• Offered by Mathematical Sciences Institute
• ANU College ANU Joint Colleges of Science
• Course subject Mathematics
• Areas of interest Mathematics
• Academic career UGRD
• Mode of delivery In Person
• Co-taught Course
• Offered in Second Semester 2019
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:

• 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.

## Learning Outcomes

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 Assessment

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)

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.

Three lectures per week and regular workshops.

## Requisite and Incompatibility

To enrol in this course you must have successfully completed MATH1116 with a mark of at least 60 or have completed MATH1115 with a mark of at least 80 and be concurrently enrolled in MATH1116. You are not able to enrol in this course if you have previously completed MATH3104.

## 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:
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

## Course fees

Domestic fee paying students
Year Fee
2019 \$3840
International fee paying students
Year Fee
2019 \$5460
Note: Please note that fee information is for current year only.

## 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.

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
7506 22 Jul 2019 29 Jul 2019 31 Aug 2019 25 Oct 2019 In Person View

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