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

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.

## Workload

Three lectures per week and regular workshops.## Requisite and Incompatibility

## Specialisations

## 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 |

**Note:**Please note that fee information is for current year only.

## Offerings and Dates

### Second Semester

Class number | Class start date | Last day to enrol | Census date | Class end date | Mode Of Delivery |
---|---|---|---|---|---|

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