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  6. MX3531: RINGS AND FIELDS

MX3531: RINGS AND FIELDS (2016-2017)

Last modified: 28 Jun 2018 10:27


Course Overview

Many examples of rings will be familiar before entering this course. Examples include the integers modulo n, the complex numbers and n-by-n matrices with real entries. The course develops from the fundamental definition of ring to study particular classes of rings and how they relate to each other. We also encounter generalisations of familiar concepts, such as what is means for a polynomial to be prime.

Course Details

Study Type Undergraduate Level 3
Term Second Term Credit Points 15 credits (7.5 ECTS credits)
Campus None. Sustained Study No
Co-ordinators
  • Dr Zur Izhakian

Qualification Prerequisites

None.

What courses & programmes must have been taken before this course?

  • Either MA2008 Linear Algebra I (Passed) or MA2506 Linear Algebra (Passed)
  • MX3020 Group Theory (Studied)
  • Any Undergraduate Programme (Studied)

What other courses must be taken with this course?

None.

What courses cannot be taken with this course?

None.

Are there a limited number of places available?

No

Course Description

  • Basic concepts and examples. Ideals, factor rings, isomorphism theorems.
  • Rings of polynomials.
  • Field of fractions of a domain.
  • Unique Factorization Domains, Principal Ideal Domains, Euclidean Domains.
  • Passage from R to R[X]. Gauss's Theorem. Eisenstein's criterion.
  • Fields : characteristic, prime subfield.
  • Finite fields, construction.
  • Algebraic and transcendental elements, algebraic closure.

Contact Teaching Time

Information on contact teaching time is available from the course guide.

Teaching Breakdown

More Information about Week Numbers


Details, including assessments, may be subject to change until 30 August 2024 for 1st term courses and 20 December 2024 for 2nd term courses.

Summative Assessments

1st Attempt: 1 two-hour written examination (80%); in-course assessment (20%). Resit: 1 two-hour examination (maximum of 100% resit and 80% resit with 20% in-course assessment). Only the marks obtained on first sitting can be used for Honours classification.

Formative Assessment

Informal assessment of weekly homework through discussions in tutorials.

Feedback

In-course assignments will normally be marked within one week and feedback provided to students in tutorials. Students will be invited to contact Course Coordinators for feedback on the final examination.

Course Learning Outcomes

None.
 

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