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Department of Mathematical Sciences, Unit Catalogue 2011/12


MA30204: Algebraic structures

Click here for further information Credits: 6
Click here for further information Level: Honours (FHEQ level 6)
Click here for further information Period: Semester 1
Click here for further information Assessment: EX 100%
Click here for further information Supplementary Assessment: MA30204 Mandatory Extra Work (where allowed by programme regulations)
Click here for further information Requisites: Before taking this unit you must take MA20217
Click here for further information Description: Aims:
To introduce the students to various algebraic structures that are essential for studies in higher algebra.

Learning Outcomes:
At the end of the course the students will be conversant with algebraic structures relating to groups, rings and modules. Moreover students will achieve a solid ground for further studies in algebra. In particular the student will be prepared for studies in MA40188, MA40037, MA40038 and MA40054.

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.
Click here for further informationProgramme availability:

MA30204 is Optional on the following programmes:

Department of Mathematical Sciences
  • USMA-AFB15 : BSc (hons) Mathematical Sciences (Full-time) - Year 3
  • USMA-AKB16 : BSc (hons) Mathematical Sciences (Full-time with Thick Sandwich Placement) - Year 4
  • USMA-AAB16 : BSc (hons) Mathematical Sciences with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
  • USMA-AFB13 : BSc (hons) Mathematics (Full-time) - Year 3
  • USMA-AKB14 : BSc (hons) Mathematics (Full-time with Thick Sandwich Placement) - Year 4
  • USMA-AFB01 : BSc (hons) Mathematics and Statistics (Full-time) - Year 3
  • USMA-AKB02 : BSc (hons) Mathematics and Statistics (Full-time with Thick Sandwich Placement) - Year 4
  • USMA-AAB02 : BSc (hons) Mathematics and Statistics with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
  • USMA-AAB14 : BSc (hons) Mathematics with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
  • USMA-AFB05 : BSc (hons) Statistics (Full-time) - Year 3
  • USMA-AKB06 : BSc (hons) Statistics (Full-time with Thick Sandwich Placement) - Year 4
  • USMA-AAB06 : BSc (hons) Statistics with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
  • USMA-AFM14 : MMath Mathematics (Full-time) - Year 3
  • USMA-AFM14 : MMath Mathematics (Full-time) - Year 4
  • USMA-AAM15 : MMath Mathematics with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
  • TSMA-AFM09 : MSc Mathematical Sciences (Full-time) - Year 1
  • TSMA-APM09 : MSc Mathematical Sciences (Part-time) - Year 1
  • TSMA-APM09 : MSc Mathematical Sciences (Part-time) - Year 2
Department of Physics
  • USXX-AFM01 : MSci (hons) Mathematics and Physics (Full-time) - Year 4

NB. Programmes and units are subject to change at any time, in accordance with normal University procedures.