Mathematical Structures (12124.1)

Please note these are the 2026 details for this unit
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Mathematical Structures
Available teaching periods Delivery mode Location
View teaching periods Hybrid
 Bruce, Canberra
EFTSL Credit points Faculty
0.125 3 Faculty Of Science And Technology
Discipline Study level HECS Bands
Academic Program Area - Technology Level 3 - Undergraduate Advanced Unit Band 1 2021 (Commenced After 1 Jan 2021)
Band 1 2021 (Commenced Before 1 Jan 2021)
This unit teaches number theory and an introduction to abstract algebra. Topics include modular arithmetic, prime numbers, groups, permutations, rings and fields. These topics have many applications to software engineering, information technology, and physics. The unit provides students with a thorough understanding of the basic techniques, together with an introduction to applications, particularly the RSA algorithm and geometric symmetry. We will cover finite field, the mathematical structures underpinning coding theory and cryptography.

Learning outcomes

On successful completion of this unit, students will be able to:
1. Demonstrate proficiency in combinatorial reasoning;
2. Examine the importance of mathematical proof and be able to devise proofs of their own;
3. Identify and implement the applications of mathematics to real problems; and
4. Explore and critique the important mathematical constructions that are the foundations to mathematical computation.


Graduate attributes

1. UC graduates are professional - display initiative and drive, and use their organisation skills to plan and manage their workload
1. UC graduates are professional - use creativity, critical thinking, analysis and research skills to solve theoretical and real-world problems
1. UC graduates are professional - work collaboratively as part of a team, negotiate, and resolve conflict
2. UC graduates are global citizens - communicate effectively in diverse cultural and social settings
3. UC graduates are lifelong learners - adapt to complexity, ambiguity and change by being flexible and keen to engage with new ideas
3. UC graduates are lifelong learners - be self-aware


Prerequisites

6698 Discrete Mathematics AND 8110 Linear Algebra

Corequisites

None.

Incompatible units

None.

Equivalent units

6543 Mathematical Structures

Assumed knowledge

None.
Availability for enrolment in 2026 is subject to change and may not be confirmed until closer to the teaching start date.
Year Location Teaching period Teaching start date Delivery mode Unit convener
2025 Bruce, Canberra Semester 1 03 February 2025 Hybrid Dr Sergey Sergeev
2026 Bruce, Canberra Semester 1 16 February 2026 Hybrid Dr Sergey Sergeev
The information provided should be used as a guide only. Timetables may not be finalised until week 2 of the teaching period and are subject to change. Search for the unit timetable.

Required texts

A unit broshure will be provided.

As an extra reading (optional), I could recommend

1. Joseph J. Rotman, Advanced Modern Algebra, UC Library code QA154.3.R68

2. Jimmie Gilbert and Linda Gilvert, Elements of Modern Algebra, UC Library code QA162.G52

3. John B. Fraleigh, A first course in Abstract Algebra, UC Library code QA162.F7

4. John R. Durbin, Modern Algebra. An introfuction. UC Library code QA162.D87 

Submission of assessment items

Special assessment requirements

Special assessment requirements.

The unit uses both formative and summative forms of assessment. Students are required to satisfactorily complete a number of assignments and assessable items and to perform satisfactorily in the final assessment. Specifications for the assignments and requirements for satisfactory completion are given on the unit website on Canvas (LearnOnline).

Assignments are meant to be individual work, although talking a problem over with another student or tutor is considered one reasonable way of learning. However, the actual assignment submission must be your own work. Students are expected to familiarise themselves with the University's Student Conduct Rules (http://www.canberra.edu.au/current-students/conduct). Experience has shown that students who do not do their own work are unlikely to pass the unit.

Assignment submissions will be assessed for addressing the specific requirements of each assignment, as stated in the assignment descriptions. All assessment items will receive a numerical mark, which together in their entirety define a student's final grade and mark as outlined in section 5a.

Responsibility for understanding

If there is any doubt with regard to the requirements of any particular assignments or assessment procedure, the onus for clarifying the issue rests with the student who should
contact the unit Convener or tutor. Further, it is the responsibility of students to ensure that they are correctly enrolled in the unit and that the tutor and Student Administration have their correct contact details.

Final Grade and Mark

To obtain a particular grade in this unit it is necessary that there are no outstanding submissions at the end of Week 13. All assessment items will receive a numerical mark. The final grade will be determined as a weighted average of the individual assessment items as follows:

Final grade = Early Assessment x 0.10 + (Test_1 mark + Test_2 mark) x 0.20 + (Assignment_1 mark  + Assignment_2 mark) x 0.25   (note that the marks for each assessment are scaled to 100 before performing this calculation)

To be awarded a particular grade, students must meet all the requirements listed below. That is, all grades are conditional upon the following minimum requirements:

Grade

Numerical Score

Fail

49% or less of combined weighted marks of all assessment items

Pass

50-64% of combined weighted marks of all assessment items

Credit

65-74% of combined weighted marks of all assessment items

Distinction

75-84% of combined weighted score of all assessment item

High Distinction

85-100% of combined weighted score of all assessment item

The unit convener reserves the right to question students orally (either online or face to face) on any assessable component of the unit and adjust grades/marks accordingly (including the final mark/grade).

Students must apply academic integrity in their learning and research activities at UC. This includes submitting authentic and original work for assessments and properly acknowledging any sources used.

Academic integrity involves the ethical, honest and responsible use, creation and sharing of information. It is critical to the quality of higher education. Our academic integrity values are honesty, trust, fairness, respect, responsibility and courage.

UC students have to complete the Academic Integrity Module annually to learn about academic integrity and to understand the consequences of academic integrity breaches (or academic misconduct).

UC uses various strategies and systems, including detection software, to identify potential breaches of academic integrity. Suspected breaches may be investigated, and action can be taken when misconduct is found to have occurred.

Information is provided in the Academic Integrity Policy, Academic Integrity Procedure, and University of Canberra (Student Conduct) Rules 2023. For further advice, visit Study Skills.

Learner engagement

Activities Hours
Weekly lectures 24
Weekly tutorials/labs 22
Preparation for assessments 48
Weekly study commitments 56
Total 150

Participation requirements

Your participation in all activities will enhance your understanding of the unit content and therefore the quality of your assessment responses. Lack of participation may result in your inability to satisfactorily pass assessment items. Experience has shown that students who do not attend the classes (either online or face to face) will have difficulty in passing the subject.

Required IT skills

It is assumed that the student has basic understanding of computers.

Work placement, internships or practicums

Not applicable to this unit.

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