- Code MATH2322
- Unit Value 6 units
- Offered by Mathematical Sciences Institute
- ANU College ANU Joint Colleges of Science
- Course subject Mathematics
- Areas of interest Mathematics
All activities that form part of this course will be delivered remotely in Sem 2 2020.
Algebra 1 is a foundational course in Mathematics, introducing some of the key concepts of modern algebra. The course leads on to other areas of algebra such as Galois Theory, Algebraic Topology and Algebraic Geometry. It also provides important tools for other areas such as theoretical computer science, physics and engineering.
Topics to be covered include:
- Group Theory - permutation groups; abstract groups, subgroups, cyclic and dihedral groups; homomorphisms; cosets, Lagrange's Theorem, quotient groups; group actions; Sylow theory.
- Ring Theory - rings and fields, polynomial rings, factorisation; homomorphisms, factor rings.
- Linear algebra - real symmetric matrices and quadratic forms, Hermitian matrices, canonical forms.
- Set Theory - cardinality.
Note: This is an HPC. It emphasises mathematical rigour and proof and develops modern algebra from an abstract viewpoint.
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 the fundamental concepts of advanced algebra such as groups and rings and their role in modern mathematics and applied contexts
2. Demonstrate accurate and efficient use of advanced algebraic techniques
3. Demonstrate capacity for mathematical reasoning through analyzing, proving and explaining concepts from advanced algebra
4. Apply problem-solving using advanced algebraic techniques applied to diverse situations in physics, engineering and other mathematical contexts
Assessment will be based on:
- Five assignments (8% each; LO 1-4)
- Mid semester exam (20%; LO 1-4)
- Final exam (40%; LO 1-4)
In response to COVID-19: Please note that Semester 2 Class Summary information (available under the classes tab) is as up to date as possible. Changes to Class Summaries not captured by this publication will be available to enrolled students via Wattle.
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WorkloadThree lectures per week and regular workshops.
Requisite and Incompatibility
Tuition fees are for the academic year indicated at the top of the page.
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- Student Contribution Band:
- Unit value:
- 6 units
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