production
Skip to Content

Log In

  1. University Home
  2. Catalogue of Courses
  3. Undergraduate
  4. 2022-2023
  5. Mathematical Sciences
  6. MX3531: Rings & Fields

MX3531: RINGS & FIELDS (2022-2023)

Last modified: 31 Jul 2023 11:19


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
Session Second Sub Session Credit Points 15 credits (7.5 ECTS credits)
Campus Aberdeen Sustained Study No
Co-ordinators
  • Dr Simona Paoli

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

  • 2 Lectures during University weeks 26 - 35, 39
  • 1 Tutorial during University weeks 27 - 35, 39

More Information about Week Numbers


Details, including assessments, may be subject to change until 31 August 2023 for 1st half-session courses and 22 December 2023 for 2nd half-session courses.

Summative Assessments

Homework

Assessment Type Summative Weighting 25
Assessment Weeks Feedback Weeks

Look up Week Numbers

Feedback
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

Exam

Assessment Type Summative Weighting 50
Assessment Weeks Feedback Weeks

Look up Week Numbers

Feedback
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

Homework

Assessment Type Summative Weighting 25
Assessment Weeks Feedback Weeks

Look up Week Numbers

Feedback
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

Formative Assessment

There are no assessments for this course.

Resit Assessments

Exam

Assessment Type Summative Weighting
Assessment Weeks Feedback Weeks

Look up Week Numbers

Feedback

Best of (resit exam mark) or (resit exam mark with carried forward CA marks).
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
FactualRememberILO’s for this course are available in the course guide.
 

Compatibility Mode

We have detected that you are have compatibility mode enabled or are using an old version of Internet Explorer. You either need to switch off compatibility mode for this site or upgrade your browser.