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
Class details
Adelaide City Campus East
Class number 27114
Section FR01
Size 25
Available 25
Class number 30124
Section TU01
Size 30
Available 30
Class number 27115
Section WS01
Size 25
Available 25
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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.