Groups, Rings and Fields

Undergraduate | 2026

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Mode icon
Mode
Mode
Your studies will be on-campus, and may include some online delivery
On campus
area/catalogue icon
Area/Catalogue
MATH X307
Course ID icon
Course ID
208395
Campus icon
Campus
Adelaide City Campus East, Mawson Lakes
Level of study
Level of study
Undergraduate
Unit value icon
Unit value
6
Course owner
Course owner
School of Mathematical Science
Course coordinator
Course coordinator
Stuart Johnson
Course level icon
Course level
3
Work Integrated Learning course
Work Integrated Learning course
No
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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

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

Availability

Census date Icon
Census date
Fri 27/03/2026
Enrol by date
Enrol by date
Fri 13/03/2026
Last day to W
Last day to W
Fri 10/04/2026
Last day to WF
Last day to WF
Fri 08/05/2026

Class details

Adelaide City Campus East

Class number
Class number 27114
Section
Section FR01
Size
Size 25
Available
Available 25
Dates Days Time Campus Location Instructor
25 Feb - 15 Apr Wednesday 10:10am - 12pm Adelaide City Campus East Engin and Maths Sciences, 324
6 May - 3 Jun Wednesday 10:10am - 12pm Adelaide City Campus East Engin and Maths Sciences, 324
Class number
Class number 30124
Section
Section TU01
Size
Size 30
Available
Available 30
Dates Days Time Campus Location Instructor
6 Apr - 6 Apr Monday 10:10am - 11am Adelaide City Campus East Napier, LG28
Class number
Class number 27115
Section
Section WS01
Size
Size 25
Available
Available 25
Dates Days Time Campus Location Instructor
24 Feb - 14 Apr Tuesday 2:10pm - 3pm Adelaide City Campus East Barr Smith South, 2052
5 May - 2 Jun Tuesday 2:10pm - 3pm Adelaide City Campus East Barr Smith South, 2052

Prerequisite(s)

  • must have completed MATHX201 Algebra

Corequisite(s)

N/A

Antirequisite(s)

N/A

Fee calculator

To display course fees, please select your status and program below:

Study Abroad student tuition fees are available here.

Only some Postgraduate Coursework programs are available as Commonwealth Supported. Please check your program for specific fee information.

The Student Contribution amount displayed below is for students commencing a new program from 2021 onwards. If you are continuing in a program you commenced prior to 1 January 2021, or are commencing an Honours degree relating to an undergraduate degree you commenced prior to 1 January 2021, you may be charged a different Student Contribution amount from the amount displayed below. Please check the Student Contribution bands for continuing students here. If you are an international student, or a domestic student studying in a full fee paying place, and are continuing study that you commenced in 2025 or earlier, your fees will be available here before enrolments open for 2026.