MTH3141 Algebra 1: Group theory
Faculty of Science
MTH3141 Algebra 1: Group theory is a level 3, 6-credit-point, undergraduate unit from the Faculty of Science, offered in 2026 in Semester 1 at Clayton. It has no prerequisites and unlocks 8 units, leading on to 17 units in all.
- Credit points
- 6
- Offered in 2026
- Semester 1
- Clayton
- Assessment
- Exam 50%
- and 1 other task
This is the 2026 handbook entry. See the 2027 entry.
Reviews
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Requisites
Before MTH3141
No prerequisites or corequisites besides the enrolment rules below.
After MTH3141
8 units list MTH3141 as a prerequisite or corequisite.
- FIT2014Theory of computationRated 4.0 out of 5 from 1 review
- MTH2137Number theory and cryptographyNo reviews yet
- MTH3115Differential geometry (Advanced)No reviews yet
- MTH3130Topology: The mathematics of shapeNo reviews yet
- MTH3137Number theory and cryptography (Advanced)No reviews yet
- MTH3150Algebra 2: Rings and fieldsNo reviews yet
- MTH3170Network mathematicsNo reviews yet
- MTH4141Computational group theoryNo reviews yet
Enrolment rules
PREREQUISITE: You must have passed one unit from MTH2021 or MTH2025 or MTH2137, or be enrolled in the Master of Mathematics.
PROHIBITION: MTH2141 , MTH3121, MTH2121
Equivalent units
The same content under another code. Only one of them counts.
Overview
Groups in geometry, linear algebra, and number theory; cyclic and abelian groups; permutation groups; subgroups; cosets; normal subgroups and quotient groups; homomorphisms, isomorphisms and isomorphism theorems; group actions; Sylow theorems and group presentations.
Offerings in 2026
| Teaching period | Campus | Mode |
|---|---|---|
| First semester | Clayton | On campus |
Assessment
- Continuous assessmentDemonstration50%
- Final assessment - Exam (3 hours and 10 minutes)Examination50%
Assessment details may change. Please refer to the assessment information in Moodle closer to the start of the teaching period.
Learning outcomes
When you finish this unit, you should be able to:
- 1
Communicate the beauty and the power of pure mathematics;
- 2
Capture the mathematical notion of symmetry via group theory;
- 3
Apply the fundamental concepts of abstract algebra;
- 4
Explain the notion of proof in mathematics and be able to carry out basic proofs;
- 5
Communicate mathematical arguments effectively, both orally and in writing, and collaborate to solve abstract algebra problems;
- 6
Extend and deepen understanding of abstract algebra through advanced proofs, generalisations, and applications, demonstrating higher levels of rigour and independence.
Workload and teaching
- Seminars36 hours
- Applied sessions22 hours
- Teaching approachProblem-based learning
- Teaching approachActive learning
- Teaching approachPeer assisted learning
- Three 1-hour seminars;
- One 2-hour applied class (in weeks 2-12) and
- 7 hours of independent study per week.
Primary content is delivered through traditional lectures (which will be recorded, and available for review via the Moodle page). Applied classes will be active learning. Small groups of students will work together around a whiteboard to solve problems. A key aspect is that this component involves writing your solutions on the board and critiquing the solutions of others, meaning that both written and spoken communication of mathematical ideas are developed (with input from your tutor). You also develop strategies for solving the questions together, meaning this is peer-assisted learning. Assignments will be problem-based learning. The questions will involve techniques from recent lectures and applied classes, but sometimes in settings or formats that are not immediately familiar. Thus, part of the challenge is adapting what you previously knew or have just learnt to a new setting.
Where it fits
MTH3141 is part of 6 areas of study in the 2026 handbook.
- APPLMTH07Additional elective unitApplied mathematicsNo reviews yet
- MTHSTAT07Additional elective unitsMathematical statisticsNo reviews yet
- MATHS09Mathematics elective unitsMathematicsNo reviews yet
- MATHS11Mathematics elective unitsMathematicsNo reviews yet
- MATPURE09Algebra and number theoryPure mathematicsNo reviews yet
- MATPURE11Algebra and number theoryPure mathematicsNo reviews yet
Contacts
- Chief Examiners
- Professor Heiko Dietrich
- Unit Coordinators
- Professor Heiko Dietrich
Common questions
What are the prerequisites for MTH3141?
MTH3141 has no prerequisites, but enrolment rules apply.
What can I take after MTH3141?
MTH3141 is a prerequisite or corequisite for 8 units, including FIT2014, MTH2137, MTH3115, MTH3130, MTH3137 and MTH3150. Those lead on to 17 units in all.
When is MTH3141 offered?
In 2026, MTH3141 runs in Semester 1 at Clayton.
Does MTH3141 have an exam?
Yes. The exam is worth 50% of the final mark, alongside 1 other task.
Which majors and minors include MTH3141?
MTH3141 is part of Applied mathematics, Mathematical statistics, Mathematics and Pure mathematics.