MATH2322 Algebra 1 Honours: Groups, Rings and Advanced Linear Algebra

Later Year Course

Offered By	Department of Maths
Academic Career	Undergraduate
Course Subject	Mathematics
Offered in	Second Semester, 2010 and Second Semester, 2011
Unit Value	6 units
Course Description	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 (10% each; LO 1-4) Final exam (50%; LO 1-4)
Workload	36 lectures and ten tutorials
Areas of Interest	Mathematics
Requisite Statement	A mark of 60 or more in MATH1021 or MATH1116.
Incompatibility	MATH2021 and MATH2028 and MATH3104.
Science Group	B
Academic Contact	Dr Jim Borger

The information published on the Study at ANU 2010 website applies to the 2010 academic year only. All information provided on this website replaces the information contained in the Study at ANU 2009 website.