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 the theory of groups and rings:
- 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.
Additional topics may be selected from the following:
- Linear Algebra - unitary matrices, Hermitian matrices, canonical forms.
- Modules - free modules, presentations, classification of finitely generated abelian groups.
Note: Graduate students attend joint classes with undergraduates, but they are assessed separately
Learning Outcomes
Upon successful completion, students will have the knowledge and skills to:
- Explain the fundamental concepts of advanced algebra such as groups and rings and their role in modern mathematics and applied contexts
- Demonstrate accurate and efficient use of advanced algebraic techniques
- Demonstrate capacity for mathematical reasoning through analyzing, proving and explaining concepts from advanced algebra
- Apply problem-solving using advanced algebraic techniques to diverse situations in scientific and mathematical contexts
- Use deep knowledge and understanding of abstract algebra to formulate responses to complex concrete and abstract problems.
Indicative Assessment
- Regular written assignments (25) [LO 1,2,3,4]
- Quizzes (15) [LO 1,2,3,4]
- Final exam (35) [LO 1,2,3,4]
- Written assignments for extension module (25) [LO 1,2,3,4,5]
The ANU uses Turnitin to enhance student citation and referencing techniques, and to assess assignment submissions as a component of the University's approach to managing Academic Integrity. While the use of Turnitin is not mandatory, the ANU highly recommends Turnitin is used by both teaching staff and students. For additional information regarding Turnitin please visit the ANU Online website.
Workload
The expected workload will consist of approximately 130 hours throughout the semester, including the following:
- Face-to face component which may consist of 3 x 1 hour lecture-based classes per week and 1 x 1 hour workshop per week (workshops normally begin in Week 3),
- Face-to face extension module which may consist of 1x1 lecture-based class per week, and
Approximately 73 hours of self-directed study which will include preparation for lectures, assignments, and other assessment tasks.
Inherent Requirements
No specific inherent requirements have been identified in this course.
Requisite and Incompatibility
You will need to contact the Mathematical Sciences Institute to request a permission code to enrol in this course.
Prescribed Texts
None
Preliminary Reading
Artin's "Algebra" textbook. (Any edition is acceptable, although the 2nd edition and later are preferred.)
Fees
Tuition fees are for the academic year indicated at the top of the page.
Commonwealth Support (CSP) Students
If you have been offered a Commonwealth supported place, your fees are set by the Australian Government for each course. At ANU 1 EFTSL is 48 units (normally 8 x 6-unit courses). More information about your student contribution amount for each course at Fees.
- Student Contribution Band:
- 1
- Unit value:
- 6 units
If you are a domestic graduate coursework student with a Domestic Tuition Fee (DTF) place or international student you will be required to pay course tuition fees (see below). Course tuition fees are indexed annually. Further information for domestic and international students about tuition and other fees can be found at Fees.
Where there is a unit range displayed for this course, not all unit options below may be available.
| Units | EFTSL |
|---|---|
| 6.00 | 0.12500 |
Course fees
- Domestic fee paying students
| Year | Fee |
|---|---|
| 2025 | $4680 |
- International fee paying students
| Year | Fee |
|---|---|
| 2025 | $6720 |
Offerings, Dates and Class Summary Links
ANU utilises MyTimetable to enable students to view the timetable for their enrolled courses, browse, then self-allocate to small teaching activities / tutorials so they can better plan their time. Find out more on the Timetable webpage.
Class summaries, if available, can be accessed by clicking on the View link for the relevant class number.
Second Semester
| Class number | Class start date | Last day to enrol | Census date | Class end date | Mode Of Delivery | Class Summary |
|---|---|---|---|---|---|---|
| 7603 | 21 Jul 2025 | 28 Jul 2025 | 31 Aug 2025 | 24 Oct 2025 | In Person | N/A |