MATH6118 Algebra 1: Groups, Rings and Advanced Linear Algebra

Offered By	Department of Maths
Academic Career	Graduate Coursework
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: Graduate students attend joint classes with undergraduates but are required to have a deeper understanding of the material, are expected to do extra work of a more theoretical nature and are assessed separately
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
Course Classification(s)	AdvancedAdvanced courses are designed for students having reached 'first degree' level of assumed knowledge, which provide a deep understanding of contemporary issues; or 'second degree' and higher levels of knowledge; or for transition to research training programs. and SpecialistSpecialist courses are designed for students having reached 'first degree' level of assumed knowledge, which provide for the acquisition of specialist skills; or 'second degree' and higher level of knowledge; or for transition to research training programs; or knowledge associated with professional accreditation.
Areas of Interest	Mathematics
Eligibility	Bachelor degree; with second year Mathematics.
Requisite Statement	Second year Mathematics is required.
Programs	Master of Mathematical Sciences
Academic Contact	Dr Jim Borger

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