Department of Mathematical Sciences, Unit Catalogue 2011/12 

Credits:  6 
Level:  Masters UG & PG (FHEQ level 7) 
Period: 
Semester 1 
Assessment:  CW25EX75 
Supplementary Assessment:  Likeforlike reassessment (where allowed by programme regulations) 
Requisites:  
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. 
Programme availability: 
MA50204 is Optional on the following programmes:Department of Mathematical Sciences
