This course is designed to show some of the interdependence of mathematics and computing, and is designed for students in both computer science and mathematics.

Topics to be covered include:

Foundations - Relations on sets, including equivalence, partial order relations and relational databases; properties of functions, permutations, arithmetic of integers modulo n.

Grammars and Automata - Phrase structure grammars, finite state automata, and the connections between the language accepted by an automaton, regular sets and regular grammars.

Graph Theory - Hamiltonian circuits, vertex colouring and the chromatic polynomial of a graph, planar graphs, applications including the travelling salesperson problem and scheduling problems.

Game Theory - Games of strategy as an application of graph theory, matrix games and solution of matrix games.

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.  Explain some of the major concepts of Discrete Mathematics and their role in modern mathematics.
2.  Explain the relationship between languages, finite state automata and regular sets.
3.  Use graph theoretic methods to solve appropriate problems.
4.  To decide appropriate methods to use when solving a problem in the topics covered.
5.  Solve problems with a good degree of accuracy.
6.  Use the internet and library to research some areas of the course.
7.  Experience working together to solve certain problems.

Required Resources

Full course notes will be available via the course website on Wattle.

Recommended Resources

The course has its own set of notes and external resources are not required. Following are some additional resources that may be handy.

• The book Epp, S, Discrete Mathematics with Applications (any edition) from MATH1005 is a good reference book.
• The book Lipschutz, S and Lipson, M, Discrete Mathematics (any edition) has some overlap in content with MATH2301 and has many solved problems.

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:

• Written comments.
• Verbal comments.
• Feedback to the whole class, to groups, to individuals, focus groups.

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.

Class Schedule

Week/Session	Summary of Activities	Assessment
1	Topics to be covered: Foundations: sets, relations, functions, partial orders, equivalence relations. Modular arithmetic. Regular expressions. Automata and their languages. Graph theory and some applications Vertex colouring. Matrix games. Games of strategy.

Tutorial Registration

Workshop registration will be via the course Wattle site. Workshops begin in Week 3.

Assessment Summary

Assessment task	Value	Due Date	Return of assessment	Learning Outcomes
Workshops preparation and participation	5 %	*	*	1,2,3,4,5,6,7
Assignments	30 %	*	*	1,2,3,4,5,6,7
Mid-semester Examination	25 %	30/08/2021	24/09/2021	1,2,3,4,5
End of Semester Examination	40 %	04/11/2021	02/12/2021	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

Lecture attendance is strongly recommended: students who do not attend lectures are statistically more likely to have difficulties managing the required assessment. When possible, lectures are recorded through the Echo360 system and recordings are made available on the course Wattle page, however these should mostly be used for review purposes. Recordings are not a full substitute for regular lecture attendance.

Workshop participation is required. These workshops are the main place students can get individual help. Students are supported to work cooperatively and share ideas. They should write the solutions to questions on whiteboards so that the demonstrators can easily interact with students during workshops. Depending on demand, some of the workshops will be set up to accommodate remote participants.

The instructor will have regular office hours (in person and Zoom), and students are encouraged to attend them to discuss class ideas and seek help. Additionally, MSI offers drop-in sessions that students are encouraged to attend to get extra support. More details about office hours and drop-in sessions will be available on the Wattle page.

Examination(s)

Mid-semester exam (worth 25%).

Final exam (worth 40%).

Please check the ANU Examination Timetable to confirm the date, time and location of exams.

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

Workshops preparation and participation

Students are expected to attend a total of 10 workshops in Weeks 3 through to 12 inclusive. Workshop participation relates to a student's active involvement in workshop discussion. In awarding marks for this task, demonstrators will take into account evidence of preparation, willingness to share solution ideas, and initiative in making suggestions or asking questions.

Students are expected to contribute in an on-going basis.

Assessment Task 2

Assignments

There will be approximately ten assignments in this course, which together are worth 30% of the final grade. It is intended that the marked assignments will be returned within a week from submission. Further details can be found on the course Wattle site.

The assignments will be due by 11:59pm on Thursday evening on each week that they are due.

Assessment Task 3

Mid-semester Examination

A mid-semester examination is included in the assessment. The examination is likely to be held in Week 6 or Week 7 (the date specified for this task is merely the first day of Week 6: the exam will probably be on a different day). Details will be made available on the examinations timetable website.

Assessment Task 4

End of Semester Examination

An end of semester examination is included in the assessment. The examination will be held during the university's official examination period for the semester (the date specified for this task is merely the first day of the exam period: the exam will probably be on a different day). Details will be made available on the examinations timetable website.

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

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. Details about online submission for this course will be made available on the Wattle page.

Hardcopy Submission

All submission is electronic.

Late Submission

Individual assessment tasks may or may not allow for late submission. Policy regarding late submission is detailed below:

Late submission not permitted. If submission of assessment tasks without an extension after the due date is not permitted, a mark of 0 will be awarded.

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

Assignments will be returned electronically.

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

Resubmission of work is not permitted in MATH2301.

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