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MA50204: Algebraic structures

Follow this link for further information on academic years Academic Year: 2012/3
Follow this link for further information on owning departmentsOwning Department/School: Department of Mathematical Sciences
Follow this link for further information on credits Credits: 6
Follow this link for further information on unit levels Level: Masters UG & PG (FHEQ level 7)
Follow this link for further information on period slots Period: Semester 1
Follow this link for further information on unit assessment Assessment: CW 25%, EX 75%
Follow this link for further information on supplementary assessment Supplementary Assessment: Like-for-like reassessment (where allowed by programme regulations)
Follow this link for further information on unit rules Requisites:
Follow this link for further information on unit content Description: Aims:
To introduce the students to various algebraic structures that are essential for studies in higher algebra.

Learning Outcomes:
After taking this unit, students will be able to state definitions and prove fundamental theorems related to groups, rings and modules. They will be able to apply concepts from the theory of groups, rings and modules to solve unseen problems. The students will achieve a solid grounding for further studies in algebra. Through their coursework, they will be able to demonstrate a deep understanding of at least one of the main topics of the unit.

Skills:
Analytic skills T/F A; Problem solving T/F A; Written communication F A.

Content:
Introduction to group theory: subgroups and Lagrange's Theorem, normal subgroups, quotient groups and the isomorphism theorems. Abelian groups. Rings. Integral domains. Fields. Field of quotients of an integral domain. Ideals and quotient rings. Polynomial rings. Factorization in integral domains. Principal ideal domains. Modules over principal ideal domains.
Follow this link for further information on programme availabilityProgramme availability:

MA50204 is Optional on the following programmes:

Department of Mathematical Sciences
Notes:
* This unit catalogue is applicable for the 2012/13 academic year only. Students continuing their studies into 2013/14 and beyond should not assume that this unit will be available in future years in the format displayed here for 2012/13.
* Programmes and units are subject to change at any time, in accordance with normal University procedures.
* Availability of units will be subject to constraints such as staff availability, minimum and maximum group sizes, and timetabling factors as well as a student's ability to meet any pre-requisite rules.