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  6. MX3531: Rings & Fields

MX3531: RINGS & FIELDS (2019-2020)

Last modified: 25 Sep 2019 09:58


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 Aberdeen Sustained Study No
Co-ordinators
  • Dr Ehud Meir

Qualification Prerequisites

  • Either Programme Level 3 or Programme Level 4

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

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.

Syllabus

  • Rings
  • Zero divisors and integral domains.
  • Homomorphisms.
  • Ideals and quotient rings.
  • Field of fractions of an ID.
  • ID, UFD, PID and ED.
  • Polynomial rings over commutative rings.
  • Field extensions
  • Splitting fields.
  • Finite fields.

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

Exam

Assessment Type Summative Weighting 80
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Learning Outcomes
Knowledge LevelThinking SkillOutcome
Sorry, we don't have this information available just now. Please check the course guide on MyAberdeen or with the Course Coordinator

3x Homework

Assessment Type Summative Weighting 20
Assessment Weeks Feedback Weeks

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Learning Outcomes
Knowledge LevelThinking SkillOutcome
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Formative Assessment

There are no assessments for this course.

Resit Assessments

Best of written exam (100%) or written exam (80%) with carried forward in-course assessment (20%)

Assessment Type Summative Weighting
Assessment Weeks Feedback Weeks

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Learning Outcomes
Knowledge LevelThinking SkillOutcome
Sorry, we don't have this information available just now. Please check the course guide on MyAberdeen or with the Course Coordinator

Course Learning Outcomes

Knowledge LevelThinking SkillOutcome
Sorry, we don't have this information available just now. Please check the course guide on MyAberdeen or with the Course Coordinator
 

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