Outline

Overview

This advanced unit will introduce you to the language and key methods of the area of Discrete Mathematics. It provides an introduction to discrete mathematics that addresses very similar material to MATH1064, while looking at mathematical concepts and their foundations in more depth. This includes an introduction into mathematical logic and set theory, concepts of proof including mathematical induction, a solid foundation in fundemental mathematical objects sucha as functions including generating functions, relations, orders, sequences, and graphs. It will delve into counting problems arising from algebraic combinatorics, such as Young tableaux and Mobius functions. The unit will also cover the foundations of asymptotic growth and computational complexity, such as O-notation, and it will cover basic ideas from the theory of computations. When you complete this unit you will (1) have the mathematical foundations to continue your studies in combinatorics, graph theory and other areas of pure mathematics; (2) to be able to understand, develop, and apply modeling techniques from discrete mathematics to fields in applied mathematics, computer science, and other disciplines; (3) be able to independently solve problems and find proofs of mathematical statements.

Unit details and rules

Academic unit	Mathematics and Statistics Academic Operations
Credit points	6
Prerequisites ?	None
Corequisites ?	None
Prohibitions ?	MATH1004 or MATH1904 or MATH1064
Assumed knowledge ?	(HSC Mathematics Extension 2) or (Band E4 in HSC Mathematics Extension 1) or equivalent
Available to study abroad and exchange students	Yes

Teaching staff

Coordinator	Jonathan Spreer, jonathan.spreer@sydney.edu.au
Lecturer(s)	Jonathan Spreer, jonathan.spreer@sydney.edu.au
Lecturer(s)	Milena Radnovic, milena.radnovic@sydney.edu.au

Assessment

The census date for this unit availability is 31 August 2026

Details
Criteria

Type	Description	Weight	Due	Length	Use of AI
Written exam	Final exam Multiple choice and written calculations or mathematical arguments	60%	Formal exam period	2 hours	AI prohibited
Outcomes assessed:
Out-of-class quiz	Weekly Online Quizzes Weekly online quizzes 3-10	6%	Multiple weeks	2 hours per week	AI allowed
Outcomes assessed:
Out-of-class quiz	Weekly Online Quizzes (Early Feedback Task) Weekly online quizzes 1-2	2%	Week 03 Due date: 23 Aug 2026 at 23:59 Closing date: 23 Aug 2026	2 hours per quiz	AI allowed
Outcomes assessed:
Written work	Assignment 1 Written mathematical problem solving or proof, reflective analysis	5%	Week 04 Due date: 30 Aug 2026 at 23:59 Closing date: 09 Sep 2026	3-4 pages	AI allowed
Outcomes assessed:
In-person written or creative task	In-person Quiz Multiple choice	15%	Week 08	40 minutes	AI prohibited
Outcomes assessed:
Written work	Assignment 2 Written mathematical problem solving or proof, reflective analysis	10%	Week 11 Due date: 25 Oct 2026 at 23:59 Closing date: 04 Nov 2026	6-8 pages	AI allowed
Outcomes assessed:
Contribution	Contribution Contribution to tutorials	2%	Weekly	50 minutes per week	AI allowed
Outcomes assessed:
= early feedback task ?

Early feedback task

This unit includes an early feedback task, designed to give you feedback prior to the census date for this unit. Details are provided in the site and your result will be recorded in your Marks page. It is important that you actively engage with this task so that the University can support you to be successful in this unit.

Assessment summary

础蝉蝉颈驳苍尘别苍迟蝉:听 There are two assignments. Each must be submitted electronically as one single typeset or scanned PDF file via Canvas by the deadline. Assignments that are illegible, incorrectly oriented or unreadable files cannot be marked. It is your responsibility to ensure that your submission is complete and viewable (please check that all pages have uploaded correctly).听
We recognise that unexpected circumstances can arise, and there are processes in place to support you if you need extra time. Simple Extensions of up to 5 calendar days are available.听If your circumstances affect you for more than 5 days, you have the option of applying for Special Consideration. Assignments submitted after the due date without an approved extension will incur a late penalty. Submissions cannot be accepted more than 10 calendar days after the original due date. This allows for timely release of marks and feedback. If your circumstances affect you for longer than 10 days, the outcome for an approved Special Consideration application will be a mark adjustment听using your mark for the other assignment. If you are granted a mark adjustment for both assignments, then your assignment marks will both be zero. If you are granted a mark adjustment for an assignment, but you choose to submit the assignment, then your mark for this submission will not count towards your final mark unless you withdraw your Special Consideration before assignment marks are released.

In-person Quiz:听One in-person quiz will be held on campus during Week 8. You must sit the quiz at the time and location that appears as Assessment in your timetable. If you are unable to sit the quiz at that time for a valid reason, then you have the option to apply for Special Consideration or Special Arrangements.听There will be one opportunity to sit a replacement quiz for students with approved Special Consideration. If the Special Consideration is approved too late to be able to sit the replacement quiz, then the outcome quiz will be a mark adjustment using the final exam mark.听Quiz feedback will be returned through Canvas.

Weekly Online Quizzes: There are ten weekly online quizzes (through Canvas and equally weighted) and the marks for the best eight count towards your final grade. The first two are used for the Early Feedback Task. This scheme already allows for a small number of non-attempts. You should only apply for Special Consideration if you are affected for at least 3 quizzes.听The outcome for approved Special Consideration will be a mark adjustment using your marks for the other weekly online quizzes.听Each weekly online quiz consists of a set of randomized questions. The deadline for completion of each quiz is 23:59 on Sunday (starting in week 3). The precise schedule for the quizzes is found on Canvas. We recommend that you follow the due dates on Canvas to gain the most benefit from these quizzes.

Contribution: Tutorial contribution is assessed on a satisfactory / non-satisfactory basis and reflects your engagement in tutorial activities. It is worth 0.25 marks per tutorial class, up to 8 (out of 11). This scheme already allows for a small number of absences. You should only apply for Special Consideration if you are affected for at least 4 tutorials. Special Consideration is not required for occasional missed classes.听The outcome for approved Special Consideration will be a mark adjustment using contribution marks for non-affected tutorials.

Final Exam: The final exam for this unit is compulsory and must be attempted. Failure to attempt the final exam will result in an AF grade for the unit. Further information about the exam will be made available at a later date on Canvas. If a second replacement exam is required, this exam may be delivered via an alternative secure assessment method, such as a viva voce (in-person oral exam). The alternative assessment will meet the same learning outcomes as the original exam. The format of the alternative assessment will be determined by the unit coordinator.

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Detailed information for each assessment can be found on Canvas.

Even though the use of AI is allowed for some assessments, it is better for your learning to do your own work to complete your assessments.

Assessment criteria

The University awards common result grades, set out in the (Schedule 1).

As a general guide, a high distinction indicates work of an exceptional standard, a distinction a very high standard, a credit a good standard, and a pass an acceptable standard.

Result name	Mark range	Description
High distinction	85 - 100	Representing complete or close to complete mastery of the material.
Distinction	75 - 84	Representing excellence, but substantially less than complete mastery.
Credit	65 - 74	Representing a creditable performance that goes beyond routine knowledge and understanding, but less than excellence.
Pass	50 - 64	Representing at least routine knowledge and understanding over a spectrum of topics and important ideas and concepts in the course.
Fail	0 - 49	When you don鈥檛 meet the learning outcomes of the unit to a satisfactory standard.

For more information see guide to grades.

Use of generative artificial intelligence (AI)

You can use generative AI tools for open assessments. Restrictions on AI use apply to secure, supervised assessments used to confirm if students have met specific learning outcomes.

Refer to the assessment table above to see if AI is allowed, for assessments in this unit and check Canvas for full instructions on assessment tasks and AI use.

If you use AI, you must always acknowledge it. Misusing AI may lead to a breach of the听Academic Integrity Policy.

Visit the听Current Students website听for more information on AI in assessments, including听details on how to acknowledge its use.

Late submission

In accordance with University policy, these penalties apply when written work is submitted after 11:59pm on the due date:

Deduction of 5% of the maximum mark for each calendar day after the due date.
After ten calendar days late, a mark of zero will be awarded.

This unit has an exception to the standard University policy or supplementary information has been provided by the unit coordinator. This information is displayed below:

5% of assessment weight per day for assignments.

Academic integrity

The University expects students to act ethically and honestly and will treat all allegations of academic integrity breaches seriously.

Our website听provides information on academic integrity and the resources available to all students. This includes advice on how to avoid common breaches of academic integrity. Ensure that you have completed the听Academic Honesty Education Module (AHEM)听which is mandatory for all commencing coursework students

Penalties for serious breaches can significantly impact your studies and your career after graduation. It is important that you speak with your unit coordinator if you need help with completing assessments.

Visit the听Current Students website听for more information on AI in assessments, including听details on how to acknowledge its use.

Learning support

Simple extensions

If you encounter a problem submitting your work on time, you may be able to apply for an extension of five calendar days through a听simple extension.鈥� The application process will be different depending on the type of assessment and extensions cannot be granted for some assessment types like exams.

Special consideration

If exceptional circumstances mean you can鈥檛 complete an assessment, you need consideration for a longer period of time, or if you have essential commitments which impact your performance in an assessment, you may be eligible for听special consideration or special arrangements.

Special consideration applications will not be affected by a simple extension application.

Using AI responsibly

Co-created with students,听听includes lots of helpful examples of how students use generative AI tools to support their learning. It explains how generative AI works, the different tools available and how to use them responsibly and productively.

Support for students

The Support for Students Policy听reflects the University鈥檚 commitment to supporting students in their academic journey and making the University safe for students. It is important that you read and understand this policy so that you are familiar with the range of support services available to you and understand how to engage with them.

The University uses email as its primary source of communication with students who need support under the Support for Students Policy. Make sure you check your University email regularly and respond to any communications received from the University.

Learning resources and detailed information about weekly assessment and learning activities can be accessed via Canvas. It is essential that you visit your unit of study Canvas site to ensure you are up to date with all of your tasks.

If you are having difficulties completing your studies, or are feeling unsure about your progress, we are here to help. You can access the support services offered by the University at any time:

Support and Services (including health and wellbeing services, financial support and learning support)
Course planning and administration
Meet with an Academic Adviser

Weekly schedule

WK	Topic	Learning activity
Week 01	Set Theory, Venn Diagrams, Power Set	Lecture (3 hr)
Week 02	Cartesian Products, Divisibility, Functions, Sequences	Lecture (3 hr)
	Set Theory, Venn Diagrams, Power Set	Tutorial (1 hr)
	Set Theory, Venn Diagrams, Power Set	Seminar (1 hr)
Week 03	Number Theory basics	Lecture (3 hr)
	Cartesian Products, Divisibility, Functions, Sequences	Tutorial (1 hr)
	Cartesian Products, Divisibility, Functions, Sequences	Seminar (1 hr)
Week 04	Counting, Binomial Theorem, Inclusion-Exclusion	Lecture (3 hr)
	Number Theory basics	Tutorial (1 hr)
	Number Theory basics	Seminar (1 hr)
Week 05	Discrete Probability	Lecture (3 hr)
	Counting, Binomial Theorem, Inclusion-Exclusion	Tutorial (1 hr)
	Counting, Binomial Theorem, Inclusion-Exclusion	Seminar (1 hr)
Week 06	Advanced topics in Combinatorics (Generating functions)	Lecture (3 hr)
	Discrete Probability	Tutorial (1 hr)
	Discrete Probability	Seminar (1 hr)
Week 07	Advanced topics in Combinatorics (Partitions)	Lecture (3 hr)
	Advanced topics in Combinatorics (Generating functions)	Tutorial (1 hr)
	Advanced topics in Combinatorics (Generating functions)	Seminar (1 hr)
Week 08	Graph Theory basics	Lecture (3 hr)
	Advanced topics in Combinatorics (Partitions)	Tutorial (1 hr)
	Advanced topics in Combinatorics (Partitions)	Seminar (1 hr)
Week 09	Equivalence Relations, Closures, Floyd-Warshall algorithm	Lecture (3 hr)
	Graph Theory basics	Tutorial (1 hr)
	Graph Theory basics	Seminar (1 hr)
Week 10	Logic, Prepositions, Quantifiers	Lecture (3 hr)
	Equivalence Relations, Closures, Floyd-Warshall algorithm	Tutorial (1 hr)
	Equivalence Relations, Closures, Floyd-Warshall algorithm	Seminar (1 hr)
Week 11	O-notation, Running Times	Lecture (3 hr)
	Logic, Prepositions, Quantifiers	Tutorial (1 hr)
	Logic, Prepositions, Quantifiers	Seminar (1 hr)
Week 12	Complexity Theory, Models of Computation	Lecture (3 hr)
	O-notation, Running Times	Tutorial (1 hr)
	O-notation, Running Times	Seminar (1 hr)
Week 13	Finite State Automata, Regular languages, Revision	Lecture (3 hr)
	Complexity Theory, Models of Computation, Finite State Automata, Regular languages	Tutorial (1 hr)
	Complexity Theory, Models of Computation, Finite State Automata, Regular languages	Seminar (1 hr)

Attendance and class requirements

Lecture attendance: You are expected to attend lectures. If you do not attend lectures you听should at least follow the lecture recordings available through Canvas.

Tutorial attendance: Tutorials start in Week 2. You should attend the tutorial given on your personal timetable. Attendance at tutorials and contribution will be recorded to determine the contribution mark. Your attendance will not be recorded unless you attend the tutorial in which you are enrolled. We strongly recommend you attend tutorials regularly to keep up with the material and to engage with the tutorial questions.听

Study commitment

Typically, there is a minimum expectation of 1.5-2 hours of student effort per week per credit point for units of study offered over a full semester. For a 6 credit point unit, this equates to roughly 120-150 hours of student effort in total.

Required readings

Recommended textbooks:

Discrete Mathematics and Its Applications (Eigth Edition) by Kenneth H. Rosen
A Course in Combinatorics by Lint and Wilson

Learning outcomes

Learning outcomes are what students know, understand and are able to do on completion of a unit of study. They are aligned with the University's graduate qualities and are assessed as part of the curriculum.

Outcomes
Graduate qualities

At the completion of this unit, you should be able to:

LO1. construct logically correct and mathematically sound proofs using a wide variety of proof concepts
LO2. apply concepts of logic, set theory, relations, recursion, principles of counting, combinatorics, algebraic combinatorics, probability, algebraic structures, elementary number theory, graph theory, and asymptotic growth to mathematical and computational problems in more advanced courses
LO3. demonstrate an understanding and well-founded knowledge of the mathematics presented in this course and thus be able to apply techniques from this course to solve both familiar and novel problems
LO4. understand some applications of mathematics to relevant fields, such as computer programming and logic

Graduate qualities

The graduate qualities are the qualities and skills that all 爆料王 graduates must demonstrate on successful completion of an award course. As a future Sydney graduate, the set of qualities have been designed to equip you for the contemporary world.

GQ1	Depth of disciplinary expertise Deep disciplinary expertise is the ability to integrate and rigorously apply knowledge, understanding and skills of a recognised discipline defined by scholarly activity, as well as familiarity with evolving practice of the discipline.
GQ2	Critical thinking and problem solving Critical thinking and problem solving are the questioning of ideas, evidence and assumptions in order to propose and evaluate hypotheses or alternative arguments before formulating a conclusion or a solution to an identified problem.
GQ3	Oral and written communication Effective communication, in both oral and written form, is the clear exchange of meaning in a manner that is appropriate to audience and context.
GQ4	Information and digital literacy Information and digital literacy is the ability to locate, interpret, evaluate, manage, adapt, integrate, create and convey information using appropriate resources, tools and strategies.
GQ5	Inventiveness Generating novel ideas and solutions.
GQ6	Cultural competence Cultural Competence is the ability to actively, ethically, respectfully, and successfully engage across and between cultures. In the Australian context, this includes and celebrates Aboriginal and Torres Strait Islander cultures, knowledge systems, and a mature understanding of contemporary issues.
GQ7	Interdisciplinary effectiveness Interdisciplinary effectiveness is the integration and synthesis of multiple viewpoints and practices, working effectively across disciplinary boundaries.
GQ8	Integrated professional, ethical, and personal identity An integrated professional, ethical and personal identity is understanding the interaction between one鈥檚 personal and professional selves in an ethical context.
GQ9	Influence Engaging others in a process, idea or vision.

Outcome map

Learning outcomes	Graduate qualities
Learning outcomes

Responding to student feedback

This section outlines changes made to this unit following staff and student reviews.

There are no changes since this unit was last offered.

Additional information

Lectures: Lectures are face-to-face and streamed live with online access from Canvas.

Seminars: Seminars are face-to-face classes where a lecturer presents solutions to questions on the practice class sheet. Active participation is most welcome.

Tutorials: Tutorials are small classes in which you are expected to work through questions from the tutorial sheet in small groups on the white board. The role of the tutor is to provide support and to some extent give feedback on your solutions written on the board.

Tutorial sheets: The question sheets for a given week will be available on the MATH1964 Canvas page. Solutions to tutorial exercises for week n will usually be posted on the web by the afternoon of the Friday of week n.

Ed Discussion forum:

Work, health and safety

We are governed by the Work Health and Safety Act 2011, Work Health and Safety Regulation 2011 and Codes of Practice. Penalties for non-compliance have increased. Everyone has a responsibility for health and safety at work. The University鈥檚 explains the responsibilities and expectations of workers and others, and the procedures for managing WHS risks associated with University activities.

Disclaimer

Important: the 爆料王 regularly reviews units of study and reserves the right to change the units of study available annually. To stay up to date on available study options, including unit of study details and availability, refer to the relevant handbook.

To help you understand common terms that we use at the University, we offer an .

爆料王

Current students

Overview

Overview

Unit details and rules

Teaching staff

Assessment

Assessment

Early feedback task

Assessment summary

Assessment criteria

Use of generative artificial intelligence (AI)

Late submission

Academic integrity

Learning support

Learning support

Simple extensions

Special consideration

Using AI responsibly

Support for students

Weekly schedule

Weekly schedule

Attendance and class requirements

Study commitment

Required readings

Learning outcomes

Learning outcomes

Graduate qualities

Outcome map

Responding to student feedback

Responding to student feedback

Additional information

Additional information

Work, health and safety

Disclaimer

On this page

Useful links

MATH1964: Discrete Mathematics for Computation (Adv)

Semester 2, 2026 [Normal day] - Camperdown/Darlington, Sydney

Overview

Unit details and rules

Teaching staff

Assessment

Early feedback task

Assessment summary

Assessment criteria

Use of generative artificial intelligence (AI)

Late submission

Academic integrity

Learning support

Simple extensions

Special consideration

Using AI responsibly

Support for students

Weekly schedule

Attendance and class requirements

Study commitment

Required readings

Learning outcomes

Graduate qualities

Outcome map

Responding to student feedback

Additional information

Work, health and safety

Disclaimer

On this page

Useful links