Mathematical Structures G (8938.3)

Please note these are the 2018 details for this unit
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Mathematical Structures G
Available teaching periods Delivery mode Location
View teaching periods
EFTSL Credit points Faculty
0.125 3 Faculty Of Science And Technology
Discipline Study level HECS Bands
Academic Program Area - Technology Graduate Level 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 understanding of the concepts and methods of number theory and abstract algebra;

2. Compute with the RSA algorithm and permutation groups, either manually and with mathematical software;
3. Recognise the range of applications of abstract algebra in modern information technology;
4. Analyse and solve contemporary problems of both theoretical and practical importance; and
5. Interpret and assess the real-life implications of these applications.


Graduate attributes

1. UC graduates are professional - communicate effectively
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 - employ up-to-date and relevant knowledge and skills
1. UC graduates are professional - use creativity, critical thinking, analysis and research skills to solve theoretical and real-world problems


Skills development

This unit is concerned with the mathematics that underlies numerous aspects of modern computing including computer security, data communication, compression, storage and retrieval. The unit emphasises the rigorous understanding of the mathematical tools that have proven to be of crucial importance for these applications. Students successfully completing this unit will be able to use these tools and do elementary proofs of their correctness.

Education Accreditation: AITSL and TQI Graduate Standards for Teachers
2.1 Content and teaching strategies of the teaching area - Demonstrate knowledge and understanding of the
concepts, substance and structure of the content and teaching strategies of the teaching area.


Prerequisites

6699 Discrete Mathematics G.

Corequisites

None.

Equivalent units

None.

Assumed knowledge

None.
Year Location Teaching period Teaching start date Delivery mode Unit convener
Not available

Required texts

There is no required textbook for this unit. The lecture notes will be available on the Canvas Site at the start of semester.

Submission of assessment items

Grade calculation

Your total mark is calculated as a weighted average of your mark for each assessment item according to the percentages given.

If your total mark is larger that 50%, but you do not get the required 40% on the Final Exam, you will get a grade of NX.

Otherwise, grades are calculated from your total mark using the university's standard grading schema:
http://www.canberra.edu.au/currentstudents/canberrastudents/examinationsandresults/gradingschema

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

Lectures (1 hours/week; 12 times)

12

Tutorials (2 hours/week; 12 times)

24

Weekly study (4 hours/week; 12 times)

48

In-class test revision (6 hours)

6

Assignments (18 hours; 2 times)

36

Final exam and revision (24 hours)

24            

Total

150

Participation requirements

You are expected to attend lectures and tutorials. The lectures will be recorded, but problems with the recordings will not be accepted as an excuse for anything. You are strongly encouraged to attend tutorials in person, as they will not be recorded. The tests and exam will draw upon the activities completed in tutorials.

Required IT skills

All students are expected to be able to:

  • Read and print documents on the unit website – mostly in Adobe PDF format.
  • Communicate using e-mail.
  • Use their own scientific calculator.

In-unit costs

There is no text for the unit. You will need a scientific calculator for use in tests and the final exam. We recommend the Casio fx 82 AU Plus II, which is available from the Union Shop for $35. 

Work placement, internships or practicums

None.