanding of the material presented in the course to formulate responses to complex concrete and abstract problems.
6. 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:

• 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; 3rd or 4th 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.

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

Please note, that where there are multiple assessment tasks of the same type, e.g weekly quizzes, a date range is used in the Assessment Summary. The first date is the approximate due date of the first task, the return date is the approximate return date for the final task. Further information is provided in the assessment section of the class summary, and details are provided on the course wattle site.

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.

Adjustments to delivery in 2020

Course delivery and assessment in 2020 was adjusted due to the COVID-19 pandemic. Any information below that replaces what was published in the Class Summary for Semester 1, 2020 was approved by the Associate Dean Education (as is required after 10% commencement of a course). Where an activity or assessment is not referenced below, it remains unchanged.

Teaching Activities

• Lectures were recorded and posted on Wattle.
• Workshops were done by Zoom at the regular time.

Assessment

Adjustments were made to assignment due dates; for details see the course Wattle site.

• Mid semester exam was cancelled.
• Final Exam was a one hour multiple choice quiz on Wattle followed by a written take-home exam.
• Final grades were determined as the option below that gave the higher grade:
• (i) (continuous increased) The final exam continued to be worth 50% and all other assessed items had their assessment value increased proportionately to aggregate to the other 50%.
• (ii) (exam increased) All non-exam assessed items remained at their current assessment value and the assessment value of the final exam was increased to make up the total to 100%. This means that for MATH6005 the final exam was worth 75%.

Class Schedule

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

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)	5 %	16/03/2020	05/06/2020	1,2,3,4
Weekly Online Multiple Choice Quizzes (Ten)	5 %	16/03/2020	01/06/2020	2,3,4
Participation in Workshops (Ten)	0 %	06/03/2020	29/05/2020	1,2,3,4,6
Graduate Assignment A	5 %	03/04/2020	13/04/2020	1,2,3,4,5,6
Graduate Assignment B	5 %	08/05/2020	18/05/2020	1,2,3,4,5,6
Graduate Assignment C	5 %	29/05/2020	08/06/2020	1,2,3,4,5,6
Mid-Semester Examination	25 %	20/04/2020	04/05/2020	1,2,3,4
Final Examination	50 %	04/06/2020	02/07/2020	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 Academic Integrity . 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

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

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 Department.

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 venue of the exam.

Assessment Task 1

Weekly Written Assignments (Ten)

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 given proofs (LO4) and, occasionally, creating justifications or proofs of given statements (LO4).

Assignments will be made available on the course website (Wattle) on the evening of your Workshop day for the relevant material. Answers are to be hand written in the spaces provided on the assignment. You will be allowed six days to do this.The completed assignment must be scanned and uploaded to Wattle before the deadline stated on the assignment. Except in very exceptional circumstances, late assignments will not be accepted - see "Assignment Submission" section later in this document. 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.

All ten assignments count towards your final course grade.

The date range for these tasks indicates the approximate due date for the first assignment and the approximate return date for the last assignment. There are 10 assignments due over the semester. It is intended that the marked assignments will be returned within 1 week after submission.

Assessment Task 2

Weekly Online Multiple Choice Quizzes (Ten)

Each quiz has randomly generated questions relating to current Workshop material. Question types include: selecting correct terminology (LO2), interpreting and creating diagrams and expressions (LO3), and calculating various values and expressions from given data (LO4).

Quizzes will become available on Monday evening of each teaching week, starting in Week 3. (This includes the two Monday public holidays this semester, Canberra Day in Week 3 and (for) ANZAC Day in Week 8.) Quizzes will remain open for exactly one week. Once started, you will have a fixed time limit to finish, usually 15 or 20 minutes. Quiz closing times will not be extended.

All ten quizzes count towards your final course grade.

The date range for these tasks indicates the approximate due date for the first quiz and the approximate return date for the last quiz. There are 10 quizzes due over the semester.

Assessment Task 3

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.

A worksheet will be made available on Wattle for each workshop. You are not expected to start on this before your workshop; a separate set of pre-workshop questions will be provided to help you prepare, with brief answers provided on-line before the workshop.

In the first half of 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. In the next half of the workshop your demonstrator will select students to present solutions to the class. The aim here is to give you an opportunity to practice and improve your skill in verbal communication (LO6) of mathematics, and to give the demonstrator an opportunity to correct any misconceptions that you or other class members may have about underlying theory.

For graduate students (i.e students in MATH6005) participation in Workshops does not count towards the final grade.

Workshops are provided as a valuable environment in which to engage with course material and help you regularly assess your level of comprehension.

However it is essential to be enrolled in a Workshop (even if you don't attend) in order to have access to weekly assignments (which do count towards your final grade) and to have all your assignments (regular and graduate) graded.

The date range for this task comprises the first to the last workshop of the semester..

Assessment Task 4

Graduate Assignment A

This assignment covers Section A of the course (Logic, Sets, Relations and Functions). Some questions will relate to the application of discrete mathematics to computing. Questions will require deeper knowledge and understanding (LO5) than the regular weekly assignments based on Workshop worksheets. Solutions need to be detailed and clearly written with attention to good English and mathematical rigour. The assignment may be hand-written or typeset.

Assignment A will be made available on the course website (Wattle) on Monday of teaching week 4 and is due by Friday of teaching week 6 (i.e. just prior to the mid-semester break). The completed assignment must be scanned and uploaded to Wattle. Except in very exceptional circumstances, late assignments will not be accepted - see "Assignment Submission" section later in this document. Your workshop demonstrator will grade your assignment and, barring unforeseen difficulties with marking, you should be able to view your grade and possible brief comments online about a week after the submission deadline.

Assessment Task 5

Graduate Assignment B

This assignment covers Section B of the course (Numbers, Sequences, Mathematical Induction and Matrices). Some questions will relate to the application of discrete mathematics to computing. Questions will require deeper knowledge and understanding (LO5) than the regular weekly assignments based on Workshop worksheets. Solutions need to be detailed and clearly written with attention to good English and mathematical rigour. The assignment may be hand-written or typeset.

Assignment B will be made available on the course website (Wattle) on Monday of teaching week 7 and is due by Friday of teaching week 9. The completed assignment must be scanned and uploaded to Wattle. Except in very exceptional circumstances, late assignments will not be accepted - see "Assignment Submission" section later in this document. Your workshop demonstrator will grade your assignment and, barring unforeseen difficulties with marking, you should be able to view your grade and possible brief comments online about a week after the submission deadline.

Assessment Task 6

Graduate Assignment C

This assignment covers Section C of the course (Counting, Probability and Markov Processes. ). Some questions will relate to the application of discrete mathematics to computing. Questions will require deeper knowledge and understanding (LO5) than the regular weekly assignments based on Workshop worksheets. Solutions need to be detailed and clearly written with attention to good English and mathematical rigour. The assignment may be hand-written or typeset.

Assignment C will be made available on the course website (Wattle) on Monday of teaching week 10 and is due by Friday of teaching week 12. The completed assignment must be scanned and uploaded to Wattle. Except in very exceptional circumstances, late assignments will not be accepted - see "Assignment Submission" section later in this document. Your workshop demonstrator will grade your assignment and, barring unforeseen difficulties with marking, you should be able to view your grade and possible brief comments online about a week after the submission deadline.

Assessment Task 7

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 75% instead of 25%.

The date range is a general indication of when the mid-semester exam will be held. Please check the course Wattle site and the ANU Examination Timetable to confirm the date, time and location of the mid-semester exam.

Assessment Task 8

Final Examination

180 mins + reading time. Covers the entire course, but with a very strong 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 date range in the Assessment Summary indicates the start of the end of semester exam period and the date official end of semester results are released on ISIS. 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.

Academic Integrity

Academic integrity is a core part of the ANU culture as a community of scholars. At its heart, academic integrity is about behaving ethically, committing to honest and responsible scholarly practice and upholding these values with respect and fairness.

The ANU commits to assisting all members of our community to 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 be familiar with the academic integrity principle and Academic Misconduct Rule, 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 Academic Misconduct Rule is in place to promote academic integrity and manage academic misconduct. Very minor breaches of the academic integrity principle may result in a reduction of marks of up to 10% of the total marks available for the assessment. The ANU offers a number of online and in person services to assist students with their assignments, examinations, and other learning activities. Visit the Academic Skills website for more information about academic integrity, your responsibilities and for assistance with your assignments, writing skills and study.

Online Submission

From Week 3 on, an assignment will be released each week through Wattle at 7pm 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.

Also by Monday morning in weeks 4, 7 and 10 a special graduate assignment will be released through Wattle. These assignments are more substantial than the regular ones and you will have ten full days working time. The assignment document will state the deadline for submission. Your solutions can be typed or hand-written and there is no restriction on space. You must then scan all your solution pages into a single pdf file and upload it to Wattle via the same link that provided the assignment. Again, 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.

You will be required to electronically sign a declaration as part of the submission of your assignment.

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 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 online 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 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