MTH2141 Algebra 1: Group theory
Faculty of Science
MTH2141 Algebra 1: Group theory is a level 2, 6-credit-point, undergraduate unit from the Faculty of Science, offered in 2025 in Semester 1 at Clayton. It needs MTH1030, MTH1035, MAT1830 or ENG1005 and unlocks 8 units, leading on to 18 units in all.
- Credit points
- 6
- Offered in 2025
- Semester 1
- Clayton
- Assessment
- Exam 50%
- and 1 other task
This is the 2025 handbook entry. See the 2027 entry.
Reviews
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Requisites
Before MTH2141
Prohibitions
You can't enrol if you have passed any of these.
After MTH2141
8 units list MTH2141 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
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 and normal subgroups and quotient groups; homomorphisms, isomorphisms and isomorphism theorem; group actions; Sylow theorems, group presentations.
Offerings in 2025
| Teaching period | Campus | Mode |
|---|---|---|
| First semester | Clayton | On campus |
Assessment
- Continuous assessmentDemonstration50%
- Final assessment - Exam (3 hours and 10 minutes)Examination50%
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
Describe the power of the generality of the concepts in group theory;
- 6
Pursue further studies in abstract algebra and pure mathematics more generally.
Workload and teaching
- Seminars36 hours
- Applied sessions22 hours
- Teaching approachProblem-based learning
- Teaching approachPeer assisted learning
- Teaching approachActive learning
- Three 1-hour seminars;
- One 2-hour applied class 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
MTH2141 is part of 7 areas of study in the 2025 handbook.
- APPLMTH07Additional extended major elective unitApplied mathematicsNo reviews yet
- MTHSTAT07Mathematical statistics elective unitsMathematical statisticsNo reviews yet
- MATHS07Mathematics elective unitMathematicsNo 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 MTH2141?
You need MTH1030, MTH1035, MAT1830 or ENG1005 before you enrol.
What can I take after MTH2141?
MTH2141 is a prerequisite or corequisite for 8 units, including FIT2014, MTH2137, MTH3115, MTH3130, MTH3137 and MTH3150. Those lead on to 18 units in all.
When is MTH2141 offered?
In 2025, MTH2141 runs in Semester 1 at Clayton.
Does MTH2141 have an exam?
Yes. The exam is worth 50% of the final mark, alongside 1 other task.
Which majors and minors include MTH2141?
MTH2141 is part of Applied mathematics, Mathematical statistics, Mathematics and Pure mathematics.