Groups, Rings and Fields

Undergraduate | 2026

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Mode
Mode
Your studies will be on-campus, and may include some online delivery
On campus
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Area/Catalogue
MATH X307
Course ID icon
Course ID
208395
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Campus
Adelaide City Campus East, Mawson Lakes
Level of study
Level of study
Undergraduate
Unit value icon
Unit value
6
Course owner
Course owner
Mathematical Sciences
Course level icon
Course level
3
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Inbound study abroad and exchange
Inbound study abroad and exchange
The fee you pay will depend on the number and type of courses you study.
Yes
University-wide elective icon
University-wide elective course
Yes
Single course enrollment
Single course enrolment
Yes
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Note:
Course data is interim and subject to change

Course overview

The algebraic notions of groups, rings and fields are inherently interesting, while their practical applications extend across numerous areas. This course will provide students with a comprehensive understanding of the fundamental structures and concepts in abstract algebra. The course begins with definitions and examples of groups, rings and fields. It then advances to examining and proving key theorems, culminating in establishing the connection between solving polynomials and the procedure of field extensions.

Course learning outcomes

  • Apply techniques of algebraic manipulation and reasoning to evaluate properties of an algebraic structure
  • Prove the basic results of groups, rings and field theory
  • Apply more advanced results such as Burnside's theorem and the Sylow theorems
  • Develop proficiency in constructing rigorous mathematical proofs within abstract algebra, employing various proof techniques
  • Demonstrate skills in communicating algebraic concepts and arguments effectively

Prerequisite(s)

N/A

Corequisite(s)

N/A

Antirequisite(s)

N/A