- Code MATH3104
- Unit Value 6 units
- Offered by Mathematical Sciences Institute
- ANU College ANU Joint Colleges of Science
- Course subject Mathematics
- Areas of interest Mathematics
In Sem 2 2022, this course is on campus with remote adjustments only for participants with unavoidable travel restrictions/visa delays.
This course introduces the basic concepts of modern algebra such as groups and rings. The philosophy of this course is that modern algebraic notions play a fundamental role in mathematics itself and in applications to areas such as physics, computer science, economics and engineering. This course emphasizes the application of techniques.
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 - unitary matrices, Hermitian matrices, canonical forms.
Note: This is an HPC. It emphasises the sophisticated application of deep mathematical concepts
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
Indicative AssessmentAssessment will be based on:
- Five assignments (8% each; LO 1-4)
- Mid semester exam (20%; LO 1-4)
- Final exam (40%; LO 1-4)
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WorkloadThree lectures per week, regular workshops.
Requisite and Incompatibility
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:
- 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.
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Offerings, Dates and Class Summary Links
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Class summaries, if available, can be accessed by clicking on the View link for the relevant class number.