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 2022 in Semester 1 at Clayton. It needs MTH2021, MTH2025 or MTH2137 and unlocks 3 units.
- Credit points
- 6
- Offered in 2022
- Semester 1
- Clayton
- Assessment
- Exam 60%
- and 1 other task
This is the 2022 handbook entry. See the 2027 entry.
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Requisites
Before MTH3141
Prohibitions
You can't enrol if you have passed any of these.
Prerequisites
Pass these before you enrol.
After MTH3141
3 units list MTH3141 as a prerequisite or corequisite.
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 2022
| Teaching period | Campus | Mode |
|---|---|---|
| First semester | Clayton | On campus |
Assessment
- Continuous assessmentOtherThreshold hurdle40%
- Examination (3 hours and 10 minutes)ExamThreshold hurdle60%
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
- Applied sessions16.5 hours
- Lectures36 hours
- Teaching approachActive learning
- Teaching approachProblem-based learning
- Teaching approachPeer assisted learning
- Three 1-hour lectures
- One 1.5-hour applied class (in weeks 2-12) and
- 7.5 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 7 areas of study in the 2022 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
- Unit Coordinators
- Dr Norm Do
- Chief Examiners
- Dr Norm Do
Common questions
What can I take after MTH3141?
MTH3141 is a prerequisite or corequisite for 3 units, including MTH2137, MTH3137 and MTH3150.
When is MTH3141 offered?
In 2022, MTH3141 runs in Semester 1 at Clayton.
Does MTH3141 have an exam?
Yes. The exam is worth 60% 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.