• Offered by Mathematical Sciences Institute
  • ANU College ANU Joint Colleges of Science
  • Classification Advanced
    Specialist
  • Course subject Mathematics
  • Areas of interest Mathematics
  • Academic career Postgraduate
  • Course convener
    • Dr Joan Licata
  • Mode of delivery In Person
  • Offered in Second Semester 2018
    See Future Offerings
Algebra 1: Groups, Rings and Advanced Linear Algebra (MATH6118)

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: Graduate students attend joint classes with undergraduates but are required to have a deeper understanding of the material, are expected to do extra work of a more theoretical nature and are assessed separately

Learning Outcomes

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 Assessment

Assessment will be based on:

  • Five assignments (10% each; LO 1-4)
  • Final exam (50%; LO 1-4)

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

Three lectures per week and regular workshops

Requisite and Incompatibility

You will need to contact the Mathematical Sciences Institute to request a permission code to enrol in this course.

Fees

Tuition fees are for the academic year indicated at the top of the page.  

If you are a domestic graduate coursework or international student you will be required to pay tuition fees. Tuition fees are indexed annually. Further information for domestic and international students about tuition and other fees can be found at Fees.

Student Contribution Band:
Band 2
Unit value:
6 units

If you are an undergraduate student and 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). You can find your student contribution amount for each course 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
Domestic fee paying students
Year Fee
2018 $3660
International fee paying students
Year Fee
2018 $5160
Note: Please note that fee information is for current year only.

Offerings and Dates

The list of offerings for future years is indicative only

Second Semester

Class number Class start date Last day to enrol Census date Class end date Mode Of Delivery
7744 23 Jul 2018 30 Jul 2018 31 Aug 2018 26 Oct 2018 In Person

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