• Offered by Department of Mathematics
• ANU College ANU Joint Colleges of Science
• Course subject Mathematics
• Areas of interest Mathematics
• Course convener
• Dr Joan Licata
• Mode of delivery In Person
• Co-taught Course
• Offered in Second Semester 2014
Algebra 1 Honours: Groups, Rings and Advanced 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.

36 lectures and ten tutorials

## Requisite and Incompatibility

To enrol in this course you must have successfully completed MATH1021 or MATH1116 with a mark of 60 and above. You are not able to enrol in this course if you have previously completed MATH2021 and MATH2028 and 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. Students continuing in their current program of study will have their tuition fees indexed annually from the year in which you commenced your program. 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 Description
1994-2003 \$1650
2014 \$2946
2013 \$2946
2012 \$2946
2011 \$2946
2010 \$2916
2009 \$2916
2008 \$2916
2007 \$2520
2006 \$2520
2005 \$2298
2004 \$1926
International fee paying students
Year Fee
1994-2003 \$3390
2014 \$3762
2013 \$3756
2012 \$3756
2011 \$3756
2010 \$3750
2009 \$3618
2008 \$3618
2007 \$3618
2006 \$3618
2005 \$3450
2004 \$3450
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
7318 21 Jul 2014 01 Aug 2014 31 Aug 2014 30 Oct 2014 In Person N/A