Mathematical Structures (12124.1)

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.