• Offered by Mathematical Sciences Institute
• ANU College ANU Joint Colleges of Science
• Course subject Mathematics
• Areas of interest Mathematics
• Academic career UGRD
• Course convener
• AsPr Uri Onn
• Mode of delivery In Person
• Co-taught Course
• Offered in Second Semester 2022
Advanced Algebra 1: Groups, Rings and Linear Algebra (MATH2322)

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.

As well as additional topics selected from:

• Linear Algebra - unitary matrices, Hermitian matrices, canonical forms.
• Modules - free modules, presentations, classification of finitely generated abelian groups.

Note: This is an Honours Pathway Course. It emphasises mathematical rigour and proof and develops modern algebra from an abstract viewpoint.

## Learning Outcomes

Upon successful completion, 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

1. Regular assignments (40) [LO 1,2,3,4]
2. Mid semester exam (20) [LO 1,2,3,4]
3. Final exam (40) [LO 1,2,3,4]

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

The expected workload will consist of approximately 130 hours throughout the semester including:

• Face-to face component which may consist of 3 x 1 hour lectures per week and 1 x 1 hour workshop per week (workshops normally begin in Week 3).
• Approximately 84 hours of self directed study which will include preparation for lectures, assignments and other assessment tasks.

To be determined

## Requisite and Incompatibility

To enrol in this course you must have completed MATH1116 with a mark of at least 60. Students who are concurrently enrolled in MATH1116 and have completed at least one of MATH1115 with a mark of at least 90 or MATH2222 with a mark of at least 90 can contact the course convener to request a permission code. Incompatible with MATH3104

## Prescribed Texts

Algebra by Michael Artin. (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
Note: Please note that fee information is for current year only.

## Offerings, Dates and Class Summary Links

The list of offerings for future years is indicative only.
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
6042 25 Jul 2022 01 Aug 2022 31 Aug 2022 28 Oct 2022 In Person N/A

Responsible Officer: Registrar, Student Administration / Page Contact: Website Administrator / Frequently Asked Questions