MATH3104 Applied 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	This course introduces the basic concepts of modern algebra such as groups and rings. The philosophy of this course is that modern algebraic notions play a fundamental role in mathematics itself and in applications to areas such as physics, computer science, economics and engineering. This course emphasizes the application of techniques. 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 - unitary matrices, Hermitian matrices, canonical forms. Note: This is an HPC. It emphasises the sophisticated application of deep mathematical concepts.
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, tutorials by arrangement
Areas of Interest	Mathematics
Requisite Statement	A mark of 80 or more in MATH2305 and MATH2306 or a mark of 60 or more in MATH2405
Incompatibility	MATH2322
Science Group	C
Academic Contact	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.