UnitLevel 3Undergraduate

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 2027 in Semester 1 at Clayton. It has no prerequisites and unlocks 7 units, leading on to 14 units in all.

Credit points
6
Offered in 2027
Semester 1
Clayton
Assessment
Exam 50%
and 1 other task

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Requisites

Enrolment rules

PROHIBITION: MTH2141 , MTH3121, MTH2121

PREREQUISITE: You must have passed one unit from MTH2021 or MTH2025 or MTH2137, or be enrolled in the Master of Mathematics.

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 2027

Teaching periodCampusMode
First semesterClaytonOn campus

Assessment

  • Continuous assessmentDemonstration
    50%
  • Final assessment - Exam (3 hours and 10 minutes)Examination
    50%

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. 1

    Communicate the beauty and the power of pure mathematics;

  2. 2

    Capture the mathematical notion of symmetry via group theory;

  3. 3

    Apply the fundamental concepts of abstract algebra;

  4. 4

    Explain the notion of proof in mathematics and be able to carry out basic proofs;

  5. 5

    Communicate mathematical arguments effectively, both orally and in writing, and collaborate to solve abstract algebra problems;

  6. 6

    Extend and deepen understanding of abstract algebra through advanced proofs, generalisations, and applications, demonstrating higher levels of rigour and independence.

Workload and teaching

  • Applied sessions22 hours
  • Seminars36 hours
  • Teaching approachPeer assisted learning
  • Teaching approachActive learning
  • Teaching approachProblem-based 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.

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 7 units, including FIT2014, MTH2137, MTH3115, MTH3130, MTH3137 and MTH3150. Those lead on to 14 units in all.

When is MTH3141 offered?

In 2027, 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.

More details

Credit points
6
Level
3
Study level
Undergraduate
Faculty
Faculty of Science
Organisational unit
School of Mathematics
Type
Coursework
EFTSL
0.125
Student contribution
SCA Band 1
Study abroad
Available
Handbook years
202220232024202520262027